JAMMING TRANSITION IN A HOMOGENEOUS ONE-DIMENSIONAL SYSTEM - THE BUS ROUTE MODEL

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 s ite having two binary variables, one of which is conserved (''buses'') and one of which is nonconserved (''passengers''). The buses are driv en in a preferred direction and are slowed down by the presence-of pas sengers who arrive with rate lambda. We study the model by simulation, heuristic argument, and a mean-held theory. All these approaches prov ide strong evidence of a transition between an inhomogeneous ''jammed' ' phase (where the buses bunch together) and a homogeneous phase as th e bus density is increased. However, we argue that a strict phase tran sition is present only in the limit lambda --> 0. For small lambda, we argue that the transition is replaced by an abrupt crossover that is exponentially sharp in 1/lambda. We also study the coarsening of gaps between buses in the jammed regime. An alternative interpretation of t he model is given in which the spaces between buses and the buses them selves are interchanged. This describes a system of particles whose mo bility decreases the longer they have been stationary and could provid e a model for, say, the flow of a gelling or sticky material along a p ipe.