Schloegl’s second model for autocatalysis with particle diffusion: Lattice-gas realization exhibiting generic two-phase coexistence

Date
2009-01-01
Authors
Guo, Xiaofang
Liu, Da-Jiang
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 analyze a discontinuous nonequilibrium phase transition between an active (or reactive) state and a poisoned (or extinguished) state occurring in a stochastic lattice-gas realization of Schloegl’s second model for autocatalysis. This realization, also known as the quadratic contact process, involves spontaneous annihilation, autocatalytic creation, and diffusion of particles on a square lattice, where creation at empty sites requires a suitable nearby pair of particles. The poisoned state exists for all annihilation rates p>0 and is an absorbing particle-free “vacuum” state. The populated active steady state exists only for p below a critical value, pe. If pf denotes the critical value below which a finite population can survive, then we show that pf

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The following article appeared in Journal of Chemical Physics 130, 7 (2009): 074106 and may be found at doi: 10.1063/1.3074308.

Keywords
Diffusion in solids, stochastic models, annihilation rates, autocatalytic, contact process, critical values, diffusivities, discontinuous equilibriums, finite populations, lattice gas, metastability, non-equilibrium phase transitions, particle diffusions, phase coexistences, square lattices, thermodynamic systems
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