Multiscale Problems in Three Applications - Abstract

Stinner, Björn

Systems of Allen-Cahn equations with volume constraints

Multi-phase systems are considered where the phase interfaces move according to a curvature flow and some of the phases are subject to volume constraints. An approximation of the free boundary problem by a phase field model has been developed resulting in parabolic differential equations with nonlocal terms due to the constraints. Several ideas will be presented to numerically solve the nonlocal equations, and simulations have been performed to study local minima of the system energy. Applications concern Wulff forms, bubble clusters, and tessellations problems.