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

Date
2018-09-21
Authors
Liu, Da-Jiang
Wang, Chi-Jen
Evans, James
Evans, James
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Ames Laboratory
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Physics and Astronomy
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Mathematics
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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(n−1)/[N(N−1)] 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=0.211 376 320 4 emerges imposing a Gibbs phase rule.

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