The role of multiple microscopic mechanisms in cluster interface evolution

Abstract

In this paper we discuss mesoscopic models describing pattern formation mechanisms for a prototypical model of surface processes that involves multiple microscopic mechanisms. We focus on a mean field partial differential equation, which contains qualitatively microscopic information on particle–particle interactions and multiple particle dynamics, and we rigorously derive the macroscopic cluster evolution laws and transport structure. We show that the motion by mean curvature is given by V = μ σ κ , where k is the mean curvature, σ is the surface tension and μ is an effective mobility that depends on the presence of the multiple mechanisms and speeds up the cluster evolution. This is in contrast with the Allen–Cahn equation where V = κ .