Curation of applications in the main library and others

[landinjm]

Now that #708 has made PRISMS-PF a library we are no longer constrained to having our applications in a folder with a preset path. This opens up many opportunities. For examples, users can now create and track their app with source control (excluding the main library).

This also allows us to showcase contributed applications in another repository that may not meet the standard for the applications in this main library. Furthermore, we can curate the applications in this library to be more pedagogical and methodical in the ways they showcase our features and phase-field.

The goal of this discussion is to discuss which applications we want in the main library.

[landinjm]

Currently in the main library we have these applications:

Application	Physics	Numerics	Main-library ✅ or ❌	Notes
allen_cahn_explicit	AC	FE	✅
alloy_solidification	AC, DI	FE, V-AMR	✅
cahn_hilliard_explicit	CH	FE, V-AMR	✅
coupled_allen_cahn_cahn_hilliard	AC, CH	FE, V-AMR	✅
eshelby_inclusion	EL	LS, GMG	✅
nucleation	?	?	✅
precipitate_evolution	AC, CM, MP	?	✅
spinodal_decomposition	CH	?	✅
MgNd_precipitate_single_Bpp	?	?	✅
CHAC_anisotropy	AC, DI, AN	FE	✅
CHAC_anisotropy_regularized	AC, DI, ANR	FE	✅
CHAC_performance_test	?	?	❌	Performance test applications should not be in the pedagogical part of the library. If we want to consider show scaling performance a small application will do the trick since most people don't have an HPC cluster to freely use.
allen_cahn_conserved	AC	FE, INT	✅
alloy_solidification_uniform	?	?	✅
anisotropy_facet	AC, DI, ANR	FE	✅
corrosion	?	?	✅
corrosion_microgalvanic	?	?	✅
dendritic_solidification	?	?	✅
fickian_diffusion	DI	FE	✅
grain_growth	?	?	✅
grain_growth_dream3D	?	?	✅
mechanics	EL	LS	✅
nucleation_preferential	?	?	✅

NOTE: All CHiMaD applications will be in their own repository

Key for the abbreviations
Numerical
V-AMR - Value-based adaptive mesh refinement
G-AMG - Gradient-based adaptive mesh refinement
LS - Linear solve
NS - Nonlinear solve
GMG - Geometric multigrid
TBC - time-dependent BCs
TI - time independent equation
FE - Forward Euler
BE - Backward Euler
HOE - higher order explicit
HOI - higher order implicit

Physics-specific features
NUC - Nucleation
INT - Integration

Physics attributes
AC - Allen-Cahn Dynamics
CH - Cahn-Hilliard Dynamics
DI - diffusion (no gradient term in concentration)
MP - multi-phase (multi phase field or multi order parameter)
MC - multi-component
AN - anisotropy as function of interface normal
ANR - strongly anisotropic interfacial energy with higher-order regularization
SBM - smoothed boundary method (static)
SBE - smoothed boundary method with evolution
POI - Poisson-type equation (e.g., electrostatics)
EL - elasticity
EC - electrochemistry
CM - chemomechanics (includes elasticity and diffusion)