Residence time estimates for asymmetric simple exclusion dynamics on strips

Abstract

The target of our study is to approximate numerically and, in some particular physically relevant cases, also analytically, the residence time of particles undergoing an asymmetric simple exclusion dynamics on a vertical strip. The source of asymmetry is twofold: (i) the choice of boundary conditions (different reservoir levels) and (ii) the strong anisotropy from a nonlinear drift with prescribed directionality. We focus on the effect of the choice of anisotropy in the flux on the asymptotic behavior of the residence time with respect to the length of the strip. The topic is relevant for situations occurring in pedestrian flows or biological transport in crowded environments, where lateral displacements of the particles occur predominantly affecting therefore in an essentially way the efficiency of the ENMC thanks Kerry Landman (Melbourne), Roberto Fernández (Utrecht), and Lorenzo Bertini (Roma) for very stimulating discussions and useful references. cms-serw001.tex -1 agosto 2018 22:05 arXiv:1411.5490v2 [nlin.CG] 9 Feb 2015 overall transport mechanism.

Simple diffusion hopping model with convection

“…While CDLM convective dynamics ensures particle motion using an external body force, the net transport of particles from the inlet to outlet region in traditional diffusion hopping systems is sustained by implementing a biased diffusion where the probability for a particle to diffuse to the right P D i,1 = D 1 and the probability for all other destination cells is D 0 . This approach is similar to that used in studies of residency time on vertical strips [14] and in driven diffusive systems [24] where particles can be argued to move from an inlet region to an outlet region subject to an external potential field.…”

“…An extensively used algorithm for these studies is the particle hopping model where particles can hop between discrete cells on a lattice subject to specific movement rules or by diffusing to adjacent unoccupied cells [1]. Particle hopping models have been applied to study a variety of systems such as particle transport in disordered media [2,3], diffusion at material interfaces [4,5], the diffusion of large particles in unentangled polymer solids [6], water diffusion in cell suspension systems [7], traffic flows [8][9][10], ion transport through biological membranes [11,12], biological systems involving the movement of animals, micro-organisms or cells [13], and particle residency times in two-dimensional vertical strips [14].…”

“…In the CDLM, particle positions and dynamics are restricted to district locations on a regular underlying lattice where particles interact subject to excluded volume conditions as in previous particle hopping models [3,4,14] and lattice gas methods (LGMs) which can be used to describe convective motion [15,16]. The main difference between previous hopping models and the CDLM is the inclusion of a continuous velocity field to capture memory bias in particle displacement, a core property of convection.…”

Lattice model of reduced jamming by a barrier

“…Lattice models of particle flow may show surprisingly rich behavior even when only exclusion of a particle on the same site is considered [1]. Complex percolation behavior arises in particular at increased particle concentration (see Ref.…”

“…We have explored extensively in a previous paper (see Ref. [1]) the two-dimensional (2D) diffusion-drift strip lattice model used in this context, but without barriers. In this paper, our 2D lattice is perturbed by an immobile barrier with a fixed rectangular shape.…”