%0 Generic
%A Reichert, Christian
%D 2006
%F heidok:6948
%K stochastic particle system , catalytic surface reaction , reaction-diffusion model
%R 10.11588/heidok.00006948
%T Deterministic and stochastic modelling of a catalytic surface reaction
%U https://archiv.ub.uni-heidelberg.de/volltextserver/6948/
%X Catalytic surface reactions are of great importance both for chemical industry and as model systems for the study of pattern formation far from thermodynamic equilibrium. A reaction that has been investigated extensively in experiments is the oxidation of carbon monoxide on platinum.In the present work we first develop a mathematical model for CO oxidation on Pt which is valid over a wide pressure range. This requires the use of different model types. While at low pressures in the gas phase the system can be described by a deterministic model in the form of ordinary or partial differential equations, a stochastic particle model is needed at higher pressures due to rising fluctuations. A numerical bifurcation ananalysis for the deterministic model is performed, which yields good agreement with experimental findings. Subsequently, we investigate the consistency of deterministic differential equations models and stochastic particle models for reaction-diffusion systems in a more general setting. We rigorously derive partial differential equations as limit dynamics of certain linear and nonlinear mesoscopic' stochastic particle models in the limit of large particle numbers. The convergence proofs combine techniques from numerical analysis and the theory of Markov processes. Finally, we use the stochastic particle model for CO oxidation on Pt to simulate the spontaneous nucleation and subsequent dying out of pulses (raindrop patterns') that has been observed experimentally.