论文标题
速度跳跃过程，在狭窄的频道中排除音量
Velocity jump process with volume exclusions in a narrow channel
论文作者
论文摘要
本文分析了根据速度跳跃过程驱动的$ n $相同硬核粒子系统中碰撞的影响。物理空间本质上是$ \ mathbb {r} $中的通道，占用者能够相互传递的可能性。该系统模仿自然的作用，个人在狭窄的频道中相互通过，同时与朝相反方向移动的人进行偶然接触。传递概率可能取决于粒子的大小和通道的宽度。从粒子水平模型开始，我们根据渐近扩展系统地得出非线性传输方程。在低占主导的馏分下，在偏见和无偏的随机速度变化期间，可以很好地比较动力学模型和随机粒子系统的数值解。对大种群中亚种群运动的分析表现出体积排除的后果和在行进速度上的通道限制的后果。
This paper analyses the impact of collisions in a system of $N$ identical hard-core particles driven according to a velocity jump process. The physical space is essentially a channel in $\mathbb{R}$ with a probability of occupants being able to pass each other. The system mimics what nature does, where individuals pass one another in a narrow channel while making incidental contact with those moving in the opposite direction. The passing probability may depend on the particles' size and the channel's width. Starting from the particle level model, we systematically derive a nonlinear transport equation based on an asymptotic expansion. Under low-occupied fractions, numerical solutions of both the kinetic model and the stochastic particle system are compared well during biased and unbiased random velocity changes. Analysis of the subpopulation motility within a large population exhibits the consequences of volume exclusions and channel confinements on the travelling speeds.
