Density Fluctuations in Stochastic Kinematic Flows

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