Nonequilibrium steady states in asymmetric exclusion processes on a ring with bottlenecks

Sarkar, Niladri; Basu, Abhik

doi:10.1103/physreve.90.022109

Cited by 20 publications

(31 citation statements)

References 25 publications

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“…In other words, the bulk density should be uniform for sufficiently low average density. For a ring geometry, this implies n I (x) = K/(1 + K), with n I (x) = n 0 + h having a localised peak of height h = n 0 (1 − p)/p at the location of the point defect [10,12]. This is consistent with our discussions above.…”

Section: B Mf Analysis and Mcs Results For A Point Defectsupporting

confidence: 85%

“…As argued in Refs. [10,12], for a sufficiently low average density, the effect of the point defect is confined to creating a localised peak (or a dip) that has a vanishing width in the thermodynamic limit, in an otherwise homogeneous density profiles. In other words, the bulk density should be uniform for sufficiently low average density.…”

Section: B Mf Analysis and Mcs Results For A Point Defectmentioning

confidence: 99%

“…Nonuniform or inhomogeneous steady states are expected only with explicit breakdown of the translation invariance, e.g., by means of quench disorder in the hopping rates at different sites. Exclusion processes in closed inhomogeneous rings with strict particle number conservation have been shown to display inhomogeneous NESS [11][12][13]. More recently, TASEP in a ring with quench disordered hopping rates together with nonconserving LK having equal rates of particle attachment and detachment has been studied in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Nonequilibrium steady states in a closed inhomogeneous asymmetric exclusion process with generic particle nonconservation

Daga¹,

Mondal²,

Chandra³

et al. 2017

Phys. Rev. E

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We study the totally asymmetric exclusion process (TASEP) on a nonuniform one-dimensional ring consisting of two segments having unequal hopping rates, or defects. We allow weak particle nonconservation via Langmuir kinetics (LK), which are parametrized by generic unequal attachment and detachment rates. For an extended defect, in the thermodynamic limit the system generically displays inhomogeneous density profiles in the steady state-the faster segment is either in a phase with spatially varying density having no density discontinuity, or a phase with a discontinuous density changes. Nonequilibrium phase transitions between the above phases are controlled by the inhomogeneity and LK. The slower segment displays only macroscopically uniform bulk density profiles in the steady states, reminiscent of the maximal current phase of TASEP but with a bulk density generally different from half. With a point defect, there are spatially uniform low- and high-density phases as well, in addition to the inhomogeneous density profiles observed for an extended defect. In all the cases, it is argued that the mean particle density in the steady state is controlled only by the ratio of the LK attachment and detachment rates.

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Section: B Mf Analysis and Mcs Results For A Point Defectsupporting

confidence: 85%

Section: B Mf Analysis and Mcs Results For A Point Defectmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonequilibrium steady states in a closed inhomogeneous asymmetric exclusion process with generic particle nonconservation

Daga¹,

Mondal²,

Chandra³

et al. 2017

Phys. Rev. E

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“…respectively, according to eqs. (17) and (24). We expect that the discrepancies between the prediction and simulations are due to the finite-size effect.…”

Section: -Segment Tasepmentioning

confidence: 91%

Synchronized shocks in an inhomogeneous exclusion process

Arita

2015

EPL

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We study an exclusion process with 4 segments, which was recently introduced by T Banerjee, N Sarkar and A Basu [J. Stat. Mech. (2015) P01024]. The segments have hopping rates 1, r(< 1), 1 and r, respectively. In a certain parameter region, two shocks appear, which are not static but synchronized. We explore dynamical properties of each shock and correlation of shocks, by means of the so-called second-class particle. The mean-squared displacement of shocks has three diffusive regimes, and the asymptotic diffusion coefficient is different from the known formula. In some time interval, it also exhibits sub-diffusion, being proportional to t 1/2 . Furthermore we introduce a correlation function and a crossover time, in order to quantitatively characterize the synchronization. We numerically estimate the dynamical exponent for the crossover time. We also revisit the 2-segment case and the open boundary condition for comparison.

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“…In the case of repulsive interaction, where a similar chessboardlike ordered phase is formed in the half-filled lattice [45,46], the order-disorder phase transition is modified due to the particle transport [47]. Last, we note that the effect of bottlenecks along a ring was recently studied by considering the asymmetric exclusion process [48], which is the simplest version of the driven lattice gases. The latter investigation is motivated by biological experiments indicating unidirectional circular ribosome translocations along messenger RNA loops with defects or slow codons in cells [49].…”

Section: P(dc) [P(cd)] Increases [Decreases] Linearly With With Thementioning

confidence: 99%

Congestion phenomena caused by matching pennies in evolutionary games

Szabó

Szolnoki

2015

Phys. Rev. E

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Evolutionary social dilemma games are extended by an additional matching-pennies game that modifies the collected payoffs. In a spatial version players are distributed on a square lattice and interact with their neighbors. First, we show that the matching-pennies game can be considered as the microscopic force of the Red Queen effect that breaks the detailed balance and induces eddies in the microscopic probability currents if the strategy update is analogous to the Glauber dynamics for the kinetic Ising models. The resulting loops in probability current breaks symmetry between the chessboardlike arrangements of strategies via a bottleneck effect occurring along the four-edge loops in the microscopic states. The impact of this congestion is analogous to the application of a staggered magnetic field in the Ising model; that is, the order-disorder critical transition is wiped out by noise. It is illustrated that the congestion induced symmetry breaking can be beneficial for the whole community within a certain region of parameters.

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Nonequilibrium steady states in asymmetric exclusion processes on a ring with bottlenecks

Cited by 20 publications

References 25 publications

Nonequilibrium steady states in a closed inhomogeneous asymmetric exclusion process with generic particle nonconservation

Nonequilibrium steady states in a closed inhomogeneous asymmetric exclusion process with generic particle nonconservation

Synchronized shocks in an inhomogeneous exclusion process

Congestion phenomena caused by matching pennies in evolutionary games

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