Nonlinear reactive systems viewed as Boolean dynamical systems

Details Nonlinear reactive systems viewed as Boolean dynamical systems Nonlinear reactive systems viewed as Boolean dynamical systems

2001-01-24

arxiv.org/abs/cond-mat/0101378v2

Phys. Rev. E63, 041102

Physics

Condensed Matter

Statistical Mechanics

30 pages, 9 figures

Scientific paper

10.1103/PhysRevE.63.041102

We present a stochastic, time-discrete boolean model which mimics the mesoscopic dynamics of the desorption reactions $A+A\to A+S$ and $A+A\to S+S$ in a 1D lattice. In the continuous-time limit, we derive a hierarchy of dynamical equations for the subset of moments involving contiguous lattice sites. The solution of the hierarchy allows to compute the exact dynamics of the mean coverage for both microscopic and coarse-grained initial conditions, which turn out to be different from the mean field predictions. The evolution equations for the mean coverage and the second order moments are shown to be equivalent to those provided by a time-continuous Master equation. The important role of higher order fluctuations is brought out by the failure of a truncation scheme retaining only two-particle fluctuation correlations.

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