A MultiPhase Field Concept: Numerical Simulations of Moving Phase Boundaries and Multiple Junctions

Abstract

We present numerical simulations which support the formal asymptotic analysis relating a multiorder parameter Allen--Cahn system to a multiphase interface problem with curvature-dependent evolution of the interfaces and angle conditions at triple junctions. Within the gradient energy of the Allen--Cahn system, the normal to an interface between phases i and j is modeled by the irreducible representations $(u_i\nabla u_j - u_j\nabla u_i)/{|u_i\nabla u_j - u_j\nabla u_i|}$, where ui and uj are the ith and jth components of the vectorial order parameter $\bu\in \rz^N$.In the vectorial case, the dependence of the limiting surface tensions and mobilities on the bulk potentials of the Allen--Cahn system is not given explicitly but in terms of all the N components of the planar stationary wave solutions. One of the issues of this paper is to find bulk potentials which allow a rather easy access to the resulting surface tensions and mobilities. We compare numerical computations for planar and circular phase bound...