Schloegl's Second Model for Autocatalysis on a Cubic Lattice: Mean-Field-Type Discrete Reaction-Diffusion Equation Analysis

TitleSchloegl's Second Model for Autocatalysis on a Cubic Lattice: Mean-Field-Type Discrete Reaction-Diffusion Equation Analysis
Publication TypeJournal Article
Year of Publication2011
AuthorsWang CJ, Guo XF, Liu DJ, Evans JW
Journal TitleJournal of Statistical Physics
Volume144
Pages1308-1328
Date Published09
Type of ArticleArticle
ISBN Number0022-4715
Accession NumberWOS:000297133900011
Keywordsbehavior, catalysis, Discrete, FAILURE, generic 2-phase coexistence, generic two-phase coexistence, interface, interface propagation, kinetic phase-transitions, propagation, reaction-diffusion equations, Schloegl's second model, systems, waves
Abstract

Schloegl's second model for autocatalysis on a hypercubic lattice of dimension d >= 2 involves: (i) spontaneous annihilation of particles at lattice sites with rate p; and (ii) autocatalytic creation of particles at vacant sites at a rate proportional to the number of diagonal pairs of particles on neighboring sites. Kinetic Monte Carlo simulations for a d = 3 cubic lattice reveal a discontinuous transition from a populated state to a vacuum state as p increases above p = p(e). However, stationary points, p = p(eq) (<= p(e)), for planar interfaces separating these states depend on interface orientation. Our focus is on analysis of interface dynamics via discrete reaction-diffusion equations (dRDE's) obtained from mean-field type approximations to the exact master equations for spatially inhomogeneous states. These dRDE can display propagation failure absent due to fluctuations in the stochastic model. However, accounting for this anomaly, dRDE analysis elucidates exact behavior with quantitative accuracy for higher-level approximations.

DOI10.1007/s10955-011-0288-6
Alternate JournalJ. Stat. Phys.