A kinetic Monte Carlo model for surface diffusion on a 2D lattice was proposed. An equivalent continuum cellular automaton (CA) model was derived from this. These models were shown to produce similar results at high temperatures. A hybrid KMC-CA model was derived which consistently permitted material to transfer between a deterministic CA model and a stochastic kinetic Monte Carlo model concurrently embedded within it. The quality of the model was demonstrated by simulating flattening of a sinusoidal surface profile and the evolution of an elliptical body into a circular one.

Concurrent Multiscale Kinetic Monte Carlo-Continuum Models for the Evolution of Solids via Diffusion. S.P.A.Gill, P.E.Spencer: Solid State Phenomena, 2007, 129, 19-24