On the Blockage Problem and the Non-analyticity of the Current for Parallel TASEP on a Ring

Eur. Phys. J. Spec. Top.

2019

The effect of space inhomogeneities on a diffusing particle is studied in the framework of the 1D random walk. The typical time needed by a particle to cross a onedimensional finite lane, the so-called residence time, is computed possibly in presence of a drift. A local inhomogeneity is introduced as a single defect site with jumping probabilities differing from those at all the other regular sites of the system. We find complex behaviors in the sense that the residence time is not monotonic as a function of some parameters of the model, such as the position of the defect site. In particular we show that introducing at suitable positions a defect opposing to the motion of the particles decreases the residence time, i.e., favors the flow of faster particles. The problem we study in this paper is strictly connected to the classical gambler's ruin problem, indeed, it can be thought as that problem in which the rules of the game are changed when the gambler's fortune reaches a particular a priori fixed value. The problem is approached both numerically, via Monte Carlo simulations, and analytically with two different techniques yielding different representations of the exact result.

Section: Introductionmentioning

confidence: 99%

Conditional expectation of the duration of the classical gambler problem with defects

Ciallella

Eur. Phys. J. Spec. Top.

2019

“…A classical question in this field is the so-called blockage problem, posed in [17] for the totally asymmetric simple exclusion process on a ring. The question is whether slowing down a single bond on the lattice can ultimately affect the value of the stationary current in the infinite volume limit, see also [18][19][20] for related results for different models.…”

Section: Introductionmentioning

confidence: 99%

“…Squares and circles refer, respectively, to the independent particle (left panel) and the simple exclusion-like (right panel) models. The dashed lines represent the exact solution given in(19). The stationary density profiles have been computed by averaging, after the thermalization time is reached, over a set of 10 6 instantaneous particle configurations.…”

mentioning

confidence: 99%

Stationary uphill currents in locally perturbed zero-range processes

Colangeli

2017

Phys. Rev. E

Uphill currents are observed when mass diffuses in the direction of the density gradient. We study this phenomenon in stationary conditions in the framework of locally perturbed one-dimensional zero range processes (ZRPs). We show that the onset of currents flowing from the reservoir with smaller density to the one with larger density can be caused by a local asymmetry in the hopping rates on a single site at the center of the lattice. For fixed injection rates at the boundaries, we prove that a suitable tuning of the asymmetry in the bulk may induce uphill diffusion at arbitrarily large, finite volumes. We also deduce heuristically the hydrodynamic behavior of the model and connect the local asymmetry characterizing the ZRP dynamics to a matching condition relevant for the macroscopic problem.

“…The effect of bottlenecks on a flow in a lane is relevant in many applied contexts such as traffic [1,2] and pedestrian [3,4,5,6,7] flows, motion in biological systems [9,8], but also in more abstract problems such as the study of the effect of blockage in stationary states [10,11,12] or the effect of obstacles on two-dimensional particle flows [13,14,15].…”

Section: Introductionmentioning

confidence: 99%

Trapping in bottlenecks: Interplay between microscopic dynamics and large scale effects

Physica A: Statistical Mechanics and its Applications

Colangeli

Muntean

2017

Abstract. We investigate the appearance of trapping states in pedestrian flows through bottlenecks as a result of the interplay between the geometry of the system and the microscopic stochastic dynamics. We model the flow trough a bottleneck via a Zero Range Process on a one dimensional periodic lattice. Particle are removed from the lattice sites with rates proportional to the local occupation numbers. The bottleneck is modelled by a particular site of the lattice where the updating rate saturates to a constant value as soon as the local occupation number exceeds a fixed threshold. We show that, for any finite value of such threshold, the stationary particle current saturates to the limiting bottleneck rate when the total particle density in the system exceeds the bottleneck rate itself.