1 research outputs found
Nonlinear reactive systems viewed as Boolean dynamical systems
We present a stochastic, time-discrete boolean model which mimics the
mesoscopic dynamics of the desorption reactions and
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.Comment: 30 pages, 9 figure