论文标题
随机运动学的密度波动
Density Fluctuations in Stochastic Kinematic Flows
论文作者
论文摘要
在宏观尺度上，许多集体运动的许多重要模型都属于运动流的类别，这些运动流的速度和扩散项仅取决于粒子密度。当总粒子数固定并有限时，相应的微观动力学的模拟会显示随机效应，这些效应可能会诱导大型系统极限中不存在的各种有趣的行为。在本文中，我们对一般粒子模型的有限大小波动进行了系统的检查，该模型的统计数据与随机运动学的统计数据相对应。这样做，我们能够表征现象，包括：交通流量模型中的准jam；空间耦合振荡器之间的随机模式形成；多孔培养基中的异常散装分散；和细菌蜂群模型中的行驶波波动。
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 behaviours 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 characterise phenomena including: quasi-jams in models of traffic flow; stochastic pattern formation amongst spatially-coupled oscillators; anomalous bulk sub-diffusion in porous media; and travelling wave fluctuations in a model of bacterial swarming.
