Master equation for a bistable chemical system with perturbed particle velocity distribution function

Abstract

We present a modified master equation for a homogeneous gaseous reactive system which includes nonequilibrium corrections due to the reaction-induced perturbation of the particle velocity distribution function. For the Schlögl model, the modified stochastic approach predicts nonequilibrium-induced transitions between different dynamical regimes, including the transformation of a monostable system into a bistable one, and vice versa. These predictions are confirmed by the comparison with microscopic simulations using the direct simulation Monte Carlo method. Compared to microscopic simulations of the particle dynamics, the modified master equation approach proves to be much more efficient.

Spectral and Pseudospectral Methods of Solution of the Fokker-Planck and Schrödinger Equations

“…It has been long recognized that reactive processes for gaseous systems proceed with the perturbation of the species velocity distribution functions from Maxwellian (Ross and Mazur 1961;Shizgal and Karplus 1970;Shizgal and Napier 1996;Kustova and Giordano 2011;Dziekan et al 2012). (r, v, t), of a test particle at position r and velocity v, at time t in the potential U (r ) is given by…”