MULTISCALE THEORY OF FLUCTUATING INTERFACES: RENORMALIZATION AND SELF-ORGANIZATION

Abstract

A general procedure is presented for the multiscale analysis of atomistic models of fluctuating interfaces driven by the deposition of new material. Beginning with a lattice Langevin formulation of kinetic Monte Carlo simulations, we derive stochastic partial differential equations by regularizing the atomistic transition rules. Subsequent coarse-graining is accomplished by calculating renormalization-group trajectories from initial conditions determined by the regularized equations. We apply this methodology to the Wolf–Villain model of relaxation upon deposition and to a model for the self-organization of heteroepitaxial nanostructures.