On microscopic derivation of a continuum mean-curvature flow
We derive a continuum mean-curvature flow as a scaling limit of a class of zero-range + Glauber interacting particle systems. The zero-range part moves particles while preserving particle numbers, and the Glauber part allows birth and death of particles, while favoring two levels of particle density. When the two parts are simultaneously seen in certain (different) time-scales, and the Glauber part is `bi-stable', a mean-curvature interface flow, incorporating a homogenized `surface tension' reflecting microscopic rates, between the two levels of particle density, can be captured as a limit of the mass empirical density. This is work with Perla El Kettani, Tadahisa Funaki, Danielle Hilhorst, and Hyunjoon Park.