论文标题
从微观溶液到具有后坐力相互作用的活动粒子的连续描述
From a microscopic solution to a continuum description of active particles with a recoil interaction in one dimension
论文作者
论文摘要
我们考虑一个持续的随机步行者的模型系统，该系统可以挤压，彼此穿过或在接触时跳动（后坐力）。在连续限制中，方向随机变化之间的粒子运动变得确定性，我们发现固定的粒子间分布函数受不均匀的四阶微分方程的控制。我们的主要重点是确定这些分布功能应满足的边界条件。我们发现，这些并非自然而然地来自物理考虑，而需要仔细匹配与对基本离散过程的分析产生的功能形式。粒子间分布函数或其第一个衍生物通常在边界处被发现是不连续的。
We consider a model system of persistent random walkers that can jam, pass through each other or jump apart (recoil) on contact. In a continuum limit, where particle motion between stochastic changes in direction becomes deterministic, we find that the stationary inter-particle distribution functions are governed by an inhomogeneous fourth-order differential equation. Our main focus is on determining the boundary conditions that these distribution functions should satisfy. We find that these do not arise naturally from physical considerations, but need to be carefully matched to functional forms that arise from the analysis of an underlying discrete process. The inter-particle distribution functions, or their first derivatives, are generically found to be discontinuous at the boundaries.
