Schloegl's second model for autocatalysis on hypercubic lattices: Dimension dependence of generic two-phase coexistence

TitleSchloegl's second model for autocatalysis on hypercubic lattices: Dimension dependence of generic two-phase coexistence
Publication TypeJournal Article
Year of Publication2012
AuthorsWang CJ, Liu DJ, Evans JW
Journal TitlePhysical Review E
Volume85
Pages041109
Date Published04
Type of ArticleArticle
ISBN Number1539-3755
Accession NumberWOS:000302699300004
Keywordscatalysis, dynamics, FAILURE, interface propagation, kinetic phase-transitions, systems, waves
Abstract

Schloegl's second model on a (d >= 2)-dimensional hypercubic lattice involves: (i) spontaneous annihilation of particles with rate p and (ii) autocatalytic creation of particles at vacant sites at a rate proportional to the number of suitable pairs of neighboring particles. This model provides a prototype for nonequilibrium discontinuous phase transitions. However, it also exhibits nontrivial generic two-phase coexistence: Stable populated and vacuum states coexist for a finite range, p(f)(d) < p < p(e)(d), spanned by the orientation-dependent stationary points for planar interfaces separating these states. Analysis of interface dynamics from kinetic Monte Carlo simulation and from discrete reaction-diffusion equations (dRDEs) obtained from truncation of the exact master equation, reveals that p(e(f)) similar to 0.211 3765 + c(e(f))/d as d -> infinity, where Delta c = c(e) - c(f) approximate to 0.014. A metastable populated state persists above p(e)(d) up to a spinodal p = p(s)(d), which has a well-defined limit p(s)(d -> infinity) = 1/4. The dRDEs display artificial propagation failure, absent in the stochastic model due to fluctuations. This feature is amplified for increasing d, thus complicating our analysis.

URL<Go to ISI>://WOS:000302699300004
DOI10.1103/PhysRevE.85.041109
Alternate JournalPhys. Rev. E