Effective ergodicity breaking in an exclusion process with varying system length

Schultens, Christoph; Schadschneider, Andreas; Arita, Chikashi

doi:10.1016/j.physa.2015.03.068

Cited by 4 publications

(3 citation statements)

References 34 publications

(41 reference statements)

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“…This means, that depending on the initial preparation of the system, MC/EX or EX/MC, the final state of the system is MC or EX, respectively, and thus ergodicity seems to be broken. Similar observations were made recently for an exclusive queuing model [52]. The parameter regime where the phenomenon occurs can be determined from the conditions v MC/EX > 0 and v EX/MC > 0.…”

Section: F Intermittent Phasesupporting

confidence: 75%

Traffic Dynamic Instability

Reese¹,

Melbinger²,

Frey³

2015

Preprint

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Section: F Intermittent Phasesupporting

confidence: 75%

Traffic Dynamic Instability

Reese¹,

Melbinger²,

Frey³

2015

Preprint

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“…Here one has N ∼ N * , thus the average car density is equilibrated at the threshold and the control mechanism leads to a maximization of the flow. Note that the grey shaded area is physically unreasonable in the present context but has applications in Langmuir kinetics 9 .…”

Section: Introductionmentioning

confidence: 99%

Queuing model of a traffic bottleneck with bimodal arrival rate

Woelki

2016

Int. J. Mod. Phys. B

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This paper revisits the problem of tuning the density in a traffic bottleneck by reduction of the arrival rate when the queue length exceeds a certain threshold, studied recently for variants of totally asymmetric simple exclusion process (TASEP) and Burgers equation. In the present approach, a simple finite queuing system is considered and its contrasting “phase diagram” is derived. One can observe one jammed region, one low-density region and one region where the queue length is equilibrated around the threshold. Despite the simplicity of the model the physics is in accordance with the previous approach: The density is tuned at the threshold if the exit rate lies in between the two arrival rates.

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“…In a further interesting line of research, extensions of the TASEP to dynamic lattices have been developed [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. On the one hand, motivated by the transport of vesicles along microtubules that facilitate growth of fungal hyphae, or by growth of flagellar filaments, TASEP models have been considered in which a particle that reaches the end of the lattice may extend it by a single site [12,14,15,17,22].…”

Section: Introductionmentioning

confidence: 99%

Self-organized system-size oscillation of a stochastic lattice-gas model

2018

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The totally asymmetric simple exclusion process (TASEP) is a paradigmatic stochastic model for nonequilibrium physics, and has been successfully applied to describe active transport of molecular motors along cytoskeletal filaments. Building on this simple model, we consider a two-lane lattice-gas model that couples directed transport (TASEP) to diffusive motion in a semiclosed geometry, and simultaneously accounts for spontaneous growth and particle-induced shrinkage of the system's size. This particular extension of the TASEP is motivated by the question of how active transport and diffusion might influence length regulation in confined systems. Surprisingly, we find that the size of our intrinsically stochastic system exhibits robust temporal patterns over a broad range of growth rates. More specifically, when particle diffusion is slow relative to the shrinkage dynamics, we observe quasiperiodic changes in length. We provide an intuitive explanation for the occurrence of these self-organized temporal patterns, which is based on the imbalance between the diffusion and shrinkage speed in the confined geometry. Finally, we formulate an effective theory for the oscillatory regime, which explains the origin of the oscillations and correctly predicts the dependence of key quantities, such as the oscillation frequency, on the growth rate.

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Effective ergodicity breaking in an exclusion process with varying system length

Cited by 4 publications

References 34 publications

Traffic Dynamic Instability

Traffic Dynamic Instability

Queuing model of a traffic bottleneck with bimodal arrival rate

Self-organized system-size oscillation of a stochastic lattice-gas model

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