Finite-size scaling and universality for the totally asymmetric simple-exclusion process

Brankov, J.G.; Bunzarova, Nadezhda

doi:10.1103/physreve.71.036130

Cited by 12 publications

(5 citation statements)

References 52 publications

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“…Which changes of the microscopic model details will lead to changes of the macroscopic behavior? Also, while for equilibrium systems basic notions of universality and independence from dynamic details are well understood, only initial steps are taken towards extending these notions towards non-equilibrium systems and more specifically towards non-equilibrium steady states [35,36]. We would like to conclude by pointing out that even though such simple models may not permit immediate comparisons with available experimental data, due to the significant amount of simplification and/or abstraction involved, they can still be quite useful in guiding future experimental work.…”

Section: Discussionmentioning

confidence: 99%

Position-Induced Phase Change in a TASEP with a Double-Chain Section (a Model of Biological Transport)

Pesheva

Brankov²

2012

BIOMATH

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Section: Discussionmentioning

confidence: 99%

Position-Induced Phase Change in a TASEP with a Double-Chain Section (a Model of Biological Transport)

Pesheva

Brankov²

2012

BIOMATH

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“…Exact mappings of the normalization factor for the discrete-time parallel update onto several equivalent two-dimensional lattice path problems were obtained in [18]. The applicability of the concepts of finite-size scaling and universality with respect to the different types of updates for the open TASEP has been established in [19]. For an overview on the recent breakthroughs in the extension of the Lee-Yang theory to non-equilibrium phase transitions we refer the reader to [20].…”

Section: Zeros Of the Partition Functionmentioning

confidence: 99%

“…Exact mappings of the normalization factor for the discrete-time parallel update onto several equivalent two-dimensional lattice path problems were obtained in [18]. The applicability of the concepts of finite-size scaling and universality with respect to the different types of updates for the open TASEP has been established in [19]. For an overview on the recent Let us now re-interpret the generating function (11) as a partition function of a two-dimensional lattice path problem, in which the horizontal coordinates correspond to the original lattice sites, and the vertical direction is the discrete time.…”

Section: Zeros Of the Partition Functionmentioning

confidence: 99%

The totally asymmetric exclusion process on a ring: Exact relaxation dynamics and associated model of clustering transition

Brankov¹,

Papoyan²,

Poghosyan³

et al. 2006

Physica A: Statistical Mechanics and its Applications

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The totally asymmetric simple exclusion process in discrete time is considered on finite rings with fixed number of particles. A translation-invariant version of the backward-ordered sequential update is defined for periodic boundary conditions. We prove that the so defined update leads to a stationary state in which all possible particle configurations have equal probabilities. Using the exact analytical expression for the propagator, we find the generating function for the conditional probabilities, average velocity and diffusion constant at all stages of evolution. An exact and explicit expression for the stationary velocity of TASEP on rings of arbitrary size and particle filling is derived. The evolution of small systems towards a steady state is clearly demonstrated. Considering the generating function as a partition function of a thermodynamic system, we study its zeros in planes of complex fugacities. At long enough times, the patterns of zeroes for rings with increasing size provide evidence for a transition of the associated two-dimensional lattice paths model into a clustered phase at low fugacities.

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“…Indeed, from mathematical point of view, TASEP is a discrete version of the inviscid noisy Burgers equation in the appropriate scaling limit. It was established that the versions of the TASEP, based on different update rules, belong to the same non-equilibrium finite-size scaling universality class [25].…”

Section: Introductionmentioning

confidence: 99%

“…The analytical solutions obtained for TASEP made possible the calculation in the scaling limit of the universal critical exponents and scaling functions of the Edward-Wilkinson and Kardar-Parisi-Zhang universality classes. It was established that the versions of the TASEP, based on different update rules, belong to the same non-equilibrium finite-size scaling universality class [31].…”

Section: Introdictionmentioning

confidence: 99%

On the appearance of traffic jams in a long chain with a shortcut in the bulk

Bunzarova

Pesheva

Brankov

2015

Physica A: Statistical Mechanics and its Applications

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h i g h l i g h t s • We study stationary properties of TASEP on open long chains with a shunted section. • The conditions for occurrence of traffic jams and their properties are investigated. • Monte Carlo simulations data agree fairy well with theoretical predictions. • The effective rates approximation and domain wall theory are applicable. • Traffic jams are found to disappear upon shifting the shortcut downstream. : Totally asymmetric simple exclusion process Non-equilibrium stationary states Networks with complex geometry Coexistence phase Domain wall theory a b s t r a c t The Totally Asymmetric Simple Exclusion Process (TASEP) is studied on open long chains with a shunted section between two simple chain segments in the maximum current phase. The reference case, when the two branches are chosen with equal probability, is considered. The conditions for the occurrence of traffic jams and their properties are investigated both within the effective rates approximation and by extensive Monte Carlo simulations for arbitrary length of the shortcut. Our main results are: (1) For any length of the shortcut and any values of the external rates in the domain of the maximum current phase, there exists a position of the shortcut where the shunted segment is in a phase of coexistence with a completely delocalized domain wall;(2) The main features of the coexistence phase and the density profiles in the whole network are well described by the domain wall theory. Apart from the small inter-chain correlations, they depend only on the current through the shortcut; (3) The model displays unexpected features: (a) the current through the longer shunted segment is larger than the current through the shortcut, and (b) the delocalized domain wall in the coexistence phase of the long shunted segment induces similar behavior even in shortcuts containing a small number of sites; (4) From the viewpoint of vehicular traffic, most comfortable conditions for the drivers are provided when the shortcut is shifted downstream from the position of coexistence, when both the shunted segment and the shortcut exhibit low-density lamellar flow. Most unfavorable is the opposite case of upstream shifted shortcut, when both the shunted segment and the shortcut are in a high-density phase describing congested traffic of slowly moving cars. The above results are relevant also to phenomena like crowding of molecular motors moving along twisted protofilaments.

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Finite-size scaling and universality for the totally asymmetric simple-exclusion process

Cited by 12 publications

References 52 publications

Position-Induced Phase Change in a TASEP with a Double-Chain Section (a Model of Biological Transport)

Position-Induced Phase Change in a TASEP with a Double-Chain Section (a Model of Biological Transport)

The totally asymmetric exclusion process on a ring: Exact relaxation dynamics and associated model of clustering transition

On the appearance of traffic jams in a long chain with a shortcut in the bulk

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