Exact solution of an exclusion process with three classes of particles and vacancies

Dependence of the transportation time on the sequence in which particles with different hopping probabilities enter a lattice

Smooth transportation has drawn the attention of many researchers and practitioners in several fields. In the present study, we propose a modified model of a totally asymmetric simple exclusion process (TASEP), which includes multispecies of particles and takes into account the sequence in which the particles enter a lattice. We investigate the dependence of the transportation time on this "entering sequence" and show that, for a given collection of particles, group sequence in some cases minimizes the transportation time better than a random sequence. We also introduce the "sorting cost" necessary to transform a random sequence into a group sequence and show that when this is included a random sequence can become advantageous in some conditions. We obtain these results not only from numerical simulations but also by theoretical analyses that generalize the simulation results for some special cases.

Generalized exclusion processes: Transport coefficients

A class of generalized exclusion processes with symmetric nearest-neighbor hopping which are parametrized by the maximal occupancy, k≥1, is investigated. For these processes on hypercubic lattices we compute the diffusion coefficient in all spatial dimensions. In the extreme cases of k=1 (symmetric simple exclusion process) and k=∞ (noninteracting symmetric random walks) the diffusion coefficient is constant, while for 2≤k<∞ it depends on the density and k. We also study the evolution of the tagged particle, show that it exhibits a normal diffusive behavior in all dimensions, and probe numerically the coefficient of self-diffusion.

Understanding totally asymmetric simple-exclusion-process transport on networks: generic analysis via effective rates and explicit vertices

In this paper we rationalize relevant features of totally asymmetric simple-exclusion processes on topologies more complex than a single segment. We present a mean-field framework, exploiting the previously introduced notion of effective rates, which we express in terms of the average particle density on explicitly introduced junction sites. It allows us to construct the phase behavior as well as the current-density characteristic from well-known results for a linear totally asymmetric simple-exclusion-process segment in a very systematic and generic way. We validate the approach by studying a fourfold vertex in all variations in the number of entering/exiting segments and compare our predictions to simulation data. Generalizing the notion of particle-hole symmetry to take into account the topology at a junction shows that the average particle density at the junction constitutes a relevant directly observable parameter which gives detailed insight into the transport process. This is illustrated by a complete study of a simple network with figure-of-eight topology. Finally we generalize the approach to handle rate bias at a junction and discuss the surprisingly rich phenomenology of a biased figure-of-eight structure. This example highlights that the proposed framework is generic and readily extends to other topologies.

One-dimensional partially asymmetric simple exclusion process on a ring with a defect particle

The effect of a moving defect particle for the one-dimensional partially asymmetric simple exclusion process on a ring is considered. The current of the ordinary particles, the speed of the defect particle, and the density profile of the ordinary particles are calculated exactly. The phase diagram for the correlation length is identified. As a by-product, the average and the variance of the particle density of the one-dimensional partially asymmetric simple exclusion process with open boundaries are also computed.