Dynamic Singularities in Cooperative Exclusion

Abstract

We investigate cooperative exclusion, in which the particle velocity can be an increasing function of the density. Within a hydrodynamic theory, an initial density upsteps and downsteps can evolve into: (a) shock waves, (b) continuous compression or rarefaction waves, or (c) a mixture of shocks and continuous waves. These unusual phenomena arise because of an inflection point in the current versus density relation. This anomaly leads to a group velocity that can either be an increasing or a decreasing function of the density on either side of these wave singularities.

4 pages, 4 figures, 2 column revtex 4-1 format; version 2: substantially rewritten and put in IOP format, mail results unchanged; version 3: minor changes, final version for publication in JSTAT

References in corpus (9)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Phase transitions in an exactly soluble one-dimensional exclusion process
• Jamming transition in a homogeneous one-dimensional system: the Bus Route Model
• Steady-state selection in driven diffusive systems with open boundaries
• Asymmetric exclusion process with next-nearest-neighbor interaction: some comments on traffic flow and a nonequilibrium reentrance transition
• Active Absorbing State Phase Transition Beyond Directed Percolation : A Class of Exactly Solvable Models
• Facilitated Asymmetric Exclusion
• Collective effects in intra-cellular molecular motor transport: coordination, cooperation and competetion

Cited by in corpus (7)

• Facilitated exclusion process
• Entrainment and unit velocity: Surprises in an accelerated exclusion process
• Stationary States of the One-Dimensional Discrete-Time Facilitated Symmetric Exclusion Process
• Stationary States of the One-dimensional Facilitated Asymmetric Exclusion Process
• Exclusion Processes with Avalanches
• Mass transport perspective on an accelerated exclusion process: Analysis of augmented current and unit-velocity phases
• Approach to Hyperuniformity in the One-Dimensional Facilitated Exclusion Process