Stochastic Equations for Thin Film Morphology

Abstract

Many physical phenomena can be modeled as particles on a lattice that interact according to a set of prescribed rules. Such systems are called “lattice gases”. Examples include the non-equilibrium statistical mechanics of driven systems [1, 2], cellular automata [3, 4], and interface fluctuations of growing surfaces [5, 6]. The dynamics of lattice gases are generated by transition rates for site occupancies that are determined by the occupancies of neighboring sites at the preceding time step. This provides the basis for a multi-scale approach to non-equilibrium systems in that atomistic processes are expressed as transition rates in a master equation, while a partial differential equation, derived from this master equation, embodies the macroscopic evolution of the coarse-grained system.