Oscillatory temporal behavior in an autocatalytic surface reaction model

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Abstract
We discuss an autocatalytic surface reaction model A+B→2B, where particle A (B) adsorbs (desorbs) the surface with rate constant ζ (1-ζ). We present numerical results from Monte Carlo simulations in dimensions d=1, 2, and 3, as well as some analytical results, which are valid in any dimension. Especially the static aspects of this model, like the behavior of the average coverages as a function of the control parameter ζ, are well understood from simple arguments which use the rate equations. Numerical studies of the temporal behavior of this model reveal periodic oscillations in the coverages for d=2 and 3, but not for d=1. Our data show that these periodic oscillations are related to synchronized avalanches of autocatalytic reactions. These avalanches occur with a well defined frequency, and come in all possible sizes. To explain this effect we give a heuristic argument, which postulates that the model is driven toward a critical state of a random deposition problem.