B3: Stochastic modelling and deterministic limit of catalytic surface processes

Three levels of modelling, microscopic, mesoscopic and macroscopic are dis-cussed for the CO oxidation on low-index platinum single crystal surfaces. The introduced models on the microscopic and mesoscopic level are stochas-tic while the model on the macroscopic level is deterministic. It can be derived rigorously for low-pressure conditions from the microscopic model, which is characterized as a moderately interacting many-particle system, in the limit as the particle number tends to innity. Also the mesoscopic model is given by a many-particle system. However, the state space there is a lattice, such that in contrast to the microscopic model the spatial resolution is reduced. The derivation of deterministic limit equations is in correspondence with the suc-cessful description of experiments under low-pressure conditions by determin-istic reaction-diusion equations while for intermediate pressures phenomena of stochastic origin can be observed in experiments. The models include a new approach for the platinum phase transition, which allows for a unication of existing models for Pt(100) and Pt(110). The rich nonlinear dynamical be-haviour of the macroscopic reaction kinetics is investigated and shows good agreement with low pressure experiments. Furthermore, for intermediate pres-sures, noise-induced pattern formation, which has not been captured by ear-lier models, can be reproduced in stochastic simulations with the mesoscopic model. 2 J. Starke, C. Reichert, M. Eiswirth, and K. Oelschlager