Distribuições quase estacionárias em modelos de catálise heterogênea

Abstract

Some models of nonequilibrium systems admit an active phase for a range of an external parameter. This is the case of the model proposed by Zi®, Gulari and Barshad (ZGB) for the CO + 1/2O2 ! CO2 reaction on a catalytic surface. Mean field theories show a reactive steady state for y1 < Y < y2, where Y is the arrival rate of CO on the lattice. But this is true only in the thermodynamic limit. Finite systems always die out" in one of the two absorbing states, where the surface is saturated with one species so that it blocks adsorption. In finite lattices, the system admits a quasistationary (QS) state, in which its properties become time-independent while the process is not in the absorbing state. In this way, one can obtain information about the nontrivial steady-state from the study of finite systems. In this thesis, we study the QS properties of the ZGB model and two variants. We write the master equation (truncated) for the process, which is integrated via standard methods and through a highly-e±cient iterative method. We obtain mean values and moment ratios for the coverages that are out of reach with other simpler approaches. We also present some preliminar results for a method to generate QS distributions via Monte Carlo simulations.