Stochastic Integration of Epitaxial Systems
Abstract
Stochastic integration can be used to give a more mathematical framework to the kinetic Monte Carlo (KMC) method. This method applies to Markovian systems that are governed by lattice transition rules. We first express these rules in terms of a master equation. From this we use the van Kampen expansion to obtain a Fokker-Planck equation and, by invoking the Langevin interpretation, integrate the model stochastically. We apply this procedure to three basic models: the Family model, the Wolf-Villain model, and the surface diffusion model. In all cases, the results obtained from the integration agree with those from simulations. Although, stochastic integration is more costly computationally than KMC simulations, it puts a class of algorithms used in such simulations on a firm mathematical basis and provides a means for further analysis.
- Publication:
-
APS March Meeting Abstracts
- Pub Date:
- March 2003
- Bibcode:
- 2003APS..MARW18009C