TITLE:
Numerical Simulation of a Domain-Tessellation Pattern on a Spherical Surface Using a Phase Field Model
AUTHORS:
Takuya Uehara
KEYWORDS:
Pattern Formation, Domain Tessellation, Computer Simulation, Phase Field Method
JOURNAL NAME:
Open Journal of Modelling and Simulation,
Vol.4 No.2,
April
19,
2016
ABSTRACT: A numerical simulation scheme is proposed to analyze domain tessellation and pattern formation on a spherical surface using the phase-field method. A multi-phase-field model is adopted to represent domain growth, and the finite-difference method (FDM) is used for numerical integration. The lattice points for the FDM are distributed regularly on a spherical surface so that a mostly regular triangular domain division is realized. First, a conventional diffusion process is simulated using this lattice to confirm its validity. The multi-phase-field equation is then applied, and pattern formation processes under various initial conditions are simulated. Unlike pattern formation on a flat plane, where the regular hexagonal domains are always stable, certain different patterns are generated. Specifically, characteristic stable patterns are obtained when the number of domains, n, is 6, 8, or 12; for instance, a regular pentagonal domain division pattern is generated for n = 12, which corresponds to a regular dodecahedron.