diff --git a/.gitignore b/.gitignore index e52b9be73c..6243450af1 100644 --- a/.gitignore +++ b/.gitignore @@ -4,11 +4,13 @@ *.png *.gif /local/ +.local *.DS_Store *.mat *.csv *.hidden *.pkl +.claude # don't ignore important .txt and .csv files !requirements* diff --git a/CHANGELOG.md b/CHANGELOG.md index 1d51fc7641..f5ff296807 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -13,6 +13,7 @@ ## Features +- Added uniform grid sizing across subdomains in the x-dimension, ensuring consistent grid spacing when geometries have varying lengths. ([#5253](https://github.com/pybamm-team/PyBaMM/pull/5253)) - Added the `electrode_phases` kwarg to `plot_voltage_components()` which allows choosing between plotting primary or secondary phase overpotentials. ([#5229](https://github.com/pybamm-team/PyBaMM/pull/5229)) - Added the `num_steps_no_progress` and `t_no_progress` options in the `IDAKLUSolver` to early terminate the simulation if little progress is detected. ([#5201](https://github.com/pybamm-team/PyBaMM/pull/5201)) - EvaluateAt symbol: add support for children evaluated at edges ([#5190](https://github.com/pybamm-team/PyBaMM/pull/5190)) diff --git a/src/pybamm/expression_tree/operations/serialise.py b/src/pybamm/expression_tree/operations/serialise.py index 6b733e0fad..f2e8474756 100644 --- a/src/pybamm/expression_tree/operations/serialise.py +++ b/src/pybamm/expression_tree/operations/serialise.py @@ -14,7 +14,22 @@ import pybamm -SUPPORTED_SCHEMA_VERSION = "1.0" +SUPPORTED_SCHEMA_VERSION = "1.1" + +# Module-level caches for memoization during serialization/deserialization +_serialized_symbols = {} # Maps symbol id -> (reference_id, JSON representation) +_serialized_ref_counter = 0 # Counter for generating unique reference IDs +_deserialized_symbols = {} # Maps reference_id -> deserialized symbol + + +def _reset_serialization_caches(): + """Reset the serialization and deserialization caches. + Useful for testing or when serializing multiple independent models. + """ + global _serialized_symbols, _serialized_ref_counter, _deserialized_symbols + _serialized_symbols = {} + _serialized_ref_counter = 0 + _deserialized_symbols = {} class ExpressionFunctionParameter(pybamm.UnaryOperator): @@ -358,6 +373,9 @@ def serialise_custom_model(model: pybamm.BaseModel) -> dict: AttributeError If the model is missing required sections """ + # Reset caches for a clean serialization + _reset_serialization_caches() + required_attrs = [ "rhs", "algebraic", @@ -427,7 +445,8 @@ def serialise_custom_model(model: pybamm.BaseModel) -> dict: { "name": event.name, "expression": convert_symbol_to_json(event.expression), - "event_type": event.event_type, + # Store just the enum name as a string + "event_type": event.event_type.name, } for event in getattr(model, "events", []) ], @@ -437,7 +456,7 @@ def serialise_custom_model(model: pybamm.BaseModel) -> dict: }, } - SCHEMA_VERSION = "1.0" + SCHEMA_VERSION = "1.1" model_json = { "schema_version": SCHEMA_VERSION, "pybamm_version": pybamm.__version__, @@ -557,7 +576,7 @@ def serialise_custom_geometry(geometry: pybamm.Geometry) -> dict: else: geometry_dict_serialized[domain][key] = value - SCHEMA_VERSION = "1.0" + SCHEMA_VERSION = "1.1" geometry_json = { "schema_version": SCHEMA_VERSION, "pybamm_version": pybamm.__version__, @@ -642,12 +661,12 @@ def load_custom_geometry(filename: str | dict) -> pybamm.Geometry: f"The file '{filename}' contains invalid JSON: {e!s}" ) from e - # Validate schema version + # Validate schema version (accept 1.0 for backward compatibility) schema_version = data.get("schema_version", SUPPORTED_SCHEMA_VERSION) - if schema_version != SUPPORTED_SCHEMA_VERSION: + if schema_version not in ["1.0", SUPPORTED_SCHEMA_VERSION]: raise ValueError( f"Unsupported schema version: {schema_version}. " - f"Expected: {SUPPORTED_SCHEMA_VERSION}" + f"Expected: 1.0 or {SUPPORTED_SCHEMA_VERSION}" ) # Extract geometry data @@ -722,7 +741,7 @@ def serialise_spatial_methods(spatial_methods: dict) -> dict: "options": method.options if hasattr(method, "options") else {}, } - SCHEMA_VERSION = "1.0" + SCHEMA_VERSION = "1.1" spatial_methods_json = { "schema_version": SCHEMA_VERSION, "pybamm_version": pybamm.__version__, @@ -810,12 +829,12 @@ def load_spatial_methods(filename: str | dict) -> dict: f"The file '{filename}' contains invalid JSON: {e!s}" ) from e - # Validate schema version + # Validate schema version (accept 1.0 for backward compatibility) schema_version = data.get("schema_version", SUPPORTED_SCHEMA_VERSION) - if schema_version != SUPPORTED_SCHEMA_VERSION: + if schema_version not in ["1.0", SUPPORTED_SCHEMA_VERSION]: raise ValueError( f"Unsupported schema version: {schema_version}. " - f"Expected: {SUPPORTED_SCHEMA_VERSION}" + f"Expected: 1.0 or {SUPPORTED_SCHEMA_VERSION}" ) # Extract spatial methods data @@ -876,7 +895,7 @@ def serialise_var_pts(var_pts: dict) -> dict: else: raise ValueError(f"Unexpected key type in var_pts: {type(key)}") - SCHEMA_VERSION = "1.0" + SCHEMA_VERSION = "1.1" var_pts_json = { "schema_version": SCHEMA_VERSION, "pybamm_version": pybamm.__version__, @@ -959,12 +978,12 @@ def load_var_pts(filename: str | dict) -> dict: f"The file '{filename}' contains invalid JSON: {e!s}" ) from e - # Validate schema version + # Validate schema version (accept 1.0 for backward compatibility) schema_version = data.get("schema_version", SUPPORTED_SCHEMA_VERSION) - if schema_version != SUPPORTED_SCHEMA_VERSION: + if schema_version not in ["1.0", SUPPORTED_SCHEMA_VERSION]: raise ValueError( f"Unsupported schema version: {schema_version}. " - f"Expected: {SUPPORTED_SCHEMA_VERSION}" + f"Expected: 1.0 or {SUPPORTED_SCHEMA_VERSION}" ) # Extract var_pts data @@ -1002,7 +1021,7 @@ def serialise_submesh_types(submesh_types: dict) -> dict: "module": submesh_class.__module__, } - SCHEMA_VERSION = "1.0" + SCHEMA_VERSION = "1.1" submesh_types_json = { "schema_version": SCHEMA_VERSION, "pybamm_version": pybamm.__version__, @@ -1087,12 +1106,12 @@ def load_submesh_types(filename: str | dict) -> dict: f"The file '{filename}' contains invalid JSON: {e!s}" ) from e - # Validate schema version + # Validate schema version (accept 1.0 for backward compatibility) schema_version = data.get("schema_version", SUPPORTED_SCHEMA_VERSION) - if schema_version != SUPPORTED_SCHEMA_VERSION: + if schema_version not in ["1.0", SUPPORTED_SCHEMA_VERSION]: raise ValueError( f"Unsupported schema version: {schema_version}. " - f"Expected: {SUPPORTED_SCHEMA_VERSION}" + f"Expected: 1.0 or {SUPPORTED_SCHEMA_VERSION}" ) # Extract submesh types data @@ -1164,6 +1183,9 @@ def load_custom_model(filename: str | dict) -> pybamm.BaseModel: >>> loaded_model = Serialise.load_custom_model("basicdfn_model.json") """ + # Reset caches for a clean deserialization + _reset_serialization_caches() + if isinstance(filename, dict): data = filename else: @@ -1177,12 +1199,12 @@ def load_custom_model(filename: str | dict) -> pybamm.BaseModel: f"The model defined in the file '{filename}' contains invalid JSON: {e!s}" ) from e - # Validate outer structure + # Validate outer structure (accept 1.0 for backward compatibility) schema_version = data.get("schema_version", SUPPORTED_SCHEMA_VERSION) - if schema_version != SUPPORTED_SCHEMA_VERSION: + if schema_version not in ["1.0", SUPPORTED_SCHEMA_VERSION]: raise ValueError( f"Unsupported schema version: {schema_version}. " - f"Expected: {SUPPORTED_SCHEMA_VERSION}" + f"Expected: 1.0 or {SUPPORTED_SCHEMA_VERSION}" ) model_data = data.get("model") @@ -1222,17 +1244,96 @@ def load_custom_model(filename: str | dict) -> pybamm.BaseModel: model = base_cls() model.name = model_data["name"] model.schema_version = schema_version + # Restore model options if present + # Convert lists back to tuples (JSON converts tuples to lists) + if "options" in model_data: + options_dict = model_data["options"] + # Recursively convert lists to tuples for options that expect tuples + # (e.g., SEI option can be a 2-tuple for different electrode behavior) + if isinstance(options_dict, dict): + converted_options = {} + for key, value in options_dict.items(): + if isinstance(value, list): + # Convert list to tuple (for options like SEI that can be tuples) + converted_options[key] = tuple(value) + else: + converted_options[key] = value + model.options = converted_options + else: + model.options = options_dict + + # Pre-populate cache by deserializing all unique symbols + # This ensures references are resolved when building the model structure + # Collect all JSON symbol definitions (not pure references) + all_symbols = [] + for _, rhs_json in model_data["rhs"]: + all_symbols.append(rhs_json) + for _, alg_json in model_data["algebraic"]: + all_symbols.append(alg_json) + for _, ic_json in model_data["initial_conditions"]: + all_symbols.append(ic_json) + for variable_json, bc_dict in model_data["boundary_conditions"]: + for side, bc_value in bc_dict.items(): + try: + expr_json, _ = bc_value + all_symbols.append(expr_json) + except (TypeError, ValueError) as e: + raise ValueError( + f"Failed to convert boundary condition for variable {variable_json} " + f"on side '{side}': {e!s}" + ) from e + for event_data in model_data["events"]: + all_symbols.append(event_data["expression"]) + for var_json in model_data["variables"].values(): + all_symbols.append(var_json) + # Also collect LHS variable definitions all_variable_keys = ( [lhs_json for lhs_json, _ in model_data["rhs"]] + [lhs_json for lhs_json, _ in model_data["initial_conditions"]] + [lhs_json for lhs_json, _ in model_data["algebraic"]] + [variable_json for variable_json, _ in model_data["boundary_conditions"]] ) - + all_symbols.extend(all_variable_keys) + + # Deserialize all symbols to populate cache (ignore pure references) + # Do multiple passes until no new symbols are cached (handles forward references) + max_passes = 3 + for _ in range(max_passes): + newly_cached = 0 + for symbol_json in all_symbols: + if isinstance(symbol_json, dict): + # Skip pure references + if len(symbol_json) == 1 and ( + "py/ref" in symbol_json or "r" in symbol_json + ): + continue + # Check if already cached + ref_id = symbol_json.get("py/ref") or symbol_json.get("r") + if ref_id is not None and ref_id in _deserialized_symbols: + continue + # Deserialize to populate cache + try: + convert_symbol_from_json(symbol_json) + newly_cached += 1 + except Exception: + # If it fails due to forward reference, it will work on next pass + pass + # If nothing new was cached, we're done + if newly_cached == 0: + break + + # Build symbol_map for LHS lookups symbol_map = {} for variable_json in all_variable_keys: + # Skip pure references + if isinstance(variable_json, dict): + if len(variable_json) == 1 and ( + "py/ref" in variable_json or "r" in variable_json + ): + continue try: + # Should now work since cache is populated symbol = convert_symbol_from_json(variable_json) key = Serialise._create_symbol_key(variable_json) symbol_map[key] = symbol @@ -1244,7 +1345,12 @@ def load_custom_model(filename: str | dict) -> pybamm.BaseModel: model.rhs = {} for lhs_json, rhs_expr_json in model_data["rhs"]: try: - lhs = symbol_map[Serialise._create_symbol_key(lhs_json)] + lhs_key = Serialise._create_symbol_key(lhs_json) + # Check if it's in symbol_map, otherwise deserialize from cache + if lhs_key in symbol_map: + lhs = symbol_map[lhs_key] + else: + lhs = convert_symbol_from_json(lhs_json) rhs = convert_symbol_from_json(rhs_expr_json) model.rhs[lhs] = rhs except Exception as e: @@ -1255,7 +1361,11 @@ def load_custom_model(filename: str | dict) -> pybamm.BaseModel: model.algebraic = {} for lhs_json, algebraic_expr_json in model_data["algebraic"]: try: - lhs = symbol_map[Serialise._create_symbol_key(lhs_json)] + lhs_key = Serialise._create_symbol_key(lhs_json) + if lhs_key in symbol_map: + lhs = symbol_map[lhs_key] + else: + lhs = convert_symbol_from_json(lhs_json) rhs = convert_symbol_from_json(algebraic_expr_json) model.algebraic[lhs] = rhs except Exception as e: @@ -1266,7 +1376,11 @@ def load_custom_model(filename: str | dict) -> pybamm.BaseModel: model.initial_conditions = {} for lhs_json, initial_value_json in model_data["initial_conditions"]: try: - lhs = symbol_map[Serialise._create_symbol_key(lhs_json)] + lhs_key = Serialise._create_symbol_key(lhs_json) + if lhs_key in symbol_map: + lhs = symbol_map[lhs_key] + else: + lhs = convert_symbol_from_json(lhs_json) rhs = convert_symbol_from_json(initial_value_json) model.initial_conditions[lhs] = rhs except Exception as e: @@ -1277,7 +1391,11 @@ def load_custom_model(filename: str | dict) -> pybamm.BaseModel: model.boundary_conditions = {} for variable_json, condition_dict in model_data["boundary_conditions"]: try: - variable = symbol_map[Serialise._create_symbol_key(variable_json)] + var_key = Serialise._create_symbol_key(variable_json) + if var_key in symbol_map: + variable = symbol_map[var_key] + else: + variable = convert_symbol_from_json(variable_json) sides = {} for side, (expression_json, boundary_type) in condition_dict.items(): try: @@ -1298,7 +1416,9 @@ def load_custom_model(filename: str | dict) -> pybamm.BaseModel: try: name = event_data["name"] expr = convert_symbol_from_json(event_data["expression"]) - event_type = event_data["event_type"] + # Convert event_type from string to EventType enum + event_type_str = event_data.get("event_type", "TERMINATION") + event_type = pybamm.EventType[event_type_str] model.events.append(pybamm.Event(name, expr, event_type)) except Exception as e: raise ValueError( @@ -1318,6 +1438,20 @@ def load_custom_model(filename: str | dict) -> pybamm.BaseModel: f"Failed to convert variable '{variable_name}': {e!s}" ) from e + # Ensure the model is in a clean, unprocessed state + # Reset any attributes that might interfere with processing + if hasattr(model, "_processed"): + model._processed = False + if hasattr(model, "_built"): + model._built = False + # Clear any cached geometry or mesh + if hasattr(model, "_geometry"): + model._geometry = None + if hasattr(model, "_mesh"): + model._mesh = None + if hasattr(model, "_disc"): + model._disc = None + return model @staticmethod @@ -1610,7 +1744,8 @@ def convert_symbol_from_json(json_data): pybamm.Symbol The reconstructed PyBaMM symbolic expression """ - if isinstance(json_data, float | int | bool): + # Handle non-dict types + if isinstance(json_data, float | int | bool | numbers.Number | list): return json_data if isinstance(json_data, str): @@ -1618,95 +1753,222 @@ def convert_symbol_from_json(json_data): if json_data is None: return None - if "type" not in json_data: + + # Check for reference first (handle both abbreviated "r" and full "py/ref") + if isinstance(json_data, dict): + # Check for pure reference (either "r" or "py/ref" as only key) + if len(json_data) == 1: + ref_id = None + if "r" in json_data: + ref_id = json_data["r"] + elif "py/ref" in json_data: + ref_id = json_data["py/ref"] + + if ref_id is not None: + if ref_id in _deserialized_symbols: + return _deserialized_symbols[ref_id] + else: + # Reference seen before definition - this shouldn't happen in normal flow + # but if it does, raise an error that will be caught and retried + raise ValueError( + f"Reference {ref_id} encountered before its definition. " + "This may indicate the symbol needs to be deserialized first." + ) + + if not isinstance(json_data, dict): + raise ValueError(f"Expected dict, got {type(json_data)}: {json_data}") + + # Check for type key (handles both "type" and abbreviated "t") + if "type" not in json_data and "t" not in json_data: raise ValueError(f"Missing 'type' key in JSON data: {json_data}") - if isinstance(json_data, numbers.Number | list): - return json_data - elif json_data["type"] == "Parameter": + + # Check cache - prefer ref_id if available (faster lookup, no key computation) + ref_id = json_data.get("py/ref") or json_data.get("r") + if ref_id is not None and ref_id in _deserialized_symbols: + return _deserialized_symbols[ref_id] + + # Deserialize the symbol + symbol = _deserialize_symbol_from_json(json_data) + + # Store in cache using ref_id (if available) + if ref_id is not None: + _deserialized_symbols[ref_id] = symbol + + return symbol + + +def _deserialize_symbol_from_json(json_data): + """Internal helper to deserialize a symbol without caching. + The caching is handled by convert_symbol_from_json. + """ + # Get type (handle both "type" and "t" keys) + type_name = json_data.get("type") or json_data.get("t") + if type_name is None: + raise ValueError(f"Missing 'type' key in JSON data: {json_data}") + # Expand type abbreviation if present + type_name = _TYPE_EXPANSIONS.get(type_name, type_name) + + # Helper to expand domains (handle both "domains" and "d" keys) + def get_domains(): + domains_data = json_data.get("domains") or json_data.get("d") + if domains_data is not None: + return _expand_domains(domains_data) + return {"primary": [], "secondary": [], "tertiary": [], "quaternary": []} + + if type_name == "Parameter": # Convert stored parameters back to PyBaMM Parameter objects - return pybamm.Parameter(json_data["name"]) - elif json_data["type"] == "Scalar": + return pybamm.Parameter(json_data.get("name") or json_data.get("n")) + elif type_name == "Scalar": # Convert stored numerical values back to PyBaMM Scalar objects - return pybamm.Scalar(json_data["value"]) - elif json_data["type"] == "Interpolant": + # Use explicit check to handle 0 correctly (can't use 'or' since 0 is falsy) + if "value" in json_data: + value = json_data["value"] + elif "v" in json_data: + value = json_data["v"] + else: + value = 0 # Default to 0 if not found + # Handle infinity strings + if value == "Inf": + value = float("inf") + elif value == "-Inf": + value = float("-inf") + return pybamm.Scalar(value) + + # Helper to get value with fallback for abbreviated keys + def get_key(key, abbrev=None, default=None): + if abbrev is None: + abbrev = _KEY_ABBREVIATIONS.get(key, key) + if key in json_data: + return json_data[key] + if abbrev in json_data: + return json_data[abbrev] + return default + + # Helper to get children (handle both "children" and "c") + def get_children(): + if "children" in json_data: + return json_data["children"] + if "c" in json_data: + return json_data["c"] + return [] + + if type_name == "Interpolant": return pybamm.Interpolant( [np.array(x) for x in json_data["x"]], np.array(json_data["y"]), - [convert_symbol_from_json(c) for c in json_data["children"]], - name=json_data["name"], - interpolator=json_data["interpolator"], - entries_string=json_data["entries_string"], + [convert_symbol_from_json(c) for c in get_children()], + name=get_key("name", "n"), + interpolator=get_key("interpolator", "i"), + entries_string=get_key("entries_string", "es"), ) - elif json_data["type"] == "FunctionParameter": - diff_variable = json_data["diff_variable"] + elif type_name == "FunctionParameter": + diff_variable = get_key("diff_variable", "dv") if diff_variable is not None: diff_variable = convert_symbol_from_json(diff_variable) - # Use the parameter name as print_name to avoid showing - # 'convert_symbol_from_json' in displays + inputs_key = get_key("inputs", "in", {}) return pybamm.FunctionParameter( - json_data["name"], - {k: convert_symbol_from_json(v) for k, v in json_data["inputs"].items()}, + get_key("name", "n"), + {k: convert_symbol_from_json(v) for k, v in inputs_key.items()}, diff_variable=diff_variable, - print_name=json_data["name"], + print_name=get_key("name", "n"), ) - elif json_data["type"] == "ExpressionFunctionParameter": + elif type_name == "ExpressionFunctionParameter": + children = get_children() return ExpressionFunctionParameter( - json_data["name"], - convert_symbol_from_json(json_data["children"][0]), - json_data["func_name"], - json_data["func_args"], + get_key("name", "n"), + convert_symbol_from_json(children[0]) if children else None, + get_key("func_name", "fn"), + get_key("func_args", "fa"), + ) + elif type_name == "PrimaryBroadcast": + children = get_children() + domain = get_key("broadcast_domain", "bd") + return pybamm.PrimaryBroadcast( + convert_symbol_from_json(children[0]) if children else None, domain + ) + elif type_name == "FullBroadcast": + children = get_children() + domains = _expand_domains(get_key("domains", "d")) + return pybamm.FullBroadcast( + convert_symbol_from_json(children[0]) if children else None, + broadcast_domains=domains, + ) + elif type_name == "SecondaryBroadcast": + children = get_children() + domain = get_key("broadcast_domain", "bd") + return pybamm.SecondaryBroadcast( + convert_symbol_from_json(children[0]) if children else None, domain ) - elif json_data["type"] == "PrimaryBroadcast": - child = convert_symbol_from_json(json_data["children"][0]) - domain = json_data["broadcast_domain"] - return pybamm.PrimaryBroadcast(child, domain) - elif json_data["type"] == "FullBroadcast": - child = convert_symbol_from_json(json_data["children"][0]) - domains = json_data["domains"] - return pybamm.FullBroadcast(child, broadcast_domains=domains) - elif json_data["type"] == "SecondaryBroadcast": - child = convert_symbol_from_json(json_data["children"][0]) - domain = json_data["broadcast_domain"] - return pybamm.SecondaryBroadcast(child, domain) - elif json_data["type"] == "BoundaryValue": - child = convert_symbol_from_json(json_data["children"][0]) - side = json_data["side"] - return pybamm.BoundaryValue(child, side) - elif json_data["type"] == "Variable": - bounds = tuple( - convert_symbol_from_json(b) - for b in json_data.get("bounds", [-float("inf"), float("inf")]) + elif type_name == "BoundaryValue": + children = get_children() + side = get_key("side", "s") + return pybamm.BoundaryValue( + convert_symbol_from_json(children[0]) if children else None, side ) + elif type_name == "Variable": + bounds_data = get_key("bounds", "b", [-float("inf"), float("inf")]) + bounds = tuple(convert_symbol_from_json(b) for b in bounds_data) return pybamm.Variable( - json_data["name"], - domains=json_data["domains"], + get_key("name", "n"), + domains=get_domains(), bounds=bounds, ) - elif json_data["type"] == "IndefiniteIntegral": - child = convert_symbol_from_json(json_data["children"][0]) - integration_var_json = json_data["integration_variable"] + elif type_name == "IndefiniteIntegral": + children = get_children() + integration_var_json = get_key("integration_variable", "iv") integration_variable = convert_symbol_from_json(integration_var_json) if not isinstance(integration_variable, pybamm.SpatialVariable): raise TypeError( f"Expected SpatialVariable, got {type(integration_variable)}" ) - return pybamm.IndefiniteIntegral(child, [integration_variable]) - elif json_data["type"] == "SpatialVariable": + return pybamm.IndefiniteIntegral( + convert_symbol_from_json(children[0]) if children else None, + [integration_variable], + ) + elif type_name == "SpatialVariable": return pybamm.SpatialVariable( - json_data["name"], - coord_sys=json_data.get("coord_sys", "cartesian"), - domains=json_data.get("domains"), + get_key("name", "n"), + coord_sys=get_key("coord_sys", "cs", "cartesian"), + domains=_expand_domains(get_key("domains", "d")), ) - elif json_data["type"] == "Time": + elif type_name == "Time": return pybamm.Time() - elif json_data["type"] == "Symbol": + elif type_name == "Symbol": return pybamm.Symbol( - json_data["name"], - domains=json_data.get("domains", {}), + get_key("name", "n"), + domains=get_domains(), ) - elif "children" in json_data: - return getattr(pybamm, json_data["type"])( - *[convert_symbol_from_json(c) for c in json_data["children"]] + elif type_name == "ConcatenationVariable": + children = get_children() + # Convert children to symbols, ensuring they're all Symbols + deserialized_children = [] + for i, child_json in enumerate(children): + if isinstance(child_json, str): + # If child is a string, it might be a reference or name - this shouldn't happen + raise ValueError( + f"ConcatenationVariable child [{i}] is a string '{child_json}' " + f"instead of a symbol dict. This may indicate a serialization issue." + ) + try: + child_symbol = convert_symbol_from_json(child_json) + except Exception as e: + raise ValueError( + f"Failed to deserialize ConcatenationVariable child [{i}]: {e!s}. " + f"Child JSON: {child_json}" + ) from e + if not isinstance(child_symbol, pybamm.Symbol): + raise ValueError( + f"ConcatenationVariable child [{i}] deserialized to {type(child_symbol).__name__} " + f"instead of a Symbol. Got: {child_symbol} (value: {child_symbol!r})" + ) + deserialized_children.append(child_symbol) + # ConcatenationVariable automatically derives its name from children + # Only pass name if it was explicitly stored and is different + return pybamm.ConcatenationVariable(*deserialized_children) + elif "children" in json_data or "c" in json_data: + # Use expanded type name for getattr + return getattr(pybamm, type_name)( + *[convert_symbol_from_json(c) for c in get_children()] ) else: raise ValueError(f"Unknown symbol type: {json_data['type']}") @@ -1726,6 +1988,232 @@ def convert_symbol_to_json(symbol): dict The JSON-serializable dictionary """ + # Handle non-symbol types (numbers, lists) - these don't need memoization + if isinstance(symbol, numbers.Number | list): + return symbol + + # Check cache first for memoization (only for Symbol types) + if isinstance(symbol, pybamm.Symbol): + symbol_id = id(symbol) + if symbol_id in _serialized_symbols: + # Return a reference to the already-serialized symbol + ref_id, _ = _serialized_symbols[symbol_id] + return {"py/ref": ref_id} + + # Serialize the symbol + json_dict = _serialize_symbol_to_json(symbol) + + # Store in cache if it's a Symbol type + if isinstance(symbol, pybamm.Symbol): + global _serialized_ref_counter + symbol_id = id(symbol) + ref_id = _serialized_ref_counter + _serialized_ref_counter += 1 + # Store both ref_id and full JSON in cache (before compaction for cache lookup) + _serialized_symbols[symbol_id] = (ref_id, json_dict) + # Include ref_id in the JSON so we can resolve it during deserialization + json_dict["py/ref"] = ref_id + + # Compact the JSON dict (abbreviate keys, omit nulls, etc.) + return _compact_json_dict(json_dict) + + +# Type name abbreviations to reduce JSON size +# Use mathematical symbols where appropriate for maximum compression +_TYPE_ABBREVIATIONS = { + # Binary operators - use symbols + "Multiplication": "*", + "Division": "/", + "Addition": "+", + "Subtraction": "-", + "Power": "**", + "Modulo": "%", + "MatrixMultiplication": "@", + "Equality": "==", + "Minimum": "min", + "Maximum": "max", + # Unary operators - use short names + "Negate": "neg", # Use "neg" to avoid conflict with binary "-" + "AbsoluteValue": "abs", + "Transpose": "T", + "Sign": "sign", + "Floor": "floor", + "Ceiling": "ceil", + # Other operators + "PrimaryBroadcast": "PBroad", + "SecondaryBroadcast": "SBroad", + "FullBroadcast": "FBroad", + "IndefiniteIntegral": "Int", + "BoundaryValue": "BVal", + "ConcatenationVariable": "ConcatVar", + "ExpressionFunctionParameter": "ExprFP", + "FunctionParameter": "FP", +} + +# Reverse mapping for deserialization +_TYPE_EXPANSIONS = {v: k for k, v in _TYPE_ABBREVIATIONS.items()} + +# Key abbreviations to reduce JSON size +_KEY_ABBREVIATIONS = { + "type": "t", + "children": "c", + "domains": "d", + "name": "n", + "value": "v", + "broadcast_domain": "bd", + "integration_variable": "iv", + "side": "s", + "inputs": "in", + "diff_variable": "dv", + "func_name": "fn", + "func_args": "fa", + "bounds": "b", + "coord_sys": "cs", + "interpolator": "i", + "entries_string": "es", + "py/ref": "r", # Keep short already +} + +# Reverse mapping for deserialization +_KEY_EXPANSIONS = {v: k for k, v in _KEY_ABBREVIATIONS.items()} + + +def _compact_json_dict(d): + """Compact a JSON dictionary by: + 1. Using abbreviated keys + 2. Omitting null values + 3. Omitting empty arrays + 4. Omitting redundant names (when name == type or name == '*') + 5. Recursively compacting nested structures + """ + if isinstance(d, dict): + compact = {} + type_val = d.get("type") or d.get("t") + name_val = d.get("name") or d.get("n") + + for key, value in d.items(): + # Skip null values + if value is None: + continue + + # Skip empty arrays + if isinstance(value, list) and len(value) == 0: + continue + + # Skip redundant names + if key == "name" and (name_val == type_val or name_val == "*"): + continue + + # Recursively compact nested structures + if isinstance(value, dict): + value = _compact_json_dict(value) + elif isinstance(value, list): + value = [ + _compact_json_dict(item) if isinstance(item, dict) else item + for item in value + ] + + # Use abbreviated key + abbrev_key = _KEY_ABBREVIATIONS.get(key, key) + compact[abbrev_key] = value + + return compact + elif isinstance(d, list): + return [ + _compact_json_dict(item) if isinstance(item, dict) else item for item in d + ] + else: + return d + + +def _compact_domains(domains): + """Compact domain representation by omitting empty domains and using + shorter format when possible. + """ + if not domains: + return None + + # Check if all domains are empty + if all(not v for v in domains.values()): + return None + + # Check if only primary domain is non-empty (common case) + if ( + domains.get("primary") + and not domains.get("secondary") + and not domains.get("tertiary") + and not domains.get("quaternary") + ): + return domains["primary"] + + # Return compact dict with only non-empty domains + compact = {} + for key, value in domains.items(): + if value: # Only include non-empty domains + compact[key] = value + + # If only one domain is non-empty, return just that value + if len(compact) == 1: + return next(iter(compact.values())) + + return compact if compact else None + + +def _expand_domains(domains_data): + """Expand compact domain representation back to full format.""" + if domains_data is None: + return {"primary": [], "secondary": [], "tertiary": [], "quaternary": []} + + # If it's a list, it's the primary domain + if isinstance(domains_data, list): + return { + "primary": domains_data, + "secondary": [], + "tertiary": [], + "quaternary": [], + } + + # If it's a dict, expand with defaults + if isinstance(domains_data, dict): + result = {"primary": [], "secondary": [], "tertiary": [], "quaternary": []} + result.update(domains_data) + return result + + # Fallback + return {"primary": [], "secondary": [], "tertiary": [], "quaternary": []} + + +def _expand_json_dict(d): + """Expand abbreviated keys back to full keys for deserialization.""" + if isinstance(d, dict): + expanded = {} + for key, value in d.items(): + # Expand key + full_key = _KEY_EXPANSIONS.get(key, key) + + # Recursively expand nested structures + if isinstance(value, dict): + value = _expand_json_dict(value) + elif isinstance(value, list): + value = [ + _expand_json_dict(item) if isinstance(item, dict) else item + for item in value + ] + + expanded[full_key] = value + return expanded + elif isinstance(d, list): + return [ + _expand_json_dict(item) if isinstance(item, dict) else item for item in d + ] + else: + return d + + +def _serialize_symbol_to_json(symbol): + """Internal helper to serialize a symbol without caching. + The caching is handled by convert_symbol_to_json. + """ if isinstance(symbol, ExpressionFunctionParameter): return { "type": "ExpressionFunctionParameter", @@ -1734,27 +2222,32 @@ def convert_symbol_to_json(symbol): "func_name": symbol.func_name, "func_args": symbol.func_args, } - elif isinstance(symbol, numbers.Number | list): - return symbol elif isinstance(symbol, pybamm.Parameter): # Parameters are stored with their type and name return {"type": "Parameter", "name": symbol.name} elif isinstance(symbol, pybamm.Scalar): # Scalar values are stored with their numerical value - return {"type": "Scalar", "value": symbol.value} + # Use special values for infinity to save space + value = symbol.value + if value == float("inf"): + value = "Inf" + elif value == float("-inf"): + value = "-Inf" + return {"type": "Scalar", "value": value} elif isinstance(symbol, pybamm.SpecificFunction): if symbol.__class__ == pybamm.SpecificFunction: raise NotImplementedError("SpecificFunction is not supported directly") else: # Subclasses of SpecificFunction (e.g. Exp, Sin, etc.) can be reconstructed # from only the children + type_name = symbol.__class__.__name__ return { - "type": symbol.__class__.__name__, + "type": _TYPE_ABBREVIATIONS.get(type_name, type_name), "children": [convert_symbol_to_json(c) for c in symbol.children], } elif isinstance(symbol, pybamm.PrimaryBroadcast): json_dict = { - "type": "PrimaryBroadcast", + "type": "PBroad", "children": [convert_symbol_to_json(symbol.child)], "broadcast_domain": symbol.broadcast_domain, } @@ -1766,30 +2259,30 @@ def convert_symbol_to_json(symbol): else symbol.integration_variable ) json_dict = { - "type": "IndefiniteIntegral", + "type": "Int", "children": [convert_symbol_to_json(symbol.child)], "integration_variable": convert_symbol_to_json(integration_var), } return json_dict elif isinstance(symbol, pybamm.BoundaryValue): json_dict = { - "type": "BoundaryValue", + "type": "BVal", "side": symbol.side, "children": [convert_symbol_to_json(symbol.orphans[0])], } return json_dict elif isinstance(symbol, pybamm.SecondaryBroadcast): json_dict = { - "type": "SecondaryBroadcast", + "type": "SBroad", "children": [convert_symbol_to_json(symbol.child)], "broadcast_domain": symbol.broadcast_domain, } return json_dict elif isinstance(symbol, pybamm.FullBroadcast): json_dict = { - "type": "FullBroadcast", + "type": "FBroad", "children": [convert_symbol_to_json(symbol.child)], - "domains": symbol.domains, + "domains": _compact_domains(symbol.domains), } return json_dict elif isinstance(symbol, pybamm.Interpolant): @@ -1806,16 +2299,19 @@ def convert_symbol_to_json(symbol): json_dict = { "type": "Variable", "name": symbol.name, - "domains": symbol.domains, "bounds": [ convert_symbol_to_json(symbol.bounds[0]), convert_symbol_to_json(symbol.bounds[1]), ], } + # Only include domains if non-empty + compact_domains = _compact_domains(symbol.domains) + if compact_domains is not None: + json_dict["domains"] = compact_domains return json_dict elif isinstance(symbol, pybamm.ConcatenationVariable): json_dict = { - "type": "ConcatenationVariable", + "type": "ConcatVar", "name": symbol.name, "children": [convert_symbol_to_json(child) for child in symbol.children], } @@ -1831,19 +2327,24 @@ def convert_symbol_to_json(symbol): diff_variable = symbol.diff_variable if diff_variable is not None: diff_variable = convert_symbol_to_json(diff_variable) + type_name = symbol.__class__.__name__ return { - "type": symbol.__class__.__name__, + "type": _TYPE_ABBREVIATIONS.get(type_name, type_name), "inputs": inputs, "diff_variable": diff_variable, "name": symbol.name, } elif isinstance(symbol, pybamm.Symbol): # Generic fallback for other symbols with children + type_name = symbol.__class__.__name__ json_dict = { - "type": symbol.__class__.__name__, - "domains": symbol.domains, + "type": _TYPE_ABBREVIATIONS.get(type_name, type_name), "children": [convert_symbol_to_json(c) for c in symbol.children], } + # Only include domains if non-empty + compact_domains = _compact_domains(symbol.domains) + if compact_domains is not None: + json_dict["domains"] = compact_domains if hasattr(symbol, "name"): json_dict["name"] = symbol.name return json_dict diff --git a/src/pybamm/meshes/meshes.py b/src/pybamm/meshes/meshes.py index f717b0a347..ddc295d57b 100644 --- a/src/pybamm/meshes/meshes.py +++ b/src/pybamm/meshes/meshes.py @@ -9,6 +9,39 @@ import pybamm +def compute_var_pts_from_thicknesses(electrode_thicknesses, grid_size): + """ + Compute a ``var_pts`` dictionary using electrode thicknesses and a target cell size (dx). + + Added as per maintainer feedback in issue # to make mesh generation + explicit — ``grid_size`` now represents the mesh cell size in metres. + + Parameters + ---------- + electrode_thicknesses : dict + Domain thicknesses in metres. + grid_size : float + Desired uniform mesh cell size (m). + + Returns + ------- + dict + Mapping of each domain to its computed grid points. + """ + if not isinstance(electrode_thicknesses, dict): + raise TypeError("electrode_thicknesses must be a dictionary") + + if not isinstance(grid_size, (int | float)) or grid_size <= 0: + raise ValueError("grid_size must be a positive number") + + var_pts = {} + for domain, thickness in electrode_thicknesses.items(): + npts = max(round(thickness / grid_size), 2) + var_pts[domain] = {f"x_{domain[0]}": npts} + + return var_pts + + class Mesh(dict): """ Mesh contains a list of submeshes on each subdomain. diff --git a/src/pybamm/models/submodels/interface/kinetics/butler_volmer.py b/src/pybamm/models/submodels/interface/kinetics/butler_volmer.py index c3e9ac0fc0..84cee586a3 100644 --- a/src/pybamm/models/submodels/interface/kinetics/butler_volmer.py +++ b/src/pybamm/models/submodels/interface/kinetics/butler_volmer.py @@ -12,7 +12,7 @@ class SymmetricButlerVolmer(BaseKinetics): Submodel which implements the symmetric forward Butler-Volmer equation: .. math:: - j = 2 * j_0(c) * \\sinh(ne * F * \\eta_r(c) / RT) + j = 2 * j_0(c) * \\sinh(ne * F * \\eta_r(c) / 2RT) Parameters ---------- diff --git a/src/pybamm/parameters/parameter_values.py b/src/pybamm/parameters/parameter_values.py index 2bec326a93..4135790ef8 100644 --- a/src/pybamm/parameters/parameter_values.py +++ b/src/pybamm/parameters/parameter_values.py @@ -794,7 +794,10 @@ def _process_symbol(self, symbol): # Unary operators elif isinstance(symbol, pybamm.UnaryOperator): new_child = self.process_symbol(symbol.child) - new_symbol = symbol.create_copy(new_children=[new_child]) + # Don't perform simplifications during parameter processing + new_symbol = symbol.create_copy( + new_children=[new_child], perform_simplifications=False + ) # x_average can sometimes create a new symbol with electrode thickness # parameters, so we process again to make sure these parameters are set if isinstance(symbol, pybamm.XAverage) and not isinstance( @@ -822,16 +825,22 @@ def _process_symbol(self, symbol): or isinstance(symbol, pybamm.BinaryOperator) ): new_children = [self.process_symbol(child) for child in symbol.children] - return symbol.create_copy(new_children) + # Don't perform simplifications during parameter processing to avoid + # evaluation errors (e.g., ZeroDivisionError) when creating copies + return symbol.create_copy(new_children, perform_simplifications=False) elif isinstance(symbol, pybamm.VectorField): left_symbol = self.process_symbol(symbol.lr_field) right_symbol = self.process_symbol(symbol.tb_field) - return symbol.create_copy(new_children=[left_symbol, right_symbol]) + # Don't perform simplifications during parameter processing + return symbol.create_copy( + new_children=[left_symbol, right_symbol], perform_simplifications=False + ) # Variables: update scale elif isinstance(symbol, pybamm.Variable): - new_symbol = symbol.create_copy() + # Don't perform simplifications during parameter processing + new_symbol = symbol.create_copy(perform_simplifications=False) new_symbol._scale = self.process_symbol(symbol.scale) reference = self.process_symbol(symbol.reference) if isinstance(reference, pybamm.Vector): @@ -1403,6 +1412,10 @@ def convert_parameter_values_to_json(parameter_values, filename=None): The filename to save the JSON file to. If not provided, the dictionary is not saved. """ + # Reset caches for a clean serialization + from pybamm.expression_tree.operations.serialise import _reset_serialization_caches + + _reset_serialization_caches() parameter_values_dict = {} for k, v in parameter_values.items(): diff --git a/tests/unit/test_meshes/test_meshes.py b/tests/unit/test_meshes/test_meshes.py index 8c26a0900f..15ef8317ba 100644 --- a/tests/unit/test_meshes/test_meshes.py +++ b/tests/unit/test_meshes/test_meshes.py @@ -584,6 +584,37 @@ def test_to_json(self): assert mesh_json == expected_json + def test_compute_var_pts_from_thicknesses_cell_size(self): + from pybamm.meshes.meshes import compute_var_pts_from_thicknesses + + electrode_thicknesses = { + "negative electrode": 100e-6, + "separator": 25e-6, + "positive electrode": 100e-6, + } + + cell_size = 5e-6 # 5 micrometres per cell + var_pts = compute_var_pts_from_thicknesses(electrode_thicknesses, cell_size) + + assert isinstance(var_pts, dict) + assert all(isinstance(v, dict) for v in var_pts.values()) + assert var_pts["negative electrode"]["x_n"] == 20 + assert var_pts["separator"]["x_s"] == 5 + assert var_pts["positive electrode"]["x_p"] == 20 + + def test_compute_var_pts_from_thicknesses_invalid_thickness_type(self): + from pybamm.meshes.meshes import compute_var_pts_from_thicknesses + + with pytest.raises(TypeError): + compute_var_pts_from_thicknesses(["not", "a", "dict"], 1e-6) + + def test_compute_var_pts_from_thicknesses_invalid_grid_size(self): + from pybamm.meshes.meshes import compute_var_pts_from_thicknesses + + electrode_thicknesses = {"negative electrode": 100e-6} + with pytest.raises(ValueError): + compute_var_pts_from_thicknesses(electrode_thicknesses, -1e-6) + class TestMeshGenerator: def test_init_name(self): diff --git a/tests/unit/test_serialisation/old_format_model_v1.0.json b/tests/unit/test_serialisation/old_format_model_v1.0.json new file mode 100644 index 0000000000..95ee21d99b --- /dev/null +++ b/tests/unit/test_serialisation/old_format_model_v1.0.json @@ -0,0 +1,128449 @@ +{ + "schema_version": "1.0", + "pybamm_version": "25.10.1.dev18+g29afed3a6.d20251115", + "model": { + "name": "Single Particle Model", + "base_class": "pybamm.models.full_battery_models.lithium_ion.base_lithium_ion_model.BaseModel", + "options": { + "calculate discharge energy": "false", + "calculate heat source for isothermal models": "false", + "cell geometry": "arbitrary", + "contact resistance": "false", + "convection": "none", + "current collector": "uniform", + "diffusivity": "single", + "dimensionality": 0, + "electrolyte conductivity": "default", + "exchange-current density": "single", + "heat of mixing": "false", + "hydrolysis": "false", + "intercalation kinetics": "symmetric Butler-Volmer", + "interface utilisation": "full", + "lithium plating": "none", + "lithium plating porosity change": "false", + "loss of active material": "none", + "number of MSMR reactions": "none", + "open-circuit potential": "single", + "operating mode": "current", + "particle": "Fickian diffusion", + "particle mechanics": "none", + "particle phases": "1", + "particle shape": "spherical", + "particle size": "single", + "SEI": "none", + "SEI film resistance": "none", + "SEI on cracks": "false", + "SEI porosity change": "false", + "stress-induced diffusion": "false", + "surface form": "false", + "surface temperature": "ambient", + "thermal": "isothermal", + "total interfacial current density as a state": "false", + "transport efficiency": "Bruggeman", + "voltage as a state": "false", + "working electrode": "both", + "x-average side reactions": "true", + "use lumped thermal capacity": "false" + }, + "rhs": [ + [ + { + "type": "Variable", + "name": "Discharge capacity [A.h]", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": -Infinity + }, + { + "type": "Scalar", + "value": Infinity + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.0002777777777777778 + }, + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + } + ], + "name": "*" + } + ], + [ + { + "type": "Variable", + "name": "Throughput capacity [A.h]", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": -Infinity + }, + { + "type": "Scalar", + "value": Infinity + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.0002777777777777778 + }, + { + "type": "AbsoluteValue", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + } + ], + "name": "abs" + } + ], + "name": "*" + } + ], + [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + }, + { + "type": "Divergence", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + }, + "Temperature [K]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "broadcast_domain": [ + "negative particle" + ] + } + }, + "diff_variable": null, + "name": "Negative particle diffusivity [m2.s-1]" + }, + { + "type": "Gradient", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "grad" + } + ], + "name": "*" + } + ], + "name": "div" + } + ], + [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + }, + { + "type": "Divergence", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + }, + "Temperature [K]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "broadcast_domain": [ + "positive particle" + ] + } + }, + "diff_variable": null, + "name": "Positive particle diffusivity [m2.s-1]" + }, + { + "type": "Gradient", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "grad" + } + ], + "name": "*" + } + ], + "name": "div" + } + ] + ], + "algebraic": [], + "initial_conditions": [ + [ + { + "type": "Variable", + "name": "Discharge capacity [A.h]", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": -Infinity + }, + { + "type": "Scalar", + "value": Infinity + } + ] + }, + { + "type": "Scalar", + "value": 0.0 + } + ], + [ + { + "type": "Variable", + "name": "Throughput capacity [A.h]", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": -Infinity + }, + { + "type": "Scalar", + "value": Infinity + } + ] + }, + { + "type": "Scalar", + "value": 0.0 + } + ], + [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Radial distance (r) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "negative electrode" + ], + "tertiary": [ + "current collector" + ], + "quaternary": [] + }, + "children": [], + "name": "r_n" + }, + "Through-cell distance (x) [m]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + ], + "broadcast_domain": [ + "negative particle" + ] + } + }, + "diff_variable": null, + "name": "Initial concentration in negative electrode [mol.m-3]" + } + ], + "name": "x-average" + } + ], + [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Radial distance (r) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "positive electrode" + ], + "tertiary": [ + "current collector" + ], + "quaternary": [] + }, + "children": [], + "name": "r_p" + }, + "Through-cell distance (x) [m]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + ], + "broadcast_domain": [ + "positive particle" + ] + } + }, + "diff_variable": null, + "name": "Initial concentration in positive electrode [mol.m-3]" + } + ], + "name": "x-average" + } + ] + ], + "boundary_conditions": [ + [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + }, + { + "left": [ + { + "type": "Scalar", + "value": 0.0 + }, + "Neumann" + ], + "right": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + }, + "Temperature [K]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "broadcast_domain": [ + "negative particle" + ] + } + }, + "diff_variable": null, + "name": "Negative particle diffusivity [m2.s-1]" + } + ] + } + ], + "name": "/" + }, + "Neumann" + ] + } + ], + [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + }, + { + "left": [ + { + "type": "Scalar", + "value": 0.0 + }, + "Neumann" + ], + "right": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + }, + "Temperature [K]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "broadcast_domain": [ + "positive particle" + ] + } + }, + "diff_variable": null, + "name": "Positive particle diffusivity [m2.s-1]" + } + ] + } + ], + "name": "/" + }, + "Neumann" + ] + } + ], + [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + { + "left": [ + { + "type": "Scalar", + "value": 0.0 + }, + "Neumann" + ], + "right": [ + { + "type": "Scalar", + "value": 0.0 + }, + "Neumann" + ] + } + ], + [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + { + "left": [ + { + "type": "Scalar", + "value": 0.0 + }, + "Neumann" + ], + "right": [ + { + "type": "Scalar", + "value": 0.0 + }, + "Neumann" + ] + } + ], + [ + { + "type": "FullBroadcast", + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "domains": { + "primary": [ + "negative electrode", + "separator", + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + { + "left": [ + { + "type": "Scalar", + "value": 0.0 + }, + "Neumann" + ], + "right": [ + { + "type": "Scalar", + "value": 0.0 + }, + "Neumann" + ] + } + ], + [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Negate", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + } + ], + "broadcast_domain": [ + "negative electrode", + "separator", + "positive electrode" + ] + }, + { + "left": [ + { + "type": "Scalar", + "value": 0.0 + }, + "Neumann" + ], + "right": [ + { + "type": "Scalar", + "value": 0.0 + }, + "Neumann" + ] + } + ] + ], + "events": [ + { + "name": "Minimum voltage [V]", + "expression": { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "positive tab", + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + } + ] + }, + { + "type": "Parameter", + "name": "Lower voltage cut-off [V]" + } + ], + "name": "-" + }, + "event_type": "TERMINATION" + }, + { + "name": "Maximum voltage [V]", + "expression": { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Upper voltage cut-off [V]" + }, + { + "type": "BoundaryValue", + "side": "positive tab", + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + } + ] + } + ], + "name": "-" + }, + "event_type": "TERMINATION" + }, + { + "name": "Minimum voltage switch [V]", + "expression": { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "positive tab", + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + } + ] + }, + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -0.1 + }, + { + "type": "Parameter", + "name": "Lower voltage cut-off [V]" + } + ], + "name": "+" + } + ], + "name": "-" + }, + "event_type": "SWITCH" + }, + { + "name": "Maximum voltage switch [V]", + "expression": { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "positive tab", + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + } + ] + }, + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.1 + }, + { + "type": "Parameter", + "name": "Upper voltage cut-off [V]" + } + ], + "name": "+" + } + ], + "name": "-" + }, + "event_type": "SWITCH" + } + ], + "variables": { + "Time [s]": { + "type": "Time" + }, + "Time [min]": { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.016666666666666666 + }, + { + "type": "Time" + } + ], + "name": "*" + }, + "Time [h]": { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.0002777777777777778 + }, + { + "type": "Time" + } + ], + "name": "*" + }, + "x [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode", + "separator", + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x" + }, + "x_n [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + }, + "x_s [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_s" + }, + "x_p [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + }, + "r_n [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "negative electrode" + ], + "tertiary": [ + "current collector" + ], + "quaternary": [] + }, + "children": [], + "name": "r_n" + }, + "r_p [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "positive electrode" + ], + "tertiary": [ + "current collector" + ], + "quaternary": [] + }, + "children": [], + "name": "r_p" + }, + "Current variable [A]": { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + "Total current density [A.m-2]": { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + "Current [A]": { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + "C-rate": { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Parameter", + "name": "Nominal cell capacity [A.h]" + } + ], + "name": "/" + }, + "Discharge capacity [A.h]": { + "type": "Variable", + "name": "Discharge capacity [A.h]", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": -Infinity + }, + { + "type": "Scalar", + "value": Infinity + } + ] + }, + "Throughput capacity [A.h]": { + "type": "Variable", + "name": "Throughput capacity [A.h]", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": -Infinity + }, + { + "type": "Scalar", + "value": Infinity + } + ] + }, + "Discharge energy [W.h]": { + "type": "Scalar", + "value": 0.0 + }, + "Throughput energy [W.h]": { + "type": "Scalar", + "value": 0.0 + }, + "Porosity": { + "type": "Concatenation", + "domains": { + "primary": [ + "negative electrode", + "separator", + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode porosity" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_s" + } + }, + "diff_variable": null, + "name": "Separator porosity" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode porosity" + } + ], + "name": "concatenation" + }, + "Negative electrode porosity": { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode porosity" + }, + "X-averaged negative electrode porosity": { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode porosity" + } + ], + "name": "x-average" + }, + "Separator porosity": { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_s" + } + }, + "diff_variable": null, + "name": "Separator porosity" + }, + "X-averaged separator porosity": { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_s" + } + }, + "diff_variable": null, + "name": "Separator porosity" + } + ], + "name": "x-average" + }, + "Positive electrode porosity": { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode porosity" + }, + "X-averaged positive electrode porosity": { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode porosity" + } + ], + "name": "x-average" + }, + "Porosity change": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode", + "separator", + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "Negative electrode porosity change [s-1]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative electrode porosity change [s-1]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Separator porosity change [s-1]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged separator porosity change [s-1]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Positive electrode porosity change [s-1]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive electrode porosity change [s-1]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Negative electrode interface utilisation variable": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 1.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative electrode interface utilisation variable": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 1.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Negative electrode interface utilisation": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 1.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative electrode interface utilisation": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 1.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Positive electrode interface utilisation variable": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 1.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive electrode interface utilisation variable": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 1.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Positive electrode interface utilisation": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 1.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive electrode interface utilisation": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 1.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Negative particle crack length [m]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative particle crack length [m]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Negative particle cracking rate [m.s-1]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative particle cracking rate [m.s-1]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Positive particle crack length [m]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive particle crack length [m]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Positive particle cracking rate [m.s-1]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive particle cracking rate [m.s-1]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Negative electrode active material volume fraction": { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + "X-averaged negative electrode active material volume fraction": { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + }, + "Negative electrode capacity [A.h]": { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.0002777777777777778 + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + "Negative particle radius": { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.5 + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "*" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + }, + "Negative particle radius [m]": { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + }, + "X-averaged negative particle radius [m]": { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "x-average" + }, + "Negative electrode surface area to volume ratio [m-1]": { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + }, + "X-averaged negative electrode surface area to volume ratio [m-1]": { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + }, + "Negative electrode active material volume fraction change [s-1]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative electrode active material volume fraction change [s-1]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Loss of lithium due to loss of active material in negative electrode [mol]": { + "type": "Scalar", + "value": 0.0 + }, + "Positive electrode active material volume fraction": { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + "X-averaged positive electrode active material volume fraction": { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + }, + "Positive electrode capacity [A.h]": { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.0002777777777777778 + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + "Positive particle radius": { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "Parameter", + "name": "Separator thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.5 + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "*" + } + ], + "name": "+" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + }, + "Positive particle radius [m]": { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + }, + "X-averaged positive particle radius [m]": { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "x-average" + }, + "Positive electrode surface area to volume ratio [m-1]": { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + }, + "X-averaged positive electrode surface area to volume ratio [m-1]": { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + }, + "Positive electrode active material volume fraction change [s-1]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive electrode active material volume fraction change [s-1]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Loss of lithium due to loss of active material in positive electrode [mol]": { + "type": "Scalar", + "value": 0.0 + }, + "Separator pressure [Pa]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + } + ], + "broadcast_domain": [ + "separator" + ] + }, + "X-averaged separator pressure [Pa]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "negative electrode transverse volume-averaged velocity [m.s-1]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "X-averaged negative electrode transverse volume-averaged velocity [m.s-1]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "separator transverse volume-averaged velocity [m.s-1]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + } + ], + "broadcast_domain": [ + "separator" + ] + }, + "X-averaged separator transverse volume-averaged velocity [m.s-1]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "positive electrode transverse volume-averaged velocity [m.s-1]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + "X-averaged positive electrode transverse volume-averaged velocity [m.s-1]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Transverse volume-averaged velocity [m.s-1]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + } + ], + "broadcast_domain": [ + "negative electrode", + "separator", + "positive electrode" + ] + }, + "negative electrode transverse volume-averaged acceleration [m.s-2]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "X-averaged negative electrode transverse volume-averaged acceleration [m.s-2]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "separator transverse volume-averaged acceleration [m.s-2]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + } + ], + "broadcast_domain": [ + "separator" + ] + }, + "X-averaged separator transverse volume-averaged acceleration [m.s-2]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "positive electrode transverse volume-averaged acceleration [m.s-2]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + "X-averaged positive electrode transverse volume-averaged acceleration [m.s-2]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Transverse volume-averaged acceleration [m.s-2]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + } + ], + "broadcast_domain": [ + "negative electrode", + "separator", + "positive electrode" + ] + }, + "Negative electrode volume-averaged velocity [m.s-1]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "Negative electrode volume-averaged acceleration [m.s-2]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative electrode volume-averaged acceleration [m.s-2]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Negative electrode pressure [Pa]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative electrode pressure [Pa]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Positive electrode volume-averaged velocity [m.s-1]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "Positive electrode volume-averaged acceleration [m.s-2]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive electrode volume-averaged acceleration [m.s-2]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Positive electrode pressure [Pa]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive electrode pressure [Pa]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Negative particle concentration [mol.m-3]": { + "type": "SecondaryBroadcast", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "X-averaged negative particle concentration [mol.m-3]": { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + }, + "R-averaged negative particle concentration [mol.m-3]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "Average negative particle concentration [mol.m-3]": { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "X-averaged negative particle surface concentration [mol.m-3]": { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + "Minimum negative particle concentration [mol.m-3]": { + "type": "Min", + "children": [ + { + "type": "SecondaryBroadcast", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ] + }, + "Maximum negative particle concentration [mol.m-3]": { + "type": "Max", + "children": [ + { + "type": "SecondaryBroadcast", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ] + }, + "Minimum negative particle Minimum negative particle surface concentration [mol.m-3]": { + "type": "Min", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ] + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Max", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ] + }, + "Negative particle concentration": { + "type": "SecondaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "X-averaged negative particle concentration": { + "type": "Division", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + "R-averaged negative particle concentration": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "Average negative particle concentration": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Negative particle surface concentration": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "X-averaged negative particle surface concentration": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Minimum negative particle concentration": { + "type": "Division", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "negative electrode" + ], + "tertiary": [ + "current collector" + ], + "quaternary": [] + }, + "children": [ + { + "type": "Min", + "children": [ + { + "type": "SecondaryBroadcast", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Maximum negative particle concentration": { + "type": "Division", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "negative electrode" + ], + "tertiary": [ + "current collector" + ], + "quaternary": [] + }, + "children": [ + { + "type": "Max", + "children": [ + { + "type": "SecondaryBroadcast", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Minimum negative particle surface concentration": { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Min", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Maximum negative particle surface concentration": { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Max", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Negative particle stoichiometry": { + "type": "SecondaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "X-averaged negative particle stoichiometry": { + "type": "Division", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + "R-averaged negative particle stoichiometry": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "Average negative particle stoichiometry": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Negative particle surface stoichiometry": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "X-averaged negative particle surface stoichiometry": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Minimum negative particle stoichiometry": { + "type": "Division", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "negative electrode" + ], + "tertiary": [ + "current collector" + ], + "quaternary": [] + }, + "children": [ + { + "type": "Min", + "children": [ + { + "type": "SecondaryBroadcast", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Maximum negative particle stoichiometry": { + "type": "Division", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "negative electrode" + ], + "tertiary": [ + "current collector" + ], + "quaternary": [] + }, + "children": [ + { + "type": "Max", + "children": [ + { + "type": "SecondaryBroadcast", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Minimum negative particle surface stoichiometry": { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Min", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Maximum negative particle surface stoichiometry": { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Max", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Negative electrode extent of lithiation": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "X-averaged negative electrode extent of lithiation": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Positive particle concentration [mol.m-3]": { + "type": "SecondaryBroadcast", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + "X-averaged positive particle concentration [mol.m-3]": { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + }, + "R-averaged positive particle concentration [mol.m-3]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + "Average positive particle concentration [mol.m-3]": { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + "X-averaged positive particle surface concentration [mol.m-3]": { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + "Minimum positive particle concentration [mol.m-3]": { + "type": "Min", + "children": [ + { + "type": "SecondaryBroadcast", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ] + }, + "Maximum positive particle concentration [mol.m-3]": { + "type": "Max", + "children": [ + { + "type": "SecondaryBroadcast", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ] + }, + "Minimum positive particle Minimum positive particle surface concentration [mol.m-3]": { + "type": "Min", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ] + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Max", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ] + }, + "Positive particle concentration": { + "type": "SecondaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + "X-averaged positive particle concentration": { + "type": "Division", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + "R-averaged positive particle concentration": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + "Average positive particle concentration": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Positive particle surface concentration": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + "X-averaged positive particle surface concentration": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Minimum positive particle concentration": { + "type": "Division", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "positive electrode" + ], + "tertiary": [ + "current collector" + ], + "quaternary": [] + }, + "children": [ + { + "type": "Min", + "children": [ + { + "type": "SecondaryBroadcast", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Maximum positive particle concentration": { + "type": "Division", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "positive electrode" + ], + "tertiary": [ + "current collector" + ], + "quaternary": [] + }, + "children": [ + { + "type": "Max", + "children": [ + { + "type": "SecondaryBroadcast", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Minimum positive particle surface concentration": { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Min", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Maximum positive particle surface concentration": { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Max", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Positive particle stoichiometry": { + "type": "SecondaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + "X-averaged positive particle stoichiometry": { + "type": "Division", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + "R-averaged positive particle stoichiometry": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + "Average positive particle stoichiometry": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Positive particle surface stoichiometry": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + "X-averaged positive particle surface stoichiometry": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Minimum positive particle stoichiometry": { + "type": "Division", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "positive electrode" + ], + "tertiary": [ + "current collector" + ], + "quaternary": [] + }, + "children": [ + { + "type": "Min", + "children": [ + { + "type": "SecondaryBroadcast", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Maximum positive particle stoichiometry": { + "type": "Division", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "positive electrode" + ], + "tertiary": [ + "current collector" + ], + "quaternary": [] + }, + "children": [ + { + "type": "Max", + "children": [ + { + "type": "SecondaryBroadcast", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Minimum positive particle surface stoichiometry": { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Min", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Maximum positive particle surface stoichiometry": { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Max", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Positive electrode extent of lithiation": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + "X-averaged positive electrode extent of lithiation": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Porosity times concentration [mol.m-3]": { + "type": "Concatenation", + "domains": { + "primary": [ + "negative electrode", + "separator", + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode porosity" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_s" + } + }, + "diff_variable": null, + "name": "Separator porosity" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode porosity" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "concatenation" + }, + "Negative electrode porosity times concentration [mol.m-3]": { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode porosity" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + }, + "Separator porosity times concentration [mol.m-3]": { + "type": "Multiplication", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_s" + } + }, + "diff_variable": null, + "name": "Separator porosity" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + }, + "Positive electrode porosity times concentration [mol.m-3]": { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode porosity" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + }, + "Total lithium in electrolyte [mol]": { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "Parameter", + "name": "Separator thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode porosity" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Separator thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_s" + } + }, + "diff_variable": null, + "name": "Separator porosity" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode porosity" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "Parameter", + "name": "Separator thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "yz-average" + } + ], + "name": "*" + }, + "Electrolyte flux [mol.m-2.s-1]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode", + "separator", + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "Ambient temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + "Volume-averaged ambient temperature [K]": { + "type": "ZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "z-average" + }, + "Cell temperature [K]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "broadcast_domain": [ + "negative electrode", + "separator", + "positive electrode" + ] + }, + "Negative current collector temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + "Positive current collector temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + "X-averaged cell temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + "Volume-averaged cell temperature [K]": { + "type": "ZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "z-average" + }, + "Negative electrode temperature [K]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "X-averaged negative electrode temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + "Separator temperature [K]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "broadcast_domain": [ + "separator" + ] + }, + "X-averaged separator temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + "Positive electrode temperature [K]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + "X-averaged positive electrode temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + "Ambient temperature [C]": { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -273.15 + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "+" + }, + "Volume-averaged ambient temperature [C]": { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -273.15 + }, + { + "type": "ZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "z-average" + } + ], + "name": "+" + }, + "Cell temperature [C]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -273.15 + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "+" + } + ], + "broadcast_domain": [ + "negative electrode", + "separator", + "positive electrode" + ] + }, + "Negative current collector temperature [C]": { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -273.15 + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "+" + }, + "Positive current collector temperature [C]": { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -273.15 + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "+" + }, + "X-averaged cell temperature [C]": { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -273.15 + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "+" + }, + "Volume-averaged cell temperature [C]": { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -273.15 + }, + { + "type": "ZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "z-average" + } + ], + "name": "+" + }, + "Negative electrode temperature [C]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -273.15 + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "+" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "X-averaged negative electrode temperature [C]": { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -273.15 + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "+" + }, + "Separator temperature [C]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -273.15 + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "+" + } + ], + "broadcast_domain": [ + "separator" + ] + }, + "X-averaged separator temperature [C]": { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -273.15 + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "+" + }, + "Positive electrode temperature [C]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -273.15 + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "+" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + "X-averaged positive electrode temperature [C]": { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -273.15 + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "+" + }, + "Negative current collector potential [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Negative SEI concentration [mol.m-3]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative SEI concentration [mol.m-3]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Volume-averaged negative SEI concentration [mol.m-3]": { + "type": "Scalar", + "value": 0.0 + }, + "Loss of lithium to negative SEI [mol]": { + "type": "Scalar", + "value": 0.0 + }, + "Loss of capacity to negative SEI [A.h]": { + "type": "Scalar", + "value": 0.0 + }, + "Negative electrode SEI interfacial current density [A.m-2]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative electrode SEI interfacial current density [A.m-2]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Positive SEI concentration [mol.m-3]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive SEI concentration [mol.m-3]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Volume-averaged positive SEI concentration [mol.m-3]": { + "type": "Scalar", + "value": 0.0 + }, + "Loss of lithium to positive SEI [mol]": { + "type": "Scalar", + "value": 0.0 + }, + "Loss of capacity to positive SEI [A.h]": { + "type": "Scalar", + "value": 0.0 + }, + "Positive electrode SEI interfacial current density [A.m-2]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive electrode SEI interfacial current density [A.m-2]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Negative SEI on cracks concentration [mol.m-3]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative SEI on cracks concentration [mol.m-3]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Volume-averaged negative SEI on cracks concentration [mol.m-3]": { + "type": "Scalar", + "value": 0.0 + }, + "Loss of lithium to negative SEI on cracks [mol]": { + "type": "Scalar", + "value": 0.0 + }, + "Loss of capacity to negative SEI on cracks [A.h]": { + "type": "Scalar", + "value": 0.0 + }, + "Negative electrode SEI on cracks interfacial current density [A.m-2]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative electrode SEI on cracks interfacial current density [A.m-2]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Positive SEI on cracks concentration [mol.m-3]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive SEI on cracks concentration [mol.m-3]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Volume-averaged positive SEI on cracks concentration [mol.m-3]": { + "type": "Scalar", + "value": 0.0 + }, + "Loss of lithium to positive SEI on cracks [mol]": { + "type": "Scalar", + "value": 0.0 + }, + "Loss of capacity to positive SEI on cracks [A.h]": { + "type": "Scalar", + "value": 0.0 + }, + "Positive electrode SEI on cracks interfacial current density [A.m-2]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive electrode SEI on cracks interfacial current density [A.m-2]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Negative lithium plating concentration [mol.m-3]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative lithium plating concentration [mol.m-3]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Volume-averaged negative lithium plating concentration [mol.m-3]": { + "type": "Scalar", + "value": 0.0 + }, + "Negative dead lithium concentration [mol.m-3]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative dead lithium concentration [mol.m-3]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Volume-averaged negative dead lithium concentration [mol.m-3]": { + "type": "Scalar", + "value": 0.0 + }, + "Negative lithium plating thickness [m]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative lithium plating thickness [m]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Volume-averaged negative lithium plating thickness [m]": { + "type": "Scalar", + "value": 0.0 + }, + "Negative dead lithium thickness [m]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative dead lithium thickness [m]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Volume-averaged negative dead lithium thickness [m]": { + "type": "Scalar", + "value": 0.0 + }, + "Loss of lithium to negative lithium plating [mol]": { + "type": "Scalar", + "value": 0.0 + }, + "Loss of capacity to negative lithium plating [A.h]": { + "type": "Scalar", + "value": 0.0 + }, + "Negative electrode lithium plating interfacial current density [A.m-2]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative electrode lithium plating interfacial current density [A.m-2]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Negative electrode lithium plating reaction overpotential [V]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative electrode lithium plating reaction overpotential [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Positive lithium plating concentration [mol.m-3]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive lithium plating concentration [mol.m-3]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Volume-averaged positive lithium plating concentration [mol.m-3]": { + "type": "Scalar", + "value": 0.0 + }, + "Positive dead lithium concentration [mol.m-3]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive dead lithium concentration [mol.m-3]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Volume-averaged positive dead lithium concentration [mol.m-3]": { + "type": "Scalar", + "value": 0.0 + }, + "Positive lithium plating thickness [m]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive lithium plating thickness [m]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Volume-averaged positive lithium plating thickness [m]": { + "type": "Scalar", + "value": 0.0 + }, + "Positive dead lithium thickness [m]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive dead lithium thickness [m]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Volume-averaged positive dead lithium thickness [m]": { + "type": "Scalar", + "value": 0.0 + }, + "Loss of lithium to positive lithium plating [mol]": { + "type": "Scalar", + "value": 0.0 + }, + "Loss of capacity to positive lithium plating [A.h]": { + "type": "Scalar", + "value": 0.0 + }, + "Positive electrode lithium plating interfacial current density [A.m-2]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive electrode lithium plating interfacial current density [A.m-2]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Positive electrode lithium plating reaction overpotential [V]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive electrode lithium plating reaction overpotential [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Negative crack surface to volume ratio [m-1]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "Negative electrode roughness ratio": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 1.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative electrode roughness ratio": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 1.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Positive crack surface to volume ratio [m-1]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "Positive electrode roughness ratio": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 1.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive electrode roughness ratio": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 1.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Electrolyte transport efficiency": { + "type": "Concatenation", + "domains": { + "primary": [ + "negative electrode", + "separator", + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Power", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode porosity" + }, + { + "type": "Parameter", + "name": "Negative electrode Bruggeman coefficient (electrolyte)" + } + ], + "name": "**" + }, + { + "type": "Power", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_s" + } + }, + "diff_variable": null, + "name": "Separator porosity" + }, + { + "type": "Parameter", + "name": "Separator Bruggeman coefficient (electrolyte)" + } + ], + "name": "**" + }, + { + "type": "Power", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode porosity" + }, + { + "type": "Parameter", + "name": "Positive electrode Bruggeman coefficient (electrolyte)" + } + ], + "name": "**" + } + ], + "name": "concatenation" + }, + "Negative electrolyte transport efficiency": { + "type": "Power", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode porosity" + }, + { + "type": "Parameter", + "name": "Negative electrode Bruggeman coefficient (electrolyte)" + } + ], + "name": "**" + }, + "X-averaged negative electrolyte transport efficiency": { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Power", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode porosity" + }, + { + "type": "Parameter", + "name": "Negative electrode Bruggeman coefficient (electrolyte)" + } + ], + "name": "**" + } + ], + "name": "x-average" + }, + "Separator electrolyte transport efficiency": { + "type": "Power", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_s" + } + }, + "diff_variable": null, + "name": "Separator porosity" + }, + { + "type": "Parameter", + "name": "Separator Bruggeman coefficient (electrolyte)" + } + ], + "name": "**" + }, + "X-averaged separator electrolyte transport efficiency": { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Power", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_s" + } + }, + "diff_variable": null, + "name": "Separator porosity" + }, + { + "type": "Parameter", + "name": "Separator Bruggeman coefficient (electrolyte)" + } + ], + "name": "**" + } + ], + "name": "x-average" + }, + "Positive electrolyte transport efficiency": { + "type": "Power", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode porosity" + }, + { + "type": "Parameter", + "name": "Positive electrode Bruggeman coefficient (electrolyte)" + } + ], + "name": "**" + }, + "X-averaged positive electrolyte transport efficiency": { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Power", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode porosity" + }, + { + "type": "Parameter", + "name": "Positive electrode Bruggeman coefficient (electrolyte)" + } + ], + "name": "**" + } + ], + "name": "x-average" + }, + "Electrode transport efficiency": { + "type": "Concatenation", + "domains": { + "primary": [ + "negative electrode", + "separator", + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Power", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode porosity" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Negative electrode Bruggeman coefficient (electrode)" + } + ], + "name": "**" + }, + { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + { + "type": "Power", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode porosity" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode Bruggeman coefficient (electrode)" + } + ], + "name": "**" + } + ], + "name": "concatenation" + }, + "Negative electrode transport efficiency": { + "type": "Power", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode porosity" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Negative electrode Bruggeman coefficient (electrode)" + } + ], + "name": "**" + }, + "X-averaged negative electrode transport efficiency": { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Power", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode porosity" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Negative electrode Bruggeman coefficient (electrode)" + } + ], + "name": "**" + } + ], + "name": "x-average" + }, + "Separator electrode transport efficiency": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged separator electrode transport efficiency": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Positive electrode transport efficiency": { + "type": "Power", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode porosity" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode Bruggeman coefficient (electrode)" + } + ], + "name": "**" + }, + "X-averaged positive electrode transport efficiency": { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Power", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode porosity" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode Bruggeman coefficient (electrode)" + } + ], + "name": "**" + } + ], + "name": "x-average" + }, + "Separator volume-averaged velocity [m.s-1]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "Separator volume-averaged acceleration [m.s-2]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged separator volume-averaged acceleration [m.s-2]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Volume-averaged velocity [m.s-1]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode", + "separator", + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "Volume-averaged acceleration [m.s-1]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode", + "separator", + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged volume-averaged acceleration [m.s-1]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Pressure [Pa]": { + "type": "Concatenation", + "domains": { + "primary": [ + "negative electrode", + "separator", + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + } + ], + "broadcast_domain": [ + "separator" + ] + }, + { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + } + ], + "name": "concatenation" + }, + "Negative electrode stoichiometry": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Negative electrode volume-averaged concentration": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Negative electrode volume-averaged concentration [mol.m-3]": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + "Total lithium in primary phase in negative electrode [mol]": { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + "Positive electrode stoichiometry": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Positive electrode volume-averaged concentration": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + "Positive electrode volume-averaged concentration [mol.m-3]": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + "Total lithium in primary phase in positive electrode [mol]": { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + "Electrolyte concentration concatenation [mol.m-3]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "domains": { + "primary": [ + "negative electrode", + "separator", + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "Negative electrolyte concentration [mol.m-3]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative electrolyte concentration [mol.m-3]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Separator electrolyte concentration [mol.m-3]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged separator electrolyte concentration [mol.m-3]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Positive electrolyte concentration [mol.m-3]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive electrolyte concentration [mol.m-3]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Negative electrolyte concentration [Molar]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.001 + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative electrolyte concentration [Molar]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.001 + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Separator electrolyte concentration [Molar]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.001 + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged separator electrolyte concentration [Molar]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.001 + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Positive electrolyte concentration [Molar]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.001 + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive electrolyte concentration [Molar]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.001 + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Electrolyte concentration [mol.m-3]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "domains": { + "primary": [ + "negative electrode", + "separator", + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged electrolyte concentration [mol.m-3]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Electrolyte concentration [Molar]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.001 + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "domains": { + "primary": [ + "negative electrode", + "separator", + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged electrolyte concentration [Molar]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.001 + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Ohmic heating [W.m-3]": { + "type": "Scalar", + "value": 0.0 + }, + "X-averaged Ohmic heating [W.m-3]": { + "type": "Scalar", + "value": 0.0 + }, + "Volume-averaged Ohmic heating [W.m-3]": { + "type": "Scalar", + "value": 0.0 + }, + "Ohmic heating per unit electrode-pair area [W.m-2]": { + "type": "Scalar", + "value": 0.0 + }, + "Ohmic heating [W]": { + "type": "Scalar", + "value": 0.0 + }, + "Irreversible electrochemical heating [W.m-3]": { + "type": "Scalar", + "value": 0.0 + }, + "X-averaged irreversible electrochemical heating [W.m-3]": { + "type": "Scalar", + "value": 0.0 + }, + "Volume-averaged irreversible electrochemical heating [W.m-3]": { + "type": "Scalar", + "value": 0.0 + }, + "Irreversible electrochemical heating per unit electrode-pair area [W.m-2]": { + "type": "Scalar", + "value": 0.0 + }, + "Irreversible electrochemical heating [W]": { + "type": "Scalar", + "value": 0.0 + }, + "Reversible heating [W.m-3]": { + "type": "Scalar", + "value": 0.0 + }, + "X-averaged reversible heating [W.m-3]": { + "type": "Scalar", + "value": 0.0 + }, + "Volume-averaged reversible heating [W.m-3]": { + "type": "Scalar", + "value": 0.0 + }, + "Reversible heating per unit electrode-pair area [W.m-2]": { + "type": "Scalar", + "value": 0.0 + }, + "Reversible heating [W]": { + "type": "Scalar", + "value": 0.0 + }, + "Total heating [W.m-3]": { + "type": "Scalar", + "value": 0.0 + }, + "X-averaged total heating [W.m-3]": { + "type": "Scalar", + "value": 0.0 + }, + "Volume-averaged total heating [W.m-3]": { + "type": "Scalar", + "value": 0.0 + }, + "Total heating per unit electrode-pair area [W.m-2]": { + "type": "Scalar", + "value": 0.0 + }, + "Total heating [W]": { + "type": "Scalar", + "value": 0.0 + }, + "Negative current collector Ohmic heating [W.m-3]": { + "type": "Scalar", + "value": 0.0 + }, + "Positive current collector Ohmic heating [W.m-3]": { + "type": "Scalar", + "value": 0.0 + }, + "Surface total cooling [W.m-3]": { + "type": "Scalar", + "value": 0.0 + }, + "Surface total cooling [W]": { + "type": "Scalar", + "value": 0.0 + }, + "Surface temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + "Volume-averaged surface temperature [K]": { + "type": "ZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "z-average" + }, + "Environment total cooling [W]": { + "type": "Scalar", + "value": 0.0 + }, + "Current collector current density [A.m-2]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Negative electrode SEI volumetric interfacial current density [A.m-3]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative electrode SEI volumetric interfacial current density [A.m-3]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "X-averaged negative electrode resistance [Ohm.m2]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Negative SEI thickness [m]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative SEI thickness [m]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Volume-averaged negative SEI thickness [m]": { + "type": "Scalar", + "value": 0.0 + }, + "Positive electrode SEI volumetric interfacial current density [A.m-3]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive electrode SEI volumetric interfacial current density [A.m-3]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "X-averaged positive electrode resistance [Ohm.m2]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Positive SEI thickness [m]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive SEI thickness [m]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Volume-averaged positive SEI thickness [m]": { + "type": "Scalar", + "value": 0.0 + }, + "Negative electrode SEI on cracks volumetric interfacial current density [A.m-3]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative electrode SEI on cracks volumetric interfacial current density [A.m-3]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Negative SEI on cracks thickness [m]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative SEI on cracks thickness [m]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Volume-averaged negative SEI on cracks thickness [m]": { + "type": "Scalar", + "value": 0.0 + }, + "Positive electrode SEI on cracks volumetric interfacial current density [A.m-3]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive electrode SEI on cracks volumetric interfacial current density [A.m-3]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Positive SEI on cracks thickness [m]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive SEI on cracks thickness [m]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Volume-averaged positive SEI on cracks thickness [m]": { + "type": "Scalar", + "value": 0.0 + }, + "Negative electrode lithium plating volumetric interfacial current density [A.m-3]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative electrode lithium plating volumetric interfacial current density [A.m-3]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Positive electrode lithium plating volumetric interfacial current density [A.m-3]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive electrode lithium plating volumetric interfacial current density [A.m-3]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Negative electrode equilibrium open-circuit potential [V]": { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + }, + "X-averaged negative electrode equilibrium open-circuit potential [V]": { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + }, + "Negative electrode open-circuit potential [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "X-averaged negative electrode open-circuit potential [V]": { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + }, + "Negative electrode bulk open-circuit potential [V]": { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + }, + "Negative particle concentration overpotential [V]": { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "-" + }, + "Negative electrode entropic change [V.K-1]": { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + }, + "X-averaged negative electrode entropic change [V.K-1]": { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + }, + "Positive electrode equilibrium open-circuit potential [V]": { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + }, + "X-averaged positive electrode equilibrium open-circuit potential [V]": { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + }, + "Positive electrode open-circuit potential [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + "X-averaged positive electrode open-circuit potential [V]": { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + }, + "Positive electrode bulk open-circuit potential [V]": { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + }, + "Positive particle concentration overpotential [V]": { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "-" + }, + "Positive electrode entropic change [V.K-1]": { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + }, + "X-averaged positive electrode entropic change [V.K-1]": { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + }, + "X-averaged negative electrode total interfacial current density [A.m-2]": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + "X-averaged negative electrode total volumetric interfacial current density [A.m-3]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Negative electrode SEI film overpotential [V]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged negative electrode SEI film overpotential [V]": { + "type": "Scalar", + "value": 0.0 + }, + "Negative electrode exchange current density [A.m-2]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "X-averaged negative electrode exchange current density [A.m-2]": { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + }, + "Negative electrode reaction overpotential [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "X-averaged negative electrode reaction overpotential [V]": { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + "X-averaged negative electrode surface potential difference [V]": { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + }, + "Negative electrode interfacial current density [A.m-2]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "X-averaged negative electrode interfacial current density [A.m-2]": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + "Negative electrode volumetric interfacial current density [A.m-3]": { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + }, + "X-averaged negative electrode volumetric interfacial current density [A.m-3]": { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + "X-averaged positive electrode total interfacial current density [A.m-2]": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + "X-averaged positive electrode total volumetric interfacial current density [A.m-3]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Positive electrode SEI film overpotential [V]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive electrode SEI film overpotential [V]": { + "type": "Scalar", + "value": 0.0 + }, + "Positive electrode exchange current density [A.m-2]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + "X-averaged positive electrode exchange current density [A.m-2]": { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + }, + "Positive electrode reaction overpotential [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + "X-averaged positive electrode reaction overpotential [V]": { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + "X-averaged positive electrode surface potential difference [V]": { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + }, + "Positive electrode interfacial current density [A.m-2]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + "X-averaged positive electrode interfacial current density [A.m-2]": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + "Positive electrode volumetric interfacial current density [A.m-3]": { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + }, + "X-averaged positive electrode volumetric interfacial current density [A.m-3]": { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + "Negative particle rhs [mol.m-3.s-1]": { + "type": "Divergence", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + }, + "Temperature [K]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "broadcast_domain": [ + "negative particle" + ] + } + }, + "diff_variable": null, + "name": "Negative particle diffusivity [m2.s-1]" + }, + { + "type": "Gradient", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "grad" + } + ], + "name": "*" + } + ], + "name": "div" + }, + "Negative particle bc [mol.m-4]": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + }, + "Temperature [K]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "broadcast_domain": [ + "negative particle" + ] + } + }, + "diff_variable": null, + "name": "Negative particle diffusivity [m2.s-1]" + } + ] + } + ], + "name": "/" + }, + "Negative particle effective diffusivity [m2.s-1]": { + "type": "SecondaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + }, + "Temperature [K]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "broadcast_domain": [ + "negative particle" + ] + } + }, + "diff_variable": null, + "name": "Negative particle diffusivity [m2.s-1]" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "X-averaged negative particle effective diffusivity [m2.s-1]": { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + }, + "Temperature [K]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "broadcast_domain": [ + "negative particle" + ] + } + }, + "diff_variable": null, + "name": "Negative particle diffusivity [m2.s-1]" + }, + "Volume-averaged negative particle effective diffusivity [m2.s-1]": { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + }, + "Temperature [K]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "broadcast_domain": [ + "negative particle" + ] + } + }, + "diff_variable": null, + "name": "Negative particle diffusivity [m2.s-1]" + } + ], + "name": "r-average" + }, + "Negative particle flux [mol.m-2.s-1]": { + "type": "SecondaryBroadcast", + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + }, + "Temperature [K]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "broadcast_domain": [ + "negative particle" + ] + } + }, + "diff_variable": null, + "name": "Negative particle diffusivity [m2.s-1]" + } + ], + "name": "-" + }, + { + "type": "Gradient", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "grad" + } + ], + "name": "*" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "X-averaged negative particle flux [mol.m-2.s-1]": { + "type": "Multiplication", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + }, + "Temperature [K]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "broadcast_domain": [ + "negative particle" + ] + } + }, + "diff_variable": null, + "name": "Negative particle diffusivity [m2.s-1]" + } + ], + "name": "-" + }, + { + "type": "Gradient", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "grad" + } + ], + "name": "*" + }, + "Positive particle rhs [mol.m-3.s-1]": { + "type": "Divergence", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + }, + "Temperature [K]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "broadcast_domain": [ + "positive particle" + ] + } + }, + "diff_variable": null, + "name": "Positive particle diffusivity [m2.s-1]" + }, + { + "type": "Gradient", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "grad" + } + ], + "name": "*" + } + ], + "name": "div" + }, + "Positive particle bc [mol.m-4]": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + }, + "Temperature [K]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "broadcast_domain": [ + "positive particle" + ] + } + }, + "diff_variable": null, + "name": "Positive particle diffusivity [m2.s-1]" + } + ] + } + ], + "name": "/" + }, + "Positive particle effective diffusivity [m2.s-1]": { + "type": "SecondaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + }, + "Temperature [K]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "broadcast_domain": [ + "positive particle" + ] + } + }, + "diff_variable": null, + "name": "Positive particle diffusivity [m2.s-1]" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + "X-averaged positive particle effective diffusivity [m2.s-1]": { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + }, + "Temperature [K]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "broadcast_domain": [ + "positive particle" + ] + } + }, + "diff_variable": null, + "name": "Positive particle diffusivity [m2.s-1]" + }, + "Volume-averaged positive particle effective diffusivity [m2.s-1]": { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + }, + "Temperature [K]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "broadcast_domain": [ + "positive particle" + ] + } + }, + "diff_variable": null, + "name": "Positive particle diffusivity [m2.s-1]" + } + ], + "name": "r-average" + }, + "Positive particle flux [mol.m-2.s-1]": { + "type": "SecondaryBroadcast", + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + }, + "Temperature [K]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "broadcast_domain": [ + "positive particle" + ] + } + }, + "diff_variable": null, + "name": "Positive particle diffusivity [m2.s-1]" + } + ], + "name": "-" + }, + { + "type": "Gradient", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "grad" + } + ], + "name": "*" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + "X-averaged positive particle flux [mol.m-2.s-1]": { + "type": "Multiplication", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + }, + "Temperature [K]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "broadcast_domain": [ + "positive particle" + ] + } + }, + "diff_variable": null, + "name": "Positive particle diffusivity [m2.s-1]" + } + ], + "name": "-" + }, + { + "type": "Gradient", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "grad" + } + ], + "name": "*" + }, + "Negative electrode potential [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "X-averaged negative electrode potential [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Negative electrode ohmic losses [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": -0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "X-averaged negative electrode ohmic losses [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": -0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Gradient of negative electrode potential [V.m-1]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "Negative electrode current density [A.m-2]": { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Subtraction", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + } + ], + "name": "-" + } + ], + "name": "*" + }, + "Electrolyte potential [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Negate", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + } + ], + "broadcast_domain": [ + "negative electrode", + "separator", + "positive electrode" + ] + }, + "X-averaged electrolyte potential [V]": { + "type": "Negate", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + }, + "X-averaged electrolyte overpotential [V]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + } + }, + "Gradient of electrolyte potential [V.m-1]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + } + ], + "broadcast_domain": [ + "negative electrode", + "separator", + "positive electrode" + ] + }, + "Negative electrolyte potential [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Negate", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "X-averaged negative electrolyte potential [V]": { + "type": "Negate", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + }, + "Gradient of negative electrolyte potential [V.m-1]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "Separator electrolyte potential [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Negate", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + } + ], + "broadcast_domain": [ + "separator" + ] + }, + "X-averaged separator electrolyte potential [V]": { + "type": "Negate", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + }, + "Gradient of separator electrolyte potential [V.m-1]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + } + ], + "broadcast_domain": [ + "separator" + ] + }, + "Positive electrolyte potential [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Negate", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + "X-averaged positive electrolyte potential [V]": { + "type": "Negate", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + }, + "Gradient of positive electrolyte potential [V.m-1]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + "Electrolyte current density [A.m-2]": { + "type": "Concatenation", + "domains": { + "primary": [ + "negative electrode", + "separator", + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + ], + "broadcast_domain": [ + "separator" + ] + }, + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Subtraction", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "Parameter", + "name": "Separator thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "+" + }, + { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + ], + "name": "-" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + } + ], + "name": "concatenation" + }, + "Negative electrolyte current density [A.m-2]": { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + "Positive electrolyte current density [A.m-2]": { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Subtraction", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "Parameter", + "name": "Separator thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "+" + }, + { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + ], + "name": "-" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + "X-averaged concentration overpotential [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "X-averaged electrolyte ohmic losses [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Negative electrode surface potential difference [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + "Negative electrode surface potential difference at separator interface [V]": { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + }, + "Sum of negative electrode electrolyte reaction source terms [A.m-3]": { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + }, + "Sum of x-averaged negative electrode electrolyte reaction source terms [A.m-3]": { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + "Sum of negative electrode volumetric interfacial current densities [A.m-3]": { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + }, + "Sum of x-averaged negative electrode volumetric interfacial current densities [A.m-3]": { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + "Sum of positive electrode electrolyte reaction source terms [A.m-3]": { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + }, + "Sum of x-averaged positive electrode electrolyte reaction source terms [A.m-3]": { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + "Sum of positive electrode volumetric interfacial current densities [A.m-3]": { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + }, + "Sum of x-averaged positive electrode volumetric interfacial current densities [A.m-3]": { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + "Interfacial current density [A.m-2]": { + "type": "Concatenation", + "domains": { + "primary": [ + "negative electrode", + "separator", + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "concatenation" + }, + "Exchange current density [A.m-2]": { + "type": "Concatenation", + "domains": { + "primary": [ + "negative electrode", + "separator", + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + }, + { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "concatenation" + }, + "Sum of volumetric interfacial current densities [A.m-3]": { + "type": "Concatenation", + "domains": { + "primary": [ + "negative electrode", + "separator", + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + }, + { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "concatenation" + }, + "Sum of electrolyte reaction source terms [A.m-3]": { + "type": "Concatenation", + "domains": { + "primary": [ + "negative electrode", + "separator", + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + }, + { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "concatenation" + }, + "Positive electrode potential [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + "X-averaged positive electrode potential [V]": { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + }, + "Positive electrode ohmic losses [V]": { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + "X-averaged positive electrode ohmic losses [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Gradient of positive electrode potential [V.m-1]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + "Positive electrode current density [A.m-2]": { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Subtraction", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "Parameter", + "name": "Separator thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "+" + }, + { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + } + ], + "name": "-" + } + ], + "name": "*" + }, + "Electrode current density [A.m-2]": { + "type": "Concatenation", + "domains": { + "primary": [ + "negative electrode", + "separator", + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Subtraction", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + } + ], + "name": "-" + } + ], + "name": "*" + }, + { + "type": "FullBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + } + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Subtraction", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "Parameter", + "name": "Separator thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "+" + }, + { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + } + ], + "name": "-" + } + ], + "name": "*" + } + ], + "name": "concatenation" + }, + "Positive current collector potential [V]": { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + }, + "Local voltage [V]": { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + }, + "Voltage expression [V]": { + "type": "BoundaryValue", + "side": "positive tab", + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + } + ] + }, + "Terminal voltage [V]": { + "type": "BoundaryValue", + "side": "positive tab", + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + } + ] + }, + "Contact overpotential [V]": { + "type": "Scalar", + "value": 0.0 + }, + "Voltage [V]": { + "type": "BoundaryValue", + "side": "positive tab", + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + } + ] + }, + "Positive electrode surface potential difference [V]": { + "type": "Subtraction", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Negate", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "-" + }, + "Positive electrode surface potential difference at separator interface [V]": { + "type": "BoundaryValue", + "side": "left", + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Negate", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "-" + } + ] + }, + "Surface open-circuit voltage [V]": { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "-" + }, + "Bulk open-circuit voltage [V]": { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "-" + }, + "Particle concentration overpotential [V]": { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "-" + }, + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "-" + } + ], + "name": "-" + }, + "X-averaged reaction overpotential [V]": { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + } + ], + "name": "-" + }, + "X-averaged SEI film overpotential [V]": { + "type": "Scalar", + "value": 0.0 + }, + "X-averaged solid phase ohmic losses [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Battery open-circuit voltage [V]": { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Number of cells connected in series to make a battery" + } + ], + "name": "*" + }, + "Battery negative electrode bulk open-circuit potential [V]": { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Number of cells connected in series to make a battery" + } + ], + "name": "*" + }, + "Battery positive electrode bulk open-circuit potential [V]": { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Number of cells connected in series to make a battery" + } + ], + "name": "*" + }, + "Battery particle concentration overpotential [V]": { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "-" + }, + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "-" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Number of cells connected in series to make a battery" + } + ], + "name": "*" + }, + "Battery negative particle concentration overpotential [V]": { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Number of cells connected in series to make a battery" + } + ], + "name": "*" + }, + "Battery positive particle concentration overpotential [V]": { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Number of cells connected in series to make a battery" + } + ], + "name": "*" + }, + "X-averaged battery reaction overpotential [V]": { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Number of cells connected in series to make a battery" + } + ], + "name": "*" + }, + "X-averaged battery negative reaction overpotential [V]": { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of cells connected in series to make a battery" + } + ], + "name": "*" + }, + "X-averaged battery positive reaction overpotential [V]": { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of cells connected in series to make a battery" + } + ], + "name": "*" + }, + "X-averaged battery solid phase ohmic losses [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "X-averaged battery negative solid phase ohmic losses [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "X-averaged battery positive solid phase ohmic losses [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "X-averaged battery electrolyte ohmic losses [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "X-averaged battery concentration overpotential [V]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Scalar", + "value": 0.0 + } + ], + "broadcast_domain": [ + "current collector" + ] + }, + "Battery voltage [V]": { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "positive tab", + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + } + ] + }, + { + "type": "Parameter", + "name": "Number of cells connected in series to make a battery" + } + ], + "name": "*" + }, + "Local ECM resistance [Ohm]": { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Sign", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "sign" + }, + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "-" + }, + { + "type": "BoundaryValue", + "side": "positive tab", + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + } + ] + } + ], + "name": "-" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "NotEqualHeaviside", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "<" + }, + { + "type": "NotEqualHeaviside", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.0 + } + ], + "name": "<" + } + ], + "name": "+" + }, + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "EqualHeaviside", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "<=" + }, + { + "type": "EqualHeaviside", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.0 + } + ], + "name": "<=" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + } + ], + "name": "/" + }, + "Terminal power [W]": { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "BoundaryValue", + "side": "positive tab", + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + } + ] + } + ], + "name": "*" + }, + "Power [W]": { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "BoundaryValue", + "side": "positive tab", + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + } + ] + } + ], + "name": "*" + }, + "Resistance [Ohm]": { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Sign", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + } + ], + "name": "sign" + }, + { + "type": "BoundaryValue", + "side": "positive tab", + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Negate", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "-" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Positive particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum positive particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Positive electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Positive particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Positive electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Ideal gas constant [J.K-1.mol-1]" + }, + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "/" + }, + { + "type": "Arcsinh", + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "/" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "/" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 3.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "*" + }, + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative particle radius [m]" + } + ], + "name": "/" + } + ], + "name": "x-average" + } + ], + "name": "/" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 2.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Electrolyte concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + }, + { + "type": "Scalar", + "value": 1e-08 + } + ], + "name": "maximum" + }, + "Negative particle surface concentration [mol.m-3]": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.99999999 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "minimum" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-08 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "maximum" + }, + "Maximum negative particle surface concentration [mol.m-3]": { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + }, + "Temperature [K]": { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + } + }, + "diff_variable": null, + "name": "Negative electrode exchange-current density [A.m-2]" + } + ], + "name": "*" + } + ], + "name": "/" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP [V]" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Subtraction", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Distance across electrode width [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "y" + }, + "Distance across electrode height [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "z" + }, + "Time [s]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "Time" + } + ], + "broadcast_domain": [ + "current collector" + ] + } + }, + "diff_variable": null, + "name": "Ambient temperature [K]" + }, + { + "type": "Parameter", + "name": "Reference temperature [K]" + } + ], + "name": "-" + }, + { + "type": "FunctionParameter", + "inputs": { + "Negative particle stoichiometry": { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + }, + "diff_variable": null, + "name": "Negative electrode OCP entropic change [V.K-1]" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1e-06 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "/" + }, + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 1.0 + }, + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": -1.0 + }, + { + "type": "Maximum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Minimum", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "BoundaryValue", + "side": "right", + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ] + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "/" + }, + { + "type": "Scalar", + "value": 0.9999999999 + } + ], + "name": "minimum" + }, + { + "type": "Scalar", + "value": 1e-10 + } + ], + "name": "maximum" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "+" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "+" + } + ], + "name": "-" + } + ] + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "NotEqualHeaviside", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + } + ], + "name": "<" + }, + { + "type": "NotEqualHeaviside", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Scalar", + "value": 0.0 + } + ], + "name": "<" + } + ], + "name": "+" + }, + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "EqualHeaviside", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + } + ], + "name": "<=" + }, + { + "type": "EqualHeaviside", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Time [s]": { + "type": "Time" + } + }, + "diff_variable": null, + "name": "Current function [A]" + }, + { + "type": "Scalar", + "value": 0.0 + } + ], + "name": "<=" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "/" + }, + "Total lithium in negative electrode [mol]": { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + "LAM_ne [%]": { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 100.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 100.0 + }, + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.0002777777777777778 + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.0002777777777777778 + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "*" + } + ], + "name": "-" + }, + "Loss of active material in negative electrode [%]": { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 100.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 100.0 + }, + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.0002777777777777778 + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.0002777777777777778 + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "*" + } + ], + "name": "-" + }, + "Total lithium in positive electrode [mol]": { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + "LAM_pe [%]": { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 100.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 100.0 + }, + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.0002777777777777778 + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.0002777777777777778 + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "*" + } + ], + "name": "-" + }, + "Loss of active material in positive electrode [%]": { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 100.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 100.0 + }, + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.0002777777777777778 + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.0002777777777777778 + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + } + ], + "name": "/" + } + ], + "name": "*" + } + ], + "name": "-" + }, + "LLI [%]": { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 100.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 100.0 + }, + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "RAverage", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Radial distance (r) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "negative electrode" + ], + "tertiary": [ + "current collector" + ], + "quaternary": [] + }, + "children": [], + "name": "r_n" + }, + "Through-cell distance (x) [m]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + ], + "broadcast_domain": [ + "negative particle" + ] + } + }, + "diff_variable": null, + "name": "Initial concentration in negative electrode [mol.m-3]" + } + ], + "name": "r-average" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "RAverage", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Radial distance (r) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "positive electrode" + ], + "tertiary": [ + "current collector" + ], + "quaternary": [] + }, + "children": [], + "name": "r_p" + }, + "Through-cell distance (x) [m]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + ], + "broadcast_domain": [ + "positive particle" + ] + } + }, + "diff_variable": null, + "name": "Initial concentration in positive electrode [mol.m-3]" + } + ], + "name": "r-average" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "*" + } + ], + "name": "-" + }, + "Loss of lithium inventory [%]": { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 100.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 100.0 + }, + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "RAverage", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Radial distance (r) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "negative electrode" + ], + "tertiary": [ + "current collector" + ], + "quaternary": [] + }, + "children": [], + "name": "r_n" + }, + "Through-cell distance (x) [m]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + ], + "broadcast_domain": [ + "negative particle" + ] + } + }, + "diff_variable": null, + "name": "Initial concentration in negative electrode [mol.m-3]" + } + ], + "name": "r-average" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "RAverage", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Radial distance (r) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "positive electrode" + ], + "tertiary": [ + "current collector" + ], + "quaternary": [] + }, + "children": [], + "name": "r_p" + }, + "Through-cell distance (x) [m]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + ], + "broadcast_domain": [ + "positive particle" + ] + } + }, + "diff_variable": null, + "name": "Initial concentration in positive electrode [mol.m-3]" + } + ], + "name": "r-average" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "*" + } + ], + "name": "-" + }, + "Loss of lithium inventory, including electrolyte [%]": { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 100.0 + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 100.0 + }, + { + "type": "Division", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "Parameter", + "name": "Separator thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode porosity" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Separator thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_s" + } + }, + "diff_variable": null, + "name": "Separator porosity" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode porosity" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "Parameter", + "name": "Separator thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "yz-average" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "RAverage", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Radial distance (r) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "negative electrode" + ], + "tertiary": [ + "current collector" + ], + "quaternary": [] + }, + "children": [], + "name": "r_n" + }, + "Through-cell distance (x) [m]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + ], + "broadcast_domain": [ + "negative particle" + ] + } + }, + "diff_variable": null, + "name": "Initial concentration in negative electrode [mol.m-3]" + } + ], + "name": "r-average" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "RAverage", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Radial distance (r) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "positive electrode" + ], + "tertiary": [ + "current collector" + ], + "quaternary": [] + }, + "children": [], + "name": "r_p" + }, + "Through-cell distance (x) [m]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + ], + "broadcast_domain": [ + "positive particle" + ] + } + }, + "diff_variable": null, + "name": "Initial concentration in positive electrode [mol.m-3]" + } + ], + "name": "r-average" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode porosity" + } + ], + "name": "x-average" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Separator thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_s" + } + }, + "diff_variable": null, + "name": "Separator porosity" + } + ], + "name": "x-average" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode porosity" + } + ], + "name": "x-average" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "Parameter", + "name": "Separator thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "Parameter", + "name": "Separator thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "+" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "*" + } + ], + "name": "-" + }, + "Total lithium [mol]": { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "Parameter", + "name": "Separator thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode porosity" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Separator thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_s" + } + }, + "diff_variable": null, + "name": "Separator porosity" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode porosity" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "Parameter", + "name": "Separator thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "yz-average" + } + ], + "name": "*" + } + ], + "name": "+" + }, + "Total lithium in particles [mol]": { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + } + ], + "name": "+" + }, + "Total lithium capacity [A.h]": { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.0002777777777777778 + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "Parameter", + "name": "Separator thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode porosity" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Separator thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_s" + } + }, + "diff_variable": null, + "name": "Separator porosity" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode porosity" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "Parameter", + "name": "Separator thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "yz-average" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + "Total lithium capacity in particles [A.h]": { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Scalar", + "value": 0.0002777777777777778 + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Faraday constant [C.mol-1]" + } + ], + "name": "*" + } + ], + "name": "*" + }, + "Total lithium lost [mol]": { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "RAverage", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Radial distance (r) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "negative electrode" + ], + "tertiary": [ + "current collector" + ], + "quaternary": [] + }, + "children": [], + "name": "r_n" + }, + "Through-cell distance (x) [m]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + ], + "broadcast_domain": [ + "negative particle" + ] + } + }, + "diff_variable": null, + "name": "Initial concentration in negative electrode [mol.m-3]" + } + ], + "name": "r-average" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "RAverage", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Radial distance (r) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "positive electrode" + ], + "tertiary": [ + "current collector" + ], + "quaternary": [] + }, + "children": [], + "name": "r_p" + }, + "Through-cell distance (x) [m]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + ], + "broadcast_domain": [ + "positive particle" + ] + } + }, + "diff_variable": null, + "name": "Initial concentration in positive electrode [mol.m-3]" + } + ], + "name": "r-average" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode porosity" + } + ], + "name": "x-average" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Separator thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_s" + } + }, + "diff_variable": null, + "name": "Separator porosity" + } + ], + "name": "x-average" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode porosity" + } + ], + "name": "x-average" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "Parameter", + "name": "Separator thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "Parameter", + "name": "Separator thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "+" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "Parameter", + "name": "Separator thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode porosity" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Separator thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_s" + } + }, + "diff_variable": null, + "name": "Separator porosity" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode porosity" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "Parameter", + "name": "Separator thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "yz-average" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "-" + }, + "Total lithium lost from particles [mol]": { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "RAverage", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Radial distance (r) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "negative electrode" + ], + "tertiary": [ + "current collector" + ], + "quaternary": [] + }, + "children": [], + "name": "r_n" + }, + "Through-cell distance (x) [m]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + ], + "broadcast_domain": [ + "negative particle" + ] + } + }, + "diff_variable": null, + "name": "Initial concentration in negative electrode [mol.m-3]" + } + ], + "name": "r-average" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "RAverage", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Radial distance (r) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "positive electrode" + ], + "tertiary": [ + "current collector" + ], + "quaternary": [] + }, + "children": [], + "name": "r_p" + }, + "Through-cell distance (x) [m]": { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + ], + "broadcast_domain": [ + "positive particle" + ] + } + }, + "diff_variable": null, + "name": "Initial concentration in positive electrode [mol.m-3]" + } + ], + "name": "r-average" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged negative particle concentration [mol.m-3]", + "domains": { + "primary": [ + "negative particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in negative electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "negative electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode active material volume fraction" + }, + { + "type": "PrimaryBroadcast", + "children": [ + { + "type": "RAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Variable", + "name": "X-averaged positive particle concentration [mol.m-3]", + "domains": { + "primary": [ + "positive particle" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "bounds": [ + { + "type": "Scalar", + "value": 0.0 + }, + { + "type": "Parameter", + "name": "Maximum concentration in positive electrode [mol.m-3]" + } + ] + } + ], + "name": "r-average" + } + ], + "broadcast_domain": [ + "positive electrode" + ] + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + } + ], + "name": "+" + } + ], + "name": "-" + }, + "Total lithium lost from electrolyte [mol]": { + "type": "Subtraction", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode porosity" + } + ], + "name": "x-average" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Separator thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_s" + } + }, + "diff_variable": null, + "name": "Separator porosity" + } + ], + "name": "x-average" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode porosity" + } + ], + "name": "x-average" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "Parameter", + "name": "Separator thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "yz-average" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + }, + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "Parameter", + "name": "Separator thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "+" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "Parameter", + "name": "Separator thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Electrode width [m]" + }, + { + "type": "Parameter", + "name": "Electrode height [m]" + } + ], + "name": "*" + }, + { + "type": "Parameter", + "name": "Number of electrodes connected in parallel to make a cell" + } + ], + "name": "*" + } + ], + "name": "*" + }, + { + "type": "YZAverage", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Division", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "negative electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_n" + } + }, + "diff_variable": null, + "name": "Negative electrode porosity" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "*" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Separator thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "separator" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_s" + } + }, + "diff_variable": null, + "name": "Separator porosity" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Multiplication", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + }, + { + "type": "XAverage", + "domains": { + "primary": [ + "current collector" + ], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Multiplication", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "FunctionParameter", + "inputs": { + "Through-cell distance (x) [m]": { + "type": "SpatialVariable", + "domains": { + "primary": [ + "positive electrode" + ], + "secondary": [ + "current collector" + ], + "tertiary": [], + "quaternary": [] + }, + "children": [], + "name": "x_p" + } + }, + "diff_variable": null, + "name": "Positive electrode porosity" + }, + { + "type": "Parameter", + "name": "Initial concentration in electrolyte [mol.m-3]" + } + ], + "name": "*" + } + ], + "name": "x-average" + } + ], + "name": "*" + } + ], + "name": "+" + }, + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Addition", + "domains": { + "primary": [], + "secondary": [], + "tertiary": [], + "quaternary": [] + }, + "children": [ + { + "type": "Parameter", + "name": "Negative electrode thickness [m]" + }, + { + "type": "Parameter", + "name": "Separator thickness [m]" + } + ], + "name": "+" + }, + { + "type": "Parameter", + "name": "Positive electrode thickness [m]" + } + ], + "name": "+" + } + ], + "name": "/" + } + ], + "name": "yz-average" + } + ], + "name": "*" + } + ], + "name": "-" + }, + "Total lithium lost to side reactions [mol]": { + "type": "Scalar", + "value": 0.0 + }, + "Total capacity lost to side reactions [A.h]": { + "type": "Scalar", + "value": 0.0 + } + } + } +} diff --git a/tests/unit/test_serialisation/test_serialisation.py b/tests/unit/test_serialisation/test_serialisation.py index d6ddac10e4..f7c3886825 100644 --- a/tests/unit/test_serialisation/test_serialisation.py +++ b/tests/unit/test_serialisation/test_serialisation.py @@ -877,9 +877,13 @@ def test_function_parameter_with_diff_variable_serialisation(self): func_param = pybamm.FunctionParameter("my_func", {"x": x}, diff_var) json_dict = convert_symbol_to_json(func_param) - assert "diff_variable" in json_dict - assert json_dict["diff_variable"]["type"] == "Variable" - assert json_dict["diff_variable"]["name"] == "r" + # Check for abbreviated or full key + dv_key = "dv" if "dv" in json_dict else "diff_variable" + assert dv_key in json_dict + dv_data = json_dict[dv_key] + # Check for abbreviated or full type/name keys + assert dv_data.get("t") == "Variable" or dv_data.get("type") == "Variable" + assert dv_data.get("n") == "r" or dv_data.get("name") == "r" expr2 = convert_symbol_from_json(json_dict) assert isinstance(expr2, pybamm.FunctionParameter) @@ -892,18 +896,35 @@ def test_indefinite_integral_serialisation(self): ind_int = pybamm.IndefiniteIntegral(x, x) json_dict = convert_symbol_to_json(ind_int) - assert json_dict["type"] == "IndefiniteIntegral" + # Check abbreviated or full keys + assert ( + json_dict.get("t") == "Int" or json_dict.get("type") == "IndefiniteIntegral" + ) + children_key = "c" if "c" in json_dict else "children" assert ( - isinstance(json_dict["children"], list) and len(json_dict["children"]) == 1 + isinstance(json_dict[children_key], list) + and len(json_dict[children_key]) == 1 ) - child_json = json_dict["children"][0] - assert child_json["type"] == "SpatialVariable" - assert child_json["name"] == "x" + child_json = json_dict[children_key][0] + assert ( + child_json.get("t") == "SpatialVariable" + or child_json.get("type") == "SpatialVariable" + ) + assert child_json.get("n") == "x" or child_json.get("name") == "x" - int_var_json = json_dict["integration_variable"] - assert int_var_json["type"] == "SpatialVariable" - assert int_var_json["name"] == "x" + iv_key = "iv" if "iv" in json_dict else "integration_variable" + int_var_json = json_dict[iv_key] + # integration_variable might be a reference to the child + if "r" in int_var_json or "py/ref" in int_var_json: + # It's a reference - this is valid, deserialization will handle it + pass + else: + assert ( + int_var_json.get("t") == "SpatialVariable" + or int_var_json.get("type") == "SpatialVariable" + ) + assert int_var_json.get("n") == "x" or int_var_json.get("name") == "x" expr2 = convert_symbol_from_json(json_dict) assert isinstance(expr2, pybamm.IndefiniteIntegral) @@ -1026,6 +1047,63 @@ def test_model_has_correct_schema_version(self, tmp_path): assert hasattr(loaded_model, "schema_version") assert loaded_model.schema_version == SUPPORTED_SCHEMA_VERSION + def test_deserialize_old_format_v1_0(self): + """Test that models serialized with schema version 1.0 (old format) + can be deserialized with the current code (backward compatibility). + """ + # Path to stored old format model (serialized on develop branch) + test_dir = Path(__file__).parent + old_format_file = test_dir / "old_format_model_v1.0.json" + + if not old_format_file.exists(): + pytest.skip( + f"Old format test file not found: {old_format_file}. " + "Run test_backward_compat.py to generate it." + ) + + # Load the old format model + loaded_model = Serialise.load_custom_model(str(old_format_file)) + + # Verify it loaded correctly + assert loaded_model.name == "Single Particle Model" + assert len(loaded_model.rhs) > 0 + assert len(loaded_model.events) > 0 + assert hasattr(loaded_model, "schema_version") + # Old format models should have schema_version 1.0 + assert loaded_model.schema_version == "1.0" + + # Verify we can solve it with an experiment (termination at 2.5V) + param = pybamm.ParameterValues("Chen2020") + + # Create experiment: 1C discharge to 2.5V + experiment = pybamm.Experiment( + [ + pybamm.step.current( + value=param["Nominal cell capacity [A.h]"] * 1.0, # 1C + duration=3600, # 1 hour max + termination="2.5 V", # Stop at 2.5V + ) + ] + ) + + sim = pybamm.Simulation( + loaded_model, parameter_values=param, experiment=experiment + ) + solution = sim.solve() + + # Experiments return a list of solutions (one per step) + if isinstance(solution, list): + solution = solution[0] # Get the first (and only) step + + assert solution is not None + assert len(solution.t) > 0 + + # Verify final voltage is 2.5V (within tolerance) + final_voltage = solution["Voltage [V]"].data[-1] + assert abs(final_voltage - 2.5) < 0.01, ( + f"Final voltage should be 2.5V, got {final_voltage:.3f}V" + ) + def test_load_invalid_json(self): invalid_json = "{ invalid json"