Discontinuous Phase Transitions in Nonlocal Schloegl Models for Autocatalysis: Loss and Reemergence of a Nonequilibrium Gibbs Phase Rule

Da-Jiang Liu, Chi-Jen Wang, and James W. Evans
Phys. Rev. Lett. 121, 120603 – Published 21 September 2018

Abstract

We consider Schloegl models (or contact processes) where particles on a square grid annihilate at a rate p and are created at a rate of kn=n(n1)/[N(N1)] at empty sites with n particles in a neighborhood ΩN of size N. Simulation reveals a discontinuous transition between populated and vacuum states, but equistable p=peq determined by the stationarity of planar interfaces between these states depends on the interface orientation and on ΩN. The behavior for large ΩN follows from continuum equations. These also depend on the interface orientation and on ΩN shape, but a unique peq=0.2113763204 emerges imposing a Gibbs phase rule.

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  • Received 5 April 2018
  • Revised 25 July 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.120603

© 2018 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Da-Jiang Liu1, Chi-Jen Wang2, and James W. Evans1,3,4

  • 1Ames Laboratory—USDOE, Iowa State University, Ames, Iowa 50011, USA
  • 2Department of Mathematics, National Chung Cheng University, Chiayi 62102, Taiwan
  • 3Department of Mathematics, Iowa State University, Ames, Iowa 50011, USA
  • 4Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA

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Issue

Vol. 121, Iss. 12 — 21 September 2018

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