C. A. Haselwandter, D. D. Vvedensky:

From Atomistic to Continuum Descriptions of Morphological Evolution

Lattice Langevin equations are derived from the rules of lattice growth models. These provide an exact mathematical description that is suitable for direct analysis, such as the passage to the continuum limit, as well as a computational alternative to kinetic Monte Carlo simulations. This approach is applied to ballistic deposition and a model for conditional deposition, both of which yield the Kardar-Parisi-Zhang equation in the continuum limit, and a model of strain relaxation during heteroepitaxy.

 Bibliographical note: Published in Modeling of Morphological Evolution at Surfaces and Interface, edited by J. Evans, C. Orme, M. Asta, and Z. Zhang, Materials Research Society Symposium Proceedings, Vol. 859E (Materials Research Society, Pittsburgh, PA, 2005), pp. JJ8.8.1-JJ8.8.6.