Jamming transition in a homogeneous one-dimensional system: The bus route model

Abstract

We present a driven diffusive model that we call the bus route model. The model is defined on a one-dimensional lattice, with each lattice site having two binary variables, one of which is conserved (``buses'') and one of which is nonconserved (``passengers''). The buses are driven in a preferred direction and are slowed down by the presence of passengers who arrive with rate $\ensuremath{\lambda}.$ We study the model by simulation, heuristic argument, and a mean-field theory. All these approaches provide strong evidence of a transition between an inhomogeneous ``jammed'' phase (where the buses bunch together) and a homogeneous phase as the bus density is increased. However, we argue that a strict phase transition is present only in the limit $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\lambda}}0.$ For small $\ensuremath{\lambda},$ we argue that the transition is replaced by an abrupt crossover that is exponentially sharp in $1/\ensuremath{\lambda}.$ We also study the coarsening of gaps between buses in the jammed regime. An alternative interpretation of the model is given in which the spaces between buses and the buses themselves are interchanged. This describes a system of particles whose mobility decreases the longer they have been stationary and could provide a model for, say, the flow of a gelling or sticky material along a pipe.

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• Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics - View
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