Generic two-phase coexistence, relaxation kinetics, and interface propagation in the quadratic contact process: Analytic studies

TitleGeneric two-phase coexistence, relaxation kinetics, and interface propagation in the quadratic contact process: Analytic studies
Publication TypeJournal Article
Year of Publication2008
AuthorsGuo XF, Evans JW, Liu DH
Journal TitlePhysica a-Statistical Mechanics and Its Applications
Volume387
Pages177-201
Date PublishedJan
Type of ArticleArticle
ISBN Number0378-4371
Accession NumberISI:000251494400015
Keywordsdiscrete reaction diffusion equations, equations, FAILURE, generic two-phase coexistence, interface, master, phase-transitions, propagation, quadratic contact process, SEQUENTIAL ADSORPTION, surface-reaction model, systems, truncation
Abstract

The quadratic contact process is implemented as an adsorption-desorption model on a two-dimensional square lattice. The model involves random adsorption at empty sites, and correlated desorption requiring diagonal pairs of empty neighbors. A simulation study of this model [D.-J. Liu, X. Guo, JW. Evans, Phys. Rev. Lett. 98 (2007) 050601] revealed the existence of generic two-phase coexistence between a low-coverage active steady-state and a completely covered absorbing state. Here, an analytic treatment of model behavior is developed based on truncation approximations to the exact master equations. Applying this approach for spatially homogeneous states, we characterize steady-state behavior as well as the kinetics of relaxation to the steady-states. Extending consideration to spatially inhomogeneous states, we obtain discrete reaction-diffusion type equations characterizing evolution. These are employed to analyze an orientation-dependence of the propagation of planar interfaces between active and absorbing states which underlies the generic two-phase coexistence. We also describe the dynamics and critical forms of planar perturbations of the active state and of droplets of one phase embedded in the other. (c) 2007 Elsevier B.V. All rights reserved.

DOI10.1016/j.physa.2007.09.002
Alternate JournalPhysica A