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

Journal Article · 20 September 2018 · Physical Review Letters

DOI: https://doi.org/10.1103/PhysRevLett.121.120603 · OSTI ID:1477196

Liu, Da -Jiang ^[1]; Wang, Chi -Jen ^[2]; Evans, James W. ^[1]

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1. Ames Lab. and Iowa State Univ., Ames, IA (United States)
2. National Chung Cheng Univ., Chiayi (Taiwan)

Here, 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 k_n=n(n–1)/[N(N–1)] at empty sites with n particles in a neighborhood Ω_N of size N. Simulation reveals a discontinuous transition between populated and vacuum states, but equistable p=p_eq determined by the stationarity of planar interfaces between these states depends on the interface orientation and on Ω_N of size N. The behavior for large Ω_N of size N follows from continuum equations. These also depend on the interface orientation and on Ω_N of size N shape, but a unique p_eq=0.211 376 320 4 emerges imposing a Gibbs phase rule.

• Research Organization: Ames Laboratory (AMES), Ames, IA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
• Grant/Contract Number: AC02-07CH11358
• OSTI ID: 1477196
• Alternate ID(s): OSTI ID: 1471788
• Report Number(s): IS-J--9772; {"","Journal ID: ISSN 0031-9007","Journal ID: ISSN PRLTAO"}
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 12 Vol. 121; ISSN 0031-9007; ISSN PRLTAO
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English