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

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.