Motion by mean curvature from Glauber-Kawasaki dynamics with speed change

TL;DR

This paper derives a mean-curvature flow as a hydrodynamic limit of Glauber-Kawasaki particle dynamics with speed change, extending previous results to more general local interactions.

Contribution

It extends existing hydrodynamic limit results to include Glauber-Kawasaki dynamics with general local particle interactions, introducing a new Boltzmann-Gibbs principle.

Findings

Mean-curvature interface flow emerges under the scaling.

Homogenized surface tension-mobility parameter reflects microscopic rates.

Extension beyond nearest-neighbor interactions in hydrodynamic limits.

Abstract

We derive a continuum mean-curvature flow as a certain hydrodynamic scaling limit of Glauber-Kawasaki dynamics with speed change. The Kawasaki part describes the movement of particles through particle interactions. It is speeded up in a diffusive space-time scaling. The Glauber part governs the creation and annihilation of particles. The Glauber part is set to favor two levels of particle density. It is also speeded up in time, but at a lesser rate than the Kawasaki part. Under this scaling, a mean-curvature interface flow emerges, with a homogenized `surface tension-mobility' parameter reflecting microscopic rates. The interface separates the two levels of particle density. Similar hydrodynamic limits have been derived in two recent papers; one where the Kawasaki part describes simple nearest neighbor interactions, and one where the Kawasaki part is replaced by a zero-range process. We extend the main results of these two papers beyond nearest-neighbor interactions. The main novelty of our proof is the derivation of a `Boltzmann-Gibbs' principle which covers a class of local particle interactions.