A numerical simulation scheme is proposed to analyze domain tessellation and pattern formation\non a spherical surface using the phase-field method. A multi-phase-field model is adopted to\nrepresent domain growth, and the finite-difference method (FDM) is used for numerical integration.\nThe lattice points for the FDM are distributed regularly on a spherical surface so that a mostly\nregular triangular domain division is realized. First, a conventional diffusion process is simulated\nusing this lattice to confirm its validity. The multi-phase-field equation is then applied, and\npattern formation processes under various initial conditions are simulated. Unlike pattern formation\non a flat plane, where the regular hexagonal domains are always stable, certain different patterns\nare generated. Specifically, characteristic stable patterns are obtained when the number of\ndomains, n, is 6, 8, or 12; for instance, a regular pentagonal domain division pattern is generated\nfor n = 12, which corresponds to a regular dodecahedron.
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