PMID: 11308814Apr 20, 2001Paper

Nonlinear reactive systems on a lattice viewed as Boolean dynamical systems

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
E AbadG Nicolis

Abstract

We present a stochastic, time-discrete Boolean model that mimics the mesoscopic dynamics of the desorption reactions A+A-->A+S and A+A-->S+S in a one-dimensional 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.

References

Jul 1, 1985·Physical Review A: General Physics·K Kang, S Redner
Oct 15, 1991·Physical Review. a·Y Fan, J K Percus
Jul 1, 1994·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·V Privman
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Apr 24, 2002·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·F BarasG Nicolis
Sep 23, 1988·Science·R Kopelman

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Citations

Feb 9, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·P Córdoba-TorresV Fairén
Nov 5, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·E Abad

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