DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Extended families of critical and stationary droplets for nonequilibrium phase transitions in spatially discrete bistable systems

Journal Article · · Physical Review E

Bistable nonequilibrium systems are realized in catalytic reaction-diffusion processes, biological transport and regulation, spatial epidemics, etc. Behavior in spatially continuous formulations, described at the mean-field level by reaction-diffusion type equations (RDEs), often mimics that of classic equilibrium van der Waals type systems. When accounting for noise, similarities include a discontinuous phase transition at some value, p eq , of a control parameter, p , with metastability and hysteresis around p eq . For each p , there is a unique critical droplet of the more stable phase embedded in the less stable or metastable phase which is stationary (neither shrinking nor growing), and with size diverging as p p eq . Spatially discrete analogs of these mean-field formulations, described by lattice differential equations (LDEs), are more appropriate for some applications, but have received less attention. It is recognized that LDEs can exhibit richer behavior than RDEs, specifically propagation failure for planar interphases separating distinct phases. Herein, we show that this feature, together with an orientation dependence of planar interface propagation also deriving from spatial discreteness, results in the occurrence of entire families of stationary droplets. The extent of these families increases approaching the transition and can be infinite if propagation failure is realized. In addition, there can exist a regime of generic two-phase coexistence where arbitrarily large droplets of either phase always shrink. Such rich behavior is qualitatively distinct from that for classic nucleation in equilibrium and spatially continuous nonequilibrium systems.

Research Organization:
Ames Laboratory (AMES), Ames, IA (United States)
Sponsoring Organization:
Ministry of Science and Technology (MOST) of Taiwan; USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences, and Biosciences Division
Grant/Contract Number:
105-2115-M-194-011-MY2; AC02-07CH11358
OSTI ID:
1602867
Alternate ID(s):
OSTI ID: 1602361
Report Number(s):
IS-J-10048; PLEEE8; TRN: US2104676
Journal Information:
Physical Review E, Vol. 101, Issue 2; ISSN 2470-0045
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

References (38)

A first order phase transition in the threshold θ≥2 contact process on random r-regular graphs and r-trees journal February 2013
From atomistic lattice-gas models for surface reactions to hydrodynamic reaction-diffusion equations journal March 2002
Universality of Crystallographic Pinning journal February 2010
Transitions between strongly correlated and random steady-states for catalytic CO-oxidation on surfaces at high-pressure journal April 2015
Kinetic phase transitions in catalytic reaction models journal November 1991
Self-Organized Stationary Patterns in Networks of Bistable Chemical Reactions journal October 2016
Tunable Pinning of Burst Waves in Extended Systems with Discrete Sources journal December 1998
CO oxidation on Pd(100) at technologically relevant pressure conditions: First-principles kinetic Monte Carlo study journal April 2008
Traveling Wave Solutions for Systems of ODEs on a Two-Dimensional Spatial Lattice journal January 1998
Absence of Diffusion in Certain Random Lattices journal March 1958
Bistability in Pulse Propagation in Networks of Excitatory and Inhibitory Populations journal April 2001
Allee effects in biological invasions journal August 2005
Quadratic Contact Process: Phase Separation with Interface-Orientation-Dependent Equistability journal February 2007
Survival of Threshold Contact Processes journal January 1997
Spatially Discrete FitzHugh--Nagumo Equations journal January 2005
Kinetic Phase Transitions in an Irreversible Surface-Reaction Model journal June 1986
Dynamics of Lattice Differential Equations journal September 1996
Introduction to the Theory of Metastable and Unstable States book January 1983
Theory of crystal growth and interface motion in crystalline materials journal August 1960
Chemical reaction models for non-equilibrium phase transitions journal April 1972
Orientation‐Dependent Dissolution of Germanium journal November 1960
Nonequilibrium Phase Transitions in Lattice Models book January 2009
Stochastic Spatial Models journal January 1999
Schloegl's second model for autocatalysis on hypercubic lattices: Dimension dependence of generic two-phase coexistence journal April 2012
Chemical diffusion in the lattice gas of non-interacting particles journal January 1981
Propagation failure of traveling waves in a discrete bistable medium journal May 1998
Kinetics of Phase Change. I General Theory journal December 1939
Discontinuous non-equilibrium phase transition in a threshold Schloegl model for autocatalysis: Generic two-phase coexistence and metastability journal April 2015
Discontinuous Phase Transitions in Nonlocal Schloegl Models for Autocatalysis: Loss and Reemergence of a Nonequilibrium Gibbs Phase Rule journal September 2018
Kinetic Monte Carlo Simulation of Statistical Mechanical Models and Coarse-Grained Mesoscale Descriptions of Catalytic Reaction–Diffusion Processes: 1D Nanoporous and 2D Surface Systems journal April 2015
Unidirectional Transition Waves in Bistable Lattices journal June 2016
Role of Irreversibility in Stabilizing Complex and Nonergodic Behavior in Locally Interacting Discrete Systems journal August 1985
Schloegl’s second model for autocatalysis with particle diffusion: Lattice-gas realization exhibiting generic two-phase coexistence journal February 2009
Generic two-phase coexistence, relaxation kinetics, and interface propagation in the quadratic contact process: Analytic studies journal January 2008
Stability of Localized Wave Fronts in Bistable Systems journal January 2013
Traveling and Pinned Fronts in Bistable Reaction-Diffusion Systems on Networks journal September 2012
Generic Two-Phase Coexistence and Nonequilibrium Criticality in a Lattice Version of Schlögl’s Second Model for Autocatalysis journal March 2009
Tricriticality in generalized Schloegl models for autocatalysis: Lattice-gas realization with particle diffusion journal February 2012