Hybrid-PFC: coupling the phase-field crystal model and its amplitude-equation formulation

Hybrid-phase-field crystal simulationsOpenly available Matlab simulation files used to produce the phase-field crystal, amplitude phase-field crystal, hybrid-phase field crystal results.Files are named by the corresponding figures. Simulations can be started by runnning the Figure*.m files.Figure1_GBPFC results for GB formation with fft or conv algorithm (square symmetry)Figure2_solidificationPFC results for solidification of a random initial field under PBC or DBC (triangular symmetry)Figure3_dendritePFC/APFC results for solidification of an initial crystal seed (triangular symmetry)Figure4_Figure5_pfc_apfc_hybridHybrid-PFC/PFC/APFC results for solidification of two initial seeds with GB between (triangular symmetry)Figure7_pfc_apfc_hybrid_GBenergyHybrid-PFC/PFC/APFC results for GB energy calculation (triangular symmetry) see also the Solution/Figure7_pfc_apfc_hybrid_GBenergy/ zenodo directory for solutionsOther simulationsThe remaining simulations for the Appendix can be obtained by varying the respective parameterscyconv*.m files within simulation/cyconv*.m files represent 2D implementations of non-fourier cyclic convolutions (non-standard implementations without fft, perriodic BC in x and/or y direction can be combined with homog. DBC in x and/or y direction). Decomposed arguments are accepted (see the respective documentation).svdlinImConv*.mat within simulation/Singular value decompositions (SVDs) of discretized operator R are given up to runcation m=36 according to the appendix, provided SVDs are only valid for default spatial/temporal discretization (e.g. changing the time step size changes R and therefore its SVD).energy_calculation* within simulation/Post/GB energy calculation according to Figure 7