Lattice model of reduced jamming by a barrier

Abstract

We study an asymmetric simple exclusion process in a strip in the presence of a solid impenetrable barrier. We focus on the effect of the barrier on the residence time of the particles, namely, the typical time needed by the particles to cross the whole strip. We explore the conditions for reduced jamming when varying the environment (different drifts, reservoir densities, horizontal diffusion walks, etc.). In particular, we discover an interesting nonmonotonic behavior of the residence time as a function of the barrier length. Besides recovering by means of both the lattice dynamics and the mean-field model well-known aspects like the faster-is-slower effect and the intermittence of the flow, we propose also a birth-and-death process and a reduced one-dimensional (1D) model with variable barrier permeability to capture the behavior of the residence time with respect to the parameters.

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

“…It is worth mentioning that the problem we study here shares some features with the so-called blockage problem [20][21][22], where one considers a 1D dynamics with a slow down bond or site. The main problem, there, is that of understanding the effect of the local slow down on the stationary current in the thermodynamics limit.…”

“…The residence time issue, as described above, has been firstly raised in [23,24], where the flow of particles in an horizontal strip undergoing a random walk with exclusion rule has been considered [25]. One of the most interesting results investigated in those papers is the possibility to spot complex behaviors, in the sense that the residence time unexpectedly shows up to be a not monotonic function of some parameters of the obstacles.…”

Uphill migration in coupled driven particle systems

“…In this paper we focus on the behavior of the profiles ρ i and the mass displacement χ as a function of the model parameters. For given parameters, we obtain the exact value by first solving equations (8) to compute the π i 's, and then equation (9) and (10). In the simulations, the total number of particles is N = 200 and L = 50.…”

“…Then τ up is defined as the mean time (over the evolution and over particles) between entering and exiting the upper ring, in the stationary state; τ down is defined analogously. Sojourn times are similar to the residence times that have been widely studied for the simple exclusion process [10] and for the simple symmetric random walk [11]. The main difference is that in those studies the geometry of the strip was considered and the residence time was defined conditioning the particle to exit the strip through the side opposite the one where it started the walk.…”

Residence time of symmetric random walkers in a strip with large reflective obstacles

“…In those papers a thorough study of the residence time properties as a function of the details of the dynamics, such as the horizontal drift, has been provided and in [24] two different analytic tools have been developed. In [23] it has been shown that, in some regimes, the residence time is not monotonic with respect to the size of the obstacle. This complex behavior has been related to the way in which particles are distributed along the strip at stationarity, more precisely, it has been explained in terms of the occupation number profile, which strongly depends on how particles interact due to the presence of the exclusion rule.…”