Concurrent Multiscale Kinetic Monte Carlo-Continuum Models for the Evolution of Solids via Diffusion
A kinetic Monte Carlo (KMC) model for surface diffusion on a 2D lattice is proposed. An equivalent continuum cellular automaton (CA) model is derived from this. These models are shown to produce similar results at high temperatures. A hybrid KMC-CA model is derived which consistently allows material to transfer between a deterministic CA model and a stochastic KMC model concurrently embedded within it. The quality of the model is demonstrated by simulating the flattening of a sinusoidal surface profile and the evolution of an elliptical body into a circular one.
R. Kozubski, G.E. Murch and P. Zięba
S. P.A. Gill and P. E. Spencer, "Concurrent Multiscale Kinetic Monte Carlo-Continuum Models for the Evolution of Solids via Diffusion ", Solid State Phenomena, Vol. 129, pp. 19-24, 2007