The asymmetric exclusion process: Comparison of update procedures

Abstract

The asymmetric exclusion process (ASEP) has attracted a lot of interest not only because its many applications, e.g. in the context of the kinetics of biopolymerization and traffic flow theory, but also because it is a paradigmatic model for nonequilibrium systems. Here we study the ASEP for different types of updates, namely random-sequential, sequential, sublattice-parallel and parallel. In order to compare the effects of the different update procedures on the properties of the stationary state, we use large-scale Monte Carlo simulations and analytical methods, especially the so-called matrix-product Ansatz (MPA). We present in detail the exact solution for the model with sublattice-parallel and sequential updates using the MPA. For the case of parallel update, which is important for applications like traffic flow theory, we determine the phase diagram, the current, and density profiles based on Monte Carlo simulations. We furthermore suggest a MPA for that case and derive the corresponding matrix algebra.

47 pages (11 PostScript figures included), LATEX, Two misprints in equations corrected

References in corpus (10)

• Partially Asymmetric Exclusion Process with Open Boundaries
• Exact Steady States of Disordered Hopping Particle Models with Parallel and Ordered Sequential Dynamics
• Time-dependent correlation functions in a one-dimensional asymmetric exclusion process
• Matrix Product Eigenstates for One-Dimensional Stochastic Models and Quantum Spin Chains
• Matrix Product Ground States for Asymmetric Exclusion Processes with Parallel Dynamics
• The asymmetric exclusion model with sequential update
• Experiences with a simplified microsimulation for the Dallas/Fort Worth area
• Matrix-Product States for a One-Dimensional Lattice Gas with Parallel Dynamics
• Exact results for one dimensional stochastic cellular automata for different types of updates
• Optimum ground states for spin-$\frac{3}{2}$ chains

Cited by in corpus (9)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Exact solution of a cellular automaton for traffic
• The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
• Exact solution of an exclusion process with three classes of particles and vacancies
• Matrix Ansatz for the Fluctuations of the Current in the ASEP with Open Boundaries
• Wake-mediated interaction between driven particles crossing a perpendicular flow
• Exact stationary state for a deterministic high speed traffic model with open boundaries
• Exact domain wall theory for deterministic TASEP with parallel update
• Effects of Quantum Pair Creation and Annihilation on a Classical Exclusion Process: the transverse XY model with TASEP