Stochastic Boolean Dynamics of Nonlinear Reactive Systems

摘要

The lattice dynamics of the reaction A + A → A + S is treated using a Boolean model inspired by a Monte Carlo algorithm. In the diffusionless case, we solve the relevant set of moment equations and show that the coverage θ in A particles decays exponentially to an initial-condition-dependent steady state. The same moment equations are recovered in the framework of a Master equation approach. Diffusion drives the system into the empty state predicted by the classical mean field law, but an anomalous slowing down is observed due to reaction-induced transient fluctuations.