Stochastic curvature flows: asymptotic derivation, level set formulation and numerical experiments

Abstract

We study the effects of random fluctuations included in microscopic models for phase transitions on macroscopic interface flows. We first derive asymptotically a stochastic mean curvature evolution law from the stochastic Ginzburg-Landau model and develop a corresponding level set formulation. Secondly, we demonstrate numerically, using stochastic Ginzburg-Landau and Ising algorithms, that microscopic random perturbations resolve geometric and numerical instabilities in the corresponding deterministic flow.