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

Abstract

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 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 of size N. The behavior for large ΩN of size N follows from continuum equations. These also depend on the interface orientation and on ΩN of size N shape, but a unique peq=0.211 376 320 4 emerges imposing a Gibbs phase rule.

Authors:
 [1];  [2];  [1]
+ Show Author Affiliations
  1. Ames Lab. and Iowa State Univ., Ames, IA (United States)
  2. National Chung Cheng Univ., Chiayi (Taiwan)
Publication Date:
Research Org.:
Ames Lab., Ames, IA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1477196
Alternate Identifier(s):
OSTI ID: 1471788
Report Number(s):
IS-J-9772
Journal ID: ISSN 0031-9007; PRLTAO
Grant/Contract Number:  
AC02-07CH11358; 105-2115-M-194-011-MY2
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 121; Journal Issue: 12; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Liu, Da -Jiang, Wang, Chi -Jen, and Evans, James W. Discontinuous Phase Transitions in Nonlocal Schloegl Models for Autocatalysis: Loss and Reemergence of a Nonequilibrium Gibbs Phase Rule. United States: N. p., 2018. Web. https://doi.org/10.1103/PhysRevLett.121.120603.
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Liu, Da -Jiang, Wang, Chi -Jen, & Evans, James W. Discontinuous Phase Transitions in Nonlocal Schloegl Models for Autocatalysis: Loss and Reemergence of a Nonequilibrium Gibbs Phase Rule. United States. https://doi.org/10.1103/PhysRevLett.121.120603
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Liu, Da -Jiang, Wang, Chi -Jen, and Evans, James W. Fri . "Discontinuous Phase Transitions in Nonlocal Schloegl Models for Autocatalysis: Loss and Reemergence of a Nonequilibrium Gibbs Phase Rule". United States. https://doi.org/10.1103/PhysRevLett.121.120603. https://www.osti.gov/servlets/purl/1477196.
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@article{osti_1477196,
title = {Discontinuous Phase Transitions in Nonlocal Schloegl Models for Autocatalysis: Loss and Reemergence of a Nonequilibrium Gibbs Phase Rule},
author = {Liu, Da -Jiang and Wang, Chi -Jen and Evans, James W.},
abstractNote = {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 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 of size N. The behavior for large ΩN of size N follows from continuum equations. These also depend on the interface orientation and on ΩN of size N shape, but a unique peq=0.211 376 320 4 emerges imposing a Gibbs phase rule.},
doi = {10.1103/PhysRevLett.121.120603},
journal = {Physical Review Letters},
number = 12,
volume = 121,
place = {United States},
year = {2018},
month = {9}
}
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https://doi.org/10.1103/PhysRevLett.121.120603
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Figures / Tables:

FIG. 1 FIG. 1: Steady-state C versus $p$ for square $Ω$N for $N$=$L$2-1 with L ≥ 3, and for $N$=4 from KMC; $C$=0 above the transition. MF behavior is also shown. Inset: $S$=1 strip geometries for $N$=4,128.
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A first order phase transition in the threshold <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>θ</mml:mi><mml:mo>≥</mml:mo><mml:mn>2</mml:mn></mml:math> contact process on random <mml:math altimg="si2.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>r</mml:mi></mml:math>-regular graphs and <mml:math altimg="si3.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>r</mml:mi></mml:math>-trees
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