Discontinuous non-equilibrium phase transition in a threshold Schloegl model for autocatalysis: Generic two-phase coexistence and metastability

Wang, Chi-Jen; Liu, Da-Jiang; Evans, James W.

doi:10.1063/1.4918908

Title: Discontinuous non-equilibrium phase transition in a threshold Schloegl model for autocatalysis: Generic two-phase coexistence and metastability

Journal Article · Tue Apr 28 00:00:00 EDT 2015 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4918908· OSTI ID:22415697

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

Ames Laboratory–USDOE, Iowa State University, Ames, Iowa 50011 (United States)

Threshold versions of Schloegl’s model on a lattice, which involve autocatalytic creation and spontaneous annihilation of particles, can provide a simple prototype for discontinuous non-equilibrium phase transitions. These models are equivalent to so-called threshold contact processes. A discontinuous transition between populated and vacuum states can occur selecting a threshold of N ≥ 2 for the minimum number, N, of neighboring particles enabling autocatalytic creation at an empty site. Fundamental open questions remain given the lack of a thermodynamic framework for analysis. For a square lattice with N = 2, we show that phase coexistence occurs not at a unique value but for a finite range of particle annihilation rate (the natural control parameter). This generic two-phase coexistence also persists when perturbing the model to allow spontaneous particle creation. Such behavior contrasts both the Gibbs phase rule for thermodynamic systems and also previous analysis for this model. We find metastability near the transition corresponding to a non-zero effective line tension, also contrasting previously suggested critical behavior. Mean-field type analysis, extended to treat spatially heterogeneous states, further elucidates model behavior.

Cite

Export

Save

OSTI ID:: 22415697

Journal Information:: Journal of Chemical Physics, Vol. 142, Issue 16; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9606

Country of Publication:: United States

Language:: English

References (55)

“First-Principles” kinetic monte carlo simulations revisited: CO oxidation over RuO2(110) Hess, Franziska; Farkas, Attila; Seitsonen, Ari P. Journal of Computational Chemistry, Vol. 33, Issue 7 https://doi.org/10.1002/jcc.22902	journal	January 2012
On phase transitions in Schl�gl's second model Grassberger, P. Zeitschrift f�r Physik B Condensed Matter, Vol. 47, Issue 4 https://doi.org/10.1007/bf01313803	journal	December 1982
Chemical reaction models for non-equilibrium phase transitions Schl�gl, F. Zeitschrift f�r Physik, Vol. 253, Issue 2 https://doi.org/10.1007/bf01379769	journal	April 1972
Wulff Droplets and the Metastable Relaxation of Kinetic Ising Models Schonmann, Roberto H.; Shlosman, Senya B. Communications in Mathematical Physics, Vol. 194, Issue 2 https://doi.org/10.1007/s002200050363	journal	June 1998
Threshold θ ≥ 2 contact processes on homogeneous trees Fontes, Luiz Renato; Schonmann, Roberto H. Probability Theory and Related Fields, Vol. 141, Issue 3-4 https://doi.org/10.1007/s00440-007-0092-z	journal	July 2007
Generic Two-Phase Coexistence and Nonequilibrium Criticality in a Lattice Version of Schlögl’s Second Model for Autocatalysis Liu, Da-Jiang Journal of Statistical Physics, Vol. 135, Issue 1 https://doi.org/10.1007/s10955-009-9708-2	journal	March 2009
Schloegl’s Second Model for Autocatalysis on a Cubic Lattice: Mean-Field-Type Discrete Reaction-Diffusion Equation Analysis Wang, Chi-Jen; Guo, Xiaofang; Liu, Da-Jiang Journal of Statistical Physics, Vol. 144, Issue 6 https://doi.org/10.1007/s10955-011-0288-6	journal	September 2011
Kinetic phase transitions in a model for surface catalysis Fischer, P.; Titulaer, U. M. Surface Science, Vol. 221, Issue 1-2 https://doi.org/10.1016/0039-6028(89)90589-x	journal	October 1989
Kinetic phase transitions and bistability in a model surface reaction II. Spatially inhomogeneous theories Sholl, David S.; Skodje, Rex T. Surface Science, Vol. 334, Issue 1-3 https://doi.org/10.1016/0039-6028(95)00467-x	journal	July 1995
Two versions of the threshold contact model in two dimensions da Silva, Evandro F.; de Oliveira, Mário J. Computer Physics Communications, Vol. 183, Issue 9 https://doi.org/10.1016/j.cpc.2012.05.003	journal	September 2012
Generic two-phase coexistence, relaxation kinetics, and interface propagation in the quadratic contact process: Analytic studies Guo, Xiaofang; Evans, J. W.; Liu, Da-Jiang Physica A: Statistical Mechanics and its Applications, Vol. 387, Issue 1 https://doi.org/10.1016/j.physa.2007.09.002	journal	January 2008
Realistic multisite lattice-gas modeling and KMC simulation of catalytic surface reactions: Kinetics and multiscale spatial behavior for CO-oxidation on metal (100) surfaces Liu, Da-Jiang; Evans, James W. Progress in Surface Science, Vol. 88, Issue 4 https://doi.org/10.1016/j.progsurf.2013.10.001	journal	December 2013
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 Chatterjee, Shirshendu; Durrett, Rick Stochastic Processes and their Applications, Vol. 123, Issue 2 https://doi.org/10.1016/j.spa.2012.10.001	journal	February 2013
Metastable states: smooth continuations through the critical point Shlosman, Senya Physica A: Statistical Mechanics and its Applications, Vol. 263, Issue 1-4 https://doi.org/10.1016/s0378-4371(98)00531-7	journal	February 1999
Crossover Between Mean-Field and Ising Critical Behavior in a Lattice-Gas Reaction-Diffusion Model Liu, Da-Jiang; Pavlenko, N.; Evans, J. W. Journal of Statistical Physics, Vol. 114, Issue 1/2 https://doi.org/10.1023/b:joss.0000003105.50683.c6	journal	January 2004
Kinetics of Phase Change. I General Theory Avrami, Melvin The Journal of Chemical Physics, Vol. 7, Issue 12, p. 1103-1112 https://doi.org/10.1063/1.1750380	journal	December 1939
Kinetics of Phase Change. II Transformation‐Time Relations for Random Distribution of Nuclei Avrami, Melvin The Journal of Chemical Physics, Vol. 8, Issue 2 https://doi.org/10.1063/1.1750631	journal	February 1940
Granulation, Phase Change, and Microstructure Kinetics of Phase Change. III Avrami, Melvin The Journal of Chemical Physics, Vol. 9, Issue 2, p. 177-184 https://doi.org/10.1063/1.1750872	journal	February 1941
Schloegl’s second model for autocatalysis with particle diffusion: Lattice-gas realization exhibiting generic two-phase coexistence Guo, Xiaofang; Liu, Da-Jiang; Evans, J. W. The Journal of Chemical Physics, Vol. 130, Issue 7 https://doi.org/10.1063/1.3074308	journal	February 2009
Transitions between strongly correlated and random steady-states for catalytic CO-oxidation on surfaces at high-pressure Liu, Da-Jiang; Evans, James W. The Journal of Chemical Physics, Vol. 142, Issue 13 https://doi.org/10.1063/1.4916380	journal	April 2015
Stochastic Spatial Models of Host-Pathogen and Host-Mutualist Interactions II Lanchier, N.; Neuhauser, C. Stochastic Models, Vol. 26, Issue 3 https://doi.org/10.1080/15326349.2010.498317	journal	August 2010
Nonlinearity in complexity science MacKay, R. S. Nonlinearity, Vol. 21, Issue 12 https://doi.org/10.1088/0951-7715/21/12/t03	journal	November 2008
Critical discontinuous phase transition in the threshold contact process da Silva, Evandro F.; de Oliveira, Mário J. Journal of Physics A: Mathematical and Theoretical, Vol. 44, Issue 13 https://doi.org/10.1088/1751-8113/44/13/135002	journal	March 2011
Kinetic phase transitions in a surface-reaction model: Mean-field theory Dickman, Ronald Physical Review A, Vol. 34, Issue 5 https://doi.org/10.1103/physreva.34.4246	journal	November 1986
Generic nonergodic behavior in locally interacting continuous systems He, Yu; Jayaprakash, C.; Grinstein, G. Physical Review A, Vol. 42, Issue 6 https://doi.org/10.1103/physreva.42.3348	journal	September 1990
Investigation of the first-order phase transition in the A - $B_{2}$ reaction model using a constant-coverage kinetic ensemble Ziff, Robert M.; Brosilow, Benjamin J. Physical Review A, Vol. 46, Issue 8 https://doi.org/10.1103/physreva.46.4630	journal	October 1992
Metastable lifetimes in a kinetic Ising model: Dependence on field and system size Rikvold, Per Arne; Tomita, H.; Miyashita, S. Physical Review E, Vol. 49, Issue 6 https://doi.org/10.1103/physreve.49.5080	journal	June 1994
Interface propagation and nucleation phenomena for discontinuous poisoning transitions in surface-reaction models Evans, J. W.; Ray, T. R. Physical Review E, Vol. 50, Issue 6 https://doi.org/10.1103/physreve.50.4302	journal	December 1994
Trigger waves in a model for catalysis Goodman, Roy H.; Graff, David S.; Sander, Leonard M. Physical Review E, Vol. 52, Issue 6 https://doi.org/10.1103/physreve.52.5904	journal	December 1995
First-order transition with power-law singularity in models with absorbing states Lipowski, Adam Physical Review E, Vol. 62, Issue 3 https://doi.org/10.1103/physreve.62.4401	journal	September 2000
Propagating waves in one-dimensional discrete networks of coupled units De Decker, Y.; Tsekouras, G. A.; Provata, A. Physical Review E, Vol. 69, Issue 3 https://doi.org/10.1103/physreve.69.036203	journal	March 2004
Decay of metastable phases in a model for the catalytic oxidation of CO Machado, Erik; Buendía, Gloria M.; Rikvold, Per Arne Physical Review E, Vol. 71, Issue 3 https://doi.org/10.1103/physreve.71.031603	journal	March 2005
Generic two-phase coexistence, relaxation kinetics, and interface propagation in the quadratic contact process: Simulation studies Guo, Xiaofang; Liu, Da-Jiang; Evans, J. W. Physical Review E, Vol. 75, Issue 6 https://doi.org/10.1103/physreve.75.061129	journal	June 2007
Contact process with long-range interactions: A study in the ensemble of constant particle number Fiore, Carlos E.; de Oliveira, Mário J. Physical Review E, Vol. 76, Issue 4 https://doi.org/10.1103/physreve.76.041103	journal	October 2007
Schloegl's second model for autocatalysis on hypercubic lattices: Dimension dependence of generic two-phase coexistence Wang, Chi-Jen; Liu, Da-Jiang; Evans, J. W. Physical Review E, Vol. 85, Issue 4 https://doi.org/10.1103/physreve.85.041109	journal	April 2012
Robustness of first-order phase transitions in one-dimensional long-range contact processes Fiore, Carlos E.; de Oliveira, Mário J. Physical Review E, Vol. 87, Issue 4 https://doi.org/10.1103/physreve.87.042101	journal	April 2013
Monte Carlo simulations of the critical properties of a Ziff-Gulari-Barshad model of catalytic CO oxidation with long-range reactivity Chan, C. H.; Rikvold, P. A. Physical Review E, Vol. 91, Issue 1 https://doi.org/10.1103/physreve.91.012103	journal	January 2015
Role of Irreversibility in Stabilizing Complex and Nonergodic Behavior in Locally Interacting Discrete Systems Bennett, Charles H.; Grinstein, G. Physical Review Letters, Vol. 55, Issue 7 https://doi.org/10.1103/physrevlett.55.657	journal	August 1985
Kinetic Phase Transitions in an Irreversible Surface-Reaction Model Ziff, Robert M.; Gulari, Erdagon; Barshad, Yoav Physical Review Letters, Vol. 56, Issue 24 https://doi.org/10.1103/physrevlett.56.2553	journal	June 1986
Characterizing kinetics near a first-order catalytic-poisoning transition Evans, J. W.; Miesch, M. S. Physical Review Letters, Vol. 66, Issue 6 https://doi.org/10.1103/physrevlett.66.833	journal	February 1991
Nonequilibrium Model for the Contact Process in an Ensemble of Constant Particle Number Tomé, Tânia; de Oliveira, Mário J. Physical Review Letters, Vol. 86, Issue 25 https://doi.org/10.1103/physrevlett.86.5643	journal	June 2001
Critical Coarsening without Surface Tension: The Universality Class of the Voter Model Dornic, Ivan; Chaté, Hugues; Chave, Jérôme Physical Review Letters, Vol. 87, Issue 4 https://doi.org/10.1103/physrevlett.87.045701	journal	July 2001
Quadratic Contact Process: Phase Separation with Interface-Orientation-Dependent Equistability Liu, Da-Jiang; Guo, Xiaofang; Evans, J. W. Physical Review Letters, Vol. 98, Issue 5 https://doi.org/10.1103/physrevlett.98.050601	journal	February 2007
Propagation and Its Failure in Coupled Systems of Discrete Excitable Cells Keener, James P. SIAM Journal on Applied Mathematics, Vol. 47, Issue 3 https://doi.org/10.1137/0147038	journal	June 1987
Stochastic Spatial Models Durrett, Rick SIAM Review, Vol. 41, Issue 4 https://doi.org/10.1137/s0036144599354707	journal	January 1999
Generic two-phase coexistence in nonequilibrium systems Mu�oz, M. A.; de los Santos, F.; Telo da Gama, M. M. The European Physical Journal B, Vol. 43, Issue 1 https://doi.org/10.1140/epjb/e2005-00029-3	journal	January 2005
Dynamics of Lattice Differential Equations Chow, Shui-Nee; Mallet-Paret, John; Van Vleck, Erik S. International Journal of Bifurcation and Chaos, Vol. 06, Issue 09 https://doi.org/10.1142/s0218127496000977	journal	September 1996
The survival of large dimensional threshold contact processes Mountford, Thomas; Schonmann, Roberto H. The Annals of Probability, Vol. 37, Issue 4 https://doi.org/10.1214/08-aop440	journal	July 2009
“First-Principles” kinetic monte carlo simulations revisited: CO oxidation over RuO2(110) Hess, Franziska; Farkas, Attila; Seitsonen, Ari P. Wiley-Blackwell https://doi.org/10.5167/uzh-65259	text	January 2012
Nonequilibrium Model for the Contact Process in an Ensemble of Constant Particle Number De Oliveira, Mário J.; Tomé, Tânia The American Physical Society https://doi.org/10.17877/de290r-740	text	January 2001
Kinetic phase transitions in a model for surface catalysis Fischer, P.; Titulaer, U. M. Surface Science Letters, Vol. 221, Issue 1-2 https://doi.org/10.1016/0167-2584(89)90030-3	journal	October 1989
Contact process with long-range interactions: a study in the ensemble of constant particle number Fiore, Carlos E.; de Oliveira, Mário J. arXiv https://doi.org/10.48550/arxiv.0809.2221	text	January 2008
The survival of large dimensional threshold contact processes Mountford, Thomas; Schonmann, Roberto H. arXiv https://doi.org/10.48550/arxiv.0908.4146	text	January 2009
A first-order transition with power-law singularity in models with absorbing states Lipowski, A. arXiv https://doi.org/10.48550/arxiv.cond-mat/0002378	text	January 2000
Generic two-phase coexistence in nonequilibrium systems Munoz, M. A.; Santos, F. de los; da Gama, M. M. Telo arXiv https://doi.org/10.48550/arxiv.cond-mat/0411578	text	January 2004

Cited By (1)

Discontinuous Phase Transitions in Nonlocal Schloegl Models for Autocatalysis: Loss and Reemergence of a Nonequilibrium Gibbs Phase Rule Liu, Da-Jiang; Wang, Chi-Jen; Evans, James W. Physical Review Letters, Vol. 121, Issue 12 https://doi.org/10.1103/physrevlett.121.120603	journal	September 2018

Similar Records

Discontinuous non-equilibrium phase transition in a threshold Schloegl model for autocatalysis: Generic two-phase coexistence and metastability

Journal Article · Tue Apr 28 00:00:00 EDT 2015 · Journal of Chemical Physics · OSTI ID:22415697

Wang, Chi -Jen; Liu, Da -Jiang; Evans, James W.

Generic two-phase coexistence in a type-2 Schloegl model for autocatalysis on a square lattice: Analysis via heterogeneous master equations

Journal Article · Fri Mar 03 00:00:00 EST 2023 · Physical Review. E · OSTI ID:22415697

Shen, Zheren; Liu, Da-Jiang; Evans, James W.

Phase transitions in Schloegl's second model for autocatalysis on a Bethe lattice

Journal Article · Mon Jul 26 00:00:00 EDT 2021 · Physical Review E · OSTI ID:22415697

Liu, Da-Jiang; Wang, Chi-Jen; Evans, James W.

Related Subjects

37 INORGANIC
ORGANIC
PHYSICAL AND ANALYTICAL CHEMISTRY
ANNIHILATION
EQUILIBRIUM
MEAN-FIELD THEORY
PARTICLES
PHASE RULE
PHASE STABILITY
PHASE STUDIES
PHASE TRANSFORMATIONS
TETRAGONAL LATTICES
THERMODYNAMICS
VACUUM STATES

Title: Discontinuous non-equilibrium phase transition in a threshold Schloegl model for autocatalysis: Generic two-phase coexistence and metastability

Citation Formats

References (55)

Cited By (1)

Similar Records

Related Subjects