Hydrodynamic mean-field solutions of 1D exclusion processes with spatially varying hopping rates

  title={Hydrodynamic mean-field solutions of 1D exclusion processes with spatially varying hopping rates},
  author={Greg Lakatos and Jackson O'Brien and Tom Chou},
  journal={Journal of Physics A},
We analyse the open boundary partially asymmetric exclusion process with smoothly varying internal hopping rates in the infinite-size, mean-field limit. The mean-field equations for particle densities are written in terms of Ricatti equations with the steady-state current J as a parameter. These equations are solved both analytically and numerically. Upon imposing the boundary conditions set by the injection and extraction rates, the currents J are found self-consistently. We find a number of… 

Figures from this paper

Smoothly varying hopping rates in driven flow with exclusion.
Numerical simulations of systems with hopping rates varying linearly against position (constant rate gradient), for both periodic and open-boundary conditions, provide detailed confirmation of theoretical predictions, concerning steady-state average density profiles and currents, as well as open-system phase boundaries, to excellent numerical accuracy.
Asymmetric simple exclusion process with position-dependent hopping rates: Phase diagram from boundary-layer analysis.
This paper studies a one-dimensional totally asymmetric simple exclusion process with position-dependent hopping rates that exhibits boundary-induced phase transitions in the steady state, and shows how the shape of the entire density profile including the location of the boundary layers can be predicted from the fixed points of the differential equation describing the boundary layer.
Characteristics of the asymmetric simple exclusion process in the presence of quenched spatial disorder.
It is shown that the impact of disorder crucially depends on the particle input and out rates, and in some situations, disorder can constructively enhance the current.
Macroscopic Transport Equations in Many-Body Systems from Microscopic Exclusion Processes in Disordered Media: A Review
Describing particle transport at the macroscopic or mesoscopic level in non-ideal environments poses fundamental theoretical challenges in domains ranging from inter and intra-cellular transport in
Partially asymmetric exclusion processes with sitewise disorder.
The stationary properties as well as the nonstationary dynamics of the one-dimensional partially asymmetric exclusion process with position-dependent random hop rates are studied, like coarsening and invasion.
Successive defects asymmetric simple exclusion processes with particles of arbitrary size
This paper uses various mean-field approaches and the Monte Carlo simulation to calculate asymmetric simple exclusion processes with particles of arbitrary size in the successive defects system. In
Spreading in narrow channels.
A lattice model for the spreading of fluid films, which are a few molecular layers thick, in narrow channels with inert lateral walls, finds a diffusive behavior using kinetic Monte Carlo simulations.
Local inhomogeneity in two-lane asymmetric simple exclusion processes coupled with Langmuir kinetics
The effects of local inhomogeneity in a two-lane asymmetric simple exclusion process coupled with Langmuir kinetics are studied. The model is related to some biological processes such as the movement
Non-equilibrium statistical mechanics: from a paradigmatic model to biological transport
This work provides detailed mathematical analyses of a one-dimensional continuous-time lattice gas, the totally asymmetric exclusion process, regarded as a paradigmatic model for NESM, much like the role the Ising model played for equilibrium statistical mechanics.
Stochastic models of intracellular transport
The interior of a living cell is a crowded, heterogenuous, fluctuating environment. Hence, a major challenge in modeling intracellular transport is to analyze stochastic processes within complex


Totally asymmetric simple exclusion process with Langmuir kinetics.
A class of driven lattice gas obtained by coupling the one-dimensional totally asymmetric simple exclusion process to Langmuir kinetics is discussed, and phenomena that go beyond mean-field such as the scaling properties of the domain wall are elucidated.
Steady-state properties of a totally asymmetric exclusion process with periodic structure.
The condition for particle-hole symmetry in the TASEP with periodically varying movement rates is specified, and the changes in the locations of the boundary-limited to maximal-current transition lines due to symmetry violation are investigated.
Partially asymmetric exclusion process with open boundaries.
  • Sandow
  • Mathematics, Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1994
The model is equivalent to an XXZ-Heisenberg chain with a certain type of boundary terms, the ground state of which corresponds to the stationary solution of the master equation.
Phase diagram of one-dimensional driven lattice gases with open boundaries
We consider the asymmetric simple exclusion process (ASEP) with open boundaries and other driven stochastic lattice gases of particles entering, hopping and leaving a one- dimensional lattice. The
An exact solution of a one-dimensional asymmetric exclusion model with open boundaries
A simple asymmetric exclusion model with open boundaries is solved exactly in one dimension. The exact solution is obtained by deriving a recursion relation for the steady state: if the steady state
Representations of the quadratic algebra and partially asymmetric diffusion with open boundaries
We consider the one-dimensional partially asymmetric exclusion model with open boundaries. The model describes a system of hard-core particles that hop stochastically in both directions with
Abstract A number of exact results have been obtained recently for the one-dimensional asymmetric simple exclusion process, a model of particles which hop to their right at random times, on a
Shock formation in an exclusion process with creation and annihilation.
It is shown how the continuum mean-field equations can be studied analytically and hence derive the phase diagrams of the model and the stationary distribution of shock positions is calculated, by virtue of which the numerically determined finite-size scaling behavior of the shock width is explained.
Phase transitions in an exactly soluble one-dimensional exclusion process
We consider an exclusion process with particles injected with rate α at the origin and removed with rate β at the right boundary of a one-dimensional chain of sites. The particles are allowed to hop
Asymmetric simple exclusion model with local inhomogeneity
We study a totally asymmetric simple exclusion model with open boundary conditions and a local inhomogeneity in the bulk. It consists of a one-dimensional lattice with particles hopping