Coarse-graining the computations of surface reactions: Nonlinear dynamics from atomistic simulators

We review and discuss the use of equation-free computation in extracting coarse-grained, nonlinear dynamics information from atomistic (lattice-gas) models of surface reactions. The approach is based on circumventing the explicit derivation of macroscopic equations for the system statistics (e.g., average coverage). Short bursts of appropriately initialized computational experimentation with the lattice-gas simulator are designed "on demand" and processed in the spirit of the coarse timestepper introduced in Theodoropoulos et al. (2000) (K. Theodoropoulos, Y.-H. Qian, I.G. Kevrekidis, Proc. Natl. Acad. Sci. USA 97 (2000) 9840). The information derived from these computational experiments, processed through traditional, continuum numerical methods is used to solve the macroscopic equations without ever deriving them in closed form. The approach is illustrated through two computational examples: the CO oxidation reaction, and the NO + CO/Pt(1 0 0) reaction.