论文标题
在一个维度中的边界翻滚粒子系统的精确解决方案
Exact solution of a boundary tumbling particle system in one dimension
论文作者
论文摘要
我们将完全依赖时间的解决方案推导到粒子的跑步模型，该模型限制在一维间隔的边界。这是通过利用扰动理论的优雅基础结构来通过现场理论扰动框架实现的。我们计算粒子密度，电流和方差以及边界翻滚的特征。与蒙特 - 卡洛模拟一致的分析结果表明，粒子密度如何与边界处的扩散波动的规模相关。我们方法的普遍性表明，它可以很容易地应用于包含局部反应项的Fokker-Planck方程所描述的类似问题。
We derive the fully time-dependent solution to a run-and-tumble model for a particle which has tumbling restricted to the boundaries of a one-dimensional interval. This is achieved through a field-theoretic perturbative framework by exploiting an elegant underlying structure of the perturbation theory. We calculate the particle densities, currents and variance as well as characteristics of the boundary tumbling. The analytical findings, in agreement with Monte-Carlo simulations, show how the particle densities are linked to the scale of diffusive fluctuations at the boundaries. The generality of our approach suggests it could be readily applied to similar problems described by Fokker-Planck equations containing localised reaction terms.
