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.

doi:10.1103/physrevlett.121.120603

Cited by 5 publications

(23 citation statements)

References 42 publications

(55 reference statements)

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“…The key qualitative features of behavior are similar to those predicted in the mean-field treatment (with suitable interpretation), but all features including the spinodal and equistability points are shifted to substantially smaller p. Spinodal points are difficult to assess (and actually cannot be precisely defined) in the stochastic model as a result of strong fluctuations. However, all the stochastic models with various choices of rates and without and with small perturbation exhibit a well-defined regime of generic two-phase coexistence [22,28,29,30,43]. This regime corresponds to that identified by our mean-field treatment, where it is significant to note that the regime corresponds to p eq (S → ∞) < p < p eq (S → 1).…”

Section: B Brief Remarks On Beyond-mean-field Treatments and Behaviorsupporting

confidence: 55%

“…1. Possible assignments include k n 2 = 1 (threshold choice) [26][27][28], k n = n(n-1)/12 (combinatorial choice) [27,29], or k 2L = 0, k 2D = 1 4 , k 3 = 1 2 , k 4 = 1 (Durrett choice) [12,22]. All assignments suffer from a "quirk" that infection cannot penetrate a semi-infinite healthy region with a vertical or horizontal boundary, for any p 0 (i.e., even for very slow recovery).…”

Section: A Model Descriptionmentioning

confidence: 99%

“…There also exists a KMC study for a basic threshold version including its perturbation by spontaneous infection [28]. For the combinatorial version of the QCP, KMC analysis just exists for the basic model [29]. The key qualitative features of behavior are similar to those predicted in the mean-field treatment (with suitable interpretation), but all features including the spinodal and equistability points are shifted to substantially smaller p. Spinodal points are difficult to assess (and actually cannot be precisely defined) in the stochastic model as a result of strong fluctuations.…”

Section: B Brief Remarks On Beyond-mean-field Treatments and Behaviormentioning

confidence: 99%

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

2020

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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, peq, of a control parameter, p, with metastability and hysteresis around peq. 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→peq. 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. 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.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. 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 ...

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Section: B Brief Remarks On Beyond-mean-field Treatments and Behaviorsupporting

confidence: 55%

Section: A Model Descriptionmentioning

confidence: 99%

Section: B Brief Remarks On Beyond-mean-field Treatments and Behaviormentioning

confidence: 99%

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

2020

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“…In general, it is impossible to describe the stationary state of such models in terms of equilibrium Gibbs distributions and they belong to the realm of nonequibrium statistical physics. Models of this kind include some versions of the contact process [22][23][24][25], but might describe also some adsorption-desorption systems [26,27].…”

Section: Modelmentioning

confidence: 99%

Entropic long-range ordering in an adsorption-desorption model

Lipowski

Lipowska

2019

Phys. Rev. E

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We examine a two-dimensional nonequilibrium lattice model where particles adsorb at empty sites and desorb when the number of neighbouring particles is greater than a given threshold. In a certain range of parameters the model exhibits entropic ordering similar to some hard-core systems. However, contrary to hard-core systems, upon incresing the density of particles the ordering is destroyed. In the heterogenous version of our model, a regime with slow dynamics appears, that might indicate formation of some kind of glassy structures. arXiv:1905.04802v2 [cond-mat.stat-mech]

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“…There has also been interest in so-called quadratic (rather than linear) contact processes also formulated on a d-dimensional cubic lattice. The primary difference from the linear case is that rather than just requiring one occupied neighbor to create a particle at an empty site, two are required [12,13,17,18]. Particle creation rates as a function of the number of occupied neighbors can be prescribed in various ways.…”

Section: Chapter 1 Introduciionmentioning

confidence: 99%

Generic two-phase coexistence and non-equilibrium criticality in a type-2 Schloegl model for autocatalysis on a square lattice

Shen

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

Abstract: We consider Schloegl models (or contact processes) where particles on a square grid annihilate at rate p, and are created at rate kn =

Cited by 5 publications

References 42 publications

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

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

Entropic long-range ordering in an adsorption-desorption model

Generic two-phase coexistence and non-equilibrium criticality in a type-2 Schloegl model for autocatalysis on a square lattice

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