DENSITY FLUCTUATIONS IN STOCHASTIC KINEMATIC FLOWS

At the macroscopic scale, many important models of collective motion fall into the class of kinematic flows for which both velocity and diffusion terms depend only on particle density. When total particle numbers are fixed and finite, simulations of corresponding microscopic dynamics exhibit stochastic effects which can induce a variety of interesting behaviors not present in the large system limit. In this article we undertake a systematic examination of finite-size fluctuations in a general class of particle models whose statistics correspond to those of stochastic kinematic flows. Doing so, we are able to characterize phenomena including quasi-jams in models of traffic flow; stochastic pattern formation among spatially coupled oscillators; anomalous bulk subdiffusion in porous media; and travelling wave fluctuations in a model of bacterial swarming.