@@ -1949,9 +1949,9 @@ \subsubsection{Preparing the water reservoir}
19491949\begin {figure }
19501950\centering
19511951\includegraphics [width=\linewidth ]{PEG-density}
1952- \caption {a) Temperature ( $ T$ ) of the water reservoir from
1953- \hyperref [all-atom-label]{Tutorial 3} as a function of the ( $ t$ ) . The horizontal dashed line is
1954- the target temperature of 300 \, K. b) Evolution of the system density ( $ \rho $ ) with $ t$ .}
1952+ \caption {a) Temperature, $ T$ , of the water reservoir from \hyperref [all-atom-label]{Tutorial 3}
1953+ as a function of the time, $ t$ . The horizontal dashed line is the target temperature of 300 \, K.
1954+ b) Evolution of the system density, $ \rho $ , with $ t$ .}
19551955\label {fig:PEG-density }
19561956\end {figure }
19571957
@@ -2678,9 +2678,9 @@ \subsubsection{System preparation}
26782678\begin {figure }
26792679\centering
26802680\includegraphics [width=\linewidth ]{NANOSHEAR-equilibration}
2681- \caption {a)~Pressure $ p$ of the nanosheared electrolyte system
2681+ \caption {a)~Pressure, $ p$ , of the nanosheared electrolyte system
26822682simulated in \hyperref [sheared-confined-label]{Tutorial 4} as a function of the
2683- time $ t$ . b)~Distance between the walls $ \Delta z$ as a function of time $ t$ .}
2683+ time, $ t$ . b)~Distance between the walls, $ \Delta z$ , as a function of $ t$ .}
26842684\label {fig:NANOSHEAR-equilibration }
26852685\end {figure }
26862686
@@ -2963,10 +2963,10 @@ \subsubsection{Prepare and relax}
29632963\begin {figure }
29642964\centering
29652965\includegraphics [width=\linewidth ]{SIO-charge}
2966- \caption {a) Average charge per atom of the silicon $ q_\text {Si}$ atoms as
2967- a function of time $ t$ during equilibration of the $ \text {SiO}_2 $ system
2966+ \caption {a) Average charge per atom of the silicon, $ q_\text {Si}$ , atoms as
2967+ a function of time, $ t$ , during equilibration of the $ \text {SiO}_2 $ system
29682968from \hyperref [reactive-silicon-dioxide-label]{Tutorial 5}. b) Volume of the
2969- system $ V$ as a function of time $ t$ .}
2969+ system, $ V$ , as a function of $ t$ .}
29702970\label {fig:SIO-charge }
29712971\end {figure }
29722972
@@ -2985,7 +2985,7 @@ \subsubsection{Prepare and relax}
29852985\caption {a) Probability distributions of charge of silicon (positive, blue) and oxygen
29862986(negative, orange) atoms during the equilibration of the $ \text {SiO}_2 $ system
29872987from \hyperref [reactive-silicon-dioxide-label]{Tutorial 5}. b) Same probability distributions
2988- after the deformation.}
2988+ as in panel (a) after the deformation.}
29892989\label {fig:SIO-distribution }
29902990\end {figure }
29912991
@@ -3037,10 +3037,10 @@ \subsubsection{Deform the structure}
30373037
30383038\begin {figure }
30393039\includegraphics [width=\linewidth ]{SIO-deformed-charge}
3040- \caption {a) Average charge per atom of the silicon $ q_\text {Si}$ atoms as
3041- a function of time $ t$ during deformation of the $ \text {SiO}_2 $ system
3042- from \hyperref [reactive-silicon-dioxide-label]{Tutorial 5}. b) Temperature $ T$ of the
3043- system as a function of time $ t$ .}
3040+ \caption {a) Average charge per atom of the silicon, $ q_\text {Si}$ , atoms as
3041+ a function of time, $ t$ , during deformation of the $ \text {SiO}_2 $ system
3042+ from \hyperref [reactive-silicon-dioxide-label]{Tutorial 5}. b) Temperature, $ T$ , of the
3043+ system as a function of $ t$ .}
30443044\label {fig:SIO-deformed-charge }
30453045\end {figure }
30463046
@@ -3323,9 +3323,9 @@ \subsubsection{Generation of the silica block}
33233323\begin {figure }
33243324\centering
33253325\includegraphics [width=\linewidth ]{GCMC-dimension}
3326- \caption {a) Temperature $ T$ as a function of time $ t$ during the annealing
3326+ \caption {a) Temperature, $ T$ , as a function of time, $ t$ , during the annealing
33273327of the silica system from \hyperref [gcmc-silica-label]{Tutorial 6}.
3328- b) System density $ \rho $ during the annealing process. The vertical dashed lines
3328+ b) System density, $ \rho $ , during the annealing process. The vertical dashed lines
33293329mark the transition between the different phases of the simulation.}
33303330\label {fig:GCMC-dimension }
33313331\end {figure }
@@ -3849,8 +3849,8 @@ \subsubsection{Method 1: Free sampling}
38493849\begin {figure }
38503850\centering
38513851\includegraphics [width=\linewidth ]{US-density}
3852- \caption {a) Fluid density $ \rho $ along the $ x$ direction.
3853- b) Potential $ U$ as a function of $ x$ measured using free sampling (blue disks)
3852+ \caption {a) Fluid density, $ \rho $ , along the $ x$ direction.
3853+ b) Potential, $ U$ , as a function of $ x$ measured using free sampling (blue disks)
38543854compared to the imposed potential given in Eq.~\eqref {eq:U } (dark line).
38553855Here, $ U_0 = 0.36 ~\text {kcal/mol}$ , $ \delta = 1.0 ~\text {\AA {}}$ , $ x_0 = 10 ~\text {\AA {}}$ ,
38563856and the measured reference density in the reservoir is $ \rho _\text {bulk} = 0.0009 ~\text {\AA {}}^{-3}$ .} % SG: check units of rho bulk
@@ -4031,7 +4031,7 @@ \subsubsection{Method 2: Umbrella sampling}
40314031\begin {figure }
40324032\centering
40334033\includegraphics [width=\linewidth ]{US-free-energy}
4034- \caption {The potential $ U$ as a function of $ x$ , measured using umbrella
4034+ \caption {The potential, $ U$ , as a function of $ x$ , measured using umbrella
40354035sampling during \hyperref [umbrella-sampling-label]{Tutorial 7} (blue disks),
40364036is compared to the imposed potential given in Eq.~\eqref {eq:U }
40374037(dark line). Parameters are $ U_0 = 2.38 ~\text {kcal/mol}$ , $ \delta = 1.0 ~\text {\AA {}}$ ,
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