One-dimensional irreversible aggregation with dynamics of a totally asymmetric simple exclusion process

Bunzarova, Nadezhda; Pesheva, Nina

doi:10.1103/physreve.95.052105

Cited by 7 publications

(4 citation statements)

References 58 publications

(49 reference statements)

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“…The configurations of the stationary nonequilibrium phase CF represent a completely filled chain with current J = β. The unusual phase transition, found in [24], takes place across the boundary α = p between the MPI and CF phases.…”

Section: B Known Results In Particular Casesmentioning

confidence: 88%

“…2. This indicates that the unusual phase transition, found in [24] at p m = 1 across the boundary α = p becomes a continuous one.…”

Section: A Time Evolution Of Configuration Gapsmentioning

confidence: 79%

“…We note that the above generalized backward-ordered dynamics was suggested as exactly solvable one by Wölki [20], and studied on a ring in [21][22][23]. The limit case of p m = 1 corresponds to irreversible aggregation, or jam formation in the case of vehicles, suggested and studied by Bunzarova and Pesheva [24] and further elaborated in [25,26]. Here, we focus on the stationary properties of gTASEP when p < p m < 1, describing the generic case of attraction between particles hopping stochastically and unidirectionally in discrete time along finite one-dimensional chains with given boundary conditions at the ends.…”

Section: Introductionmentioning

confidence: 90%

“…We note that the above left boundary condition was introduced first by Hrabák in [27] and, independently, in [24]. It is necessary for consistency with the special cases of backwardordered sequential update, when p m = p and α = α, as well as with the parallel one, when p m = 0 and α = 0.…”

Section: A the Modelmentioning

confidence: 99%

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One-dimensional discrete aggregation-fragmentation model

2019

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We study here one-dimensional model of aggregation and fragmentation of clusters of particles obeying the stochastic discrete-time kinetics of the generalized Totally Asymmetric Simple Exclusion Process (gTASEP) on open chains. Isolated particles and the first particle of a cluster of particles hop one site forward with probability p;when the first particle of a cluster hops, the remaining particles of the same cluster may hop with a modified probability p m , modelling a special kinematic interaction between neighboring particles, or remain in place with probability 1 − p m . The model contains as special cases the TASEP with parallel update (p m = 0) and with sequential backward-ordered update (p m = p). These cases have been exactly solved for the stationary states and their properties thoroughly studied. The limiting case of p m = 1, which corresponds to irreversible aggregation, has been recently studied too. Its phase diagram in the plane of injection (α) and ejection (β) probabilities was found to have a different topology.Here we focus on the stationary properties of the gTASEP in the generic case of attraction p < p m < 1 when aggregation-fragmentation of clusters occurs. We find that the topology of the phase diagram at p m = 1 changes sharply to the one corresponding to p m = p as soon as p m becomes less than 1. Then a maximum current phase appears in the square domain α c (p, p m ) ≤ α ≤ 1 and β c (p, p m ) ≤ β ≤ 1, where α c (p, p m ) = β c (p, p m ) ≡ σ c (p, p m ) are parameter-dependent injection/ejection critical values. The properties of the phase transitions between the three stationary phases at p < p m < 1 are assessed by computer simulations and random walk theory.

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Section: B Known Results In Particular Casesmentioning

confidence: 88%

“…2. This indicates that the unusual phase transition, found in [24] at p m = 1 across the boundary α = p becomes a continuous one.…”

Section: A Time Evolution Of Configuration Gapsmentioning

confidence: 79%

Section: Introductionmentioning

confidence: 90%

Section: A the Modelmentioning

confidence: 99%

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One-dimensional discrete aggregation-fragmentation model

2019

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Nonstationary Generalized TASEP in KPZ and Jamming Regimes

Derbyshev

Povolotsky

2021

J Stat Phys

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A model of irreversible jam formation in dense traffic

Brankov

Bunzarova

Pesheva

et al. 2018

Physica A: Statistical Mechanics and its Applications

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We study an one-dimensional stochastic model of vehicular traffic on open segments of a single-lane road of finite size L. The vehicles obey a stochastic discrete-time dynamics which is a limiting case of the generalized Totally Asymmetric Simple Exclusion Process. This dynamics has been previously used by Bunzarova and Pesheva [Phys. Rev. E 95, 052105 (2017)] for an one-dimensional model of irreversible aggregation. The model was shown to have three stationary phases: a many-particle one, MP, a phase with completely filled configuration, CF, and a boundary perturbed MP+CF phase, depending on the values of the particle injection (α), ejection (β) and hopping (p) probabilities.Here we extend the results for the stationary properties of the MP+CF phase, by deriving exact expressions for the local density at the first site of the chain and the probability P(1) of a completely jammed configuration. The unusual phase transition, characterized by jumps in both the bulk density and the current (in the thermodynamic limit), as α crosses the boundary α = p from the MP to the CF phase, is explained by the finite-size behavior of P(1).By using a random walk theory, we find that, when α approaches from below the boundary α = p, three different regimes appear, as the size L → ∞:

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One-dimensional irreversible aggregation with dynamics of a totally asymmetric simple exclusion process

Abstract: We define and study one-dimensional model of irreversible aggregation of particles obeying a discrete-time kinetics, which is a special limit of the generalized Totally

Cited by 7 publications

References 58 publications

One-dimensional discrete aggregation-fragmentation model

One-dimensional discrete aggregation-fragmentation model

Nonstationary Generalized TASEP in KPZ and Jamming Regimes

A model of irreversible jam formation in dense traffic

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