滚转粒子、电报员方程和部分反射边界的吸收问题

Superdiffusion in self-reinforcing run-and-tumble model with rests

This paper introduces a run-and-tumble model with self-reinforcing directionality and rests. We derive a single governing hyperbolic partial differential equation for the probability density of random walk position, from which we obtain the second moment in the long time limit. We find the criteria for the transition between superdiffusion and diffusion caused by the addition of a rest state. The emergence of superdiffusion depends on both the parameter representing the strength of self-reinforcement and the ratio between mean running and resting times. The mean running time must be at least $…

First hitting times between a run-and-tumble particle and a stochastically-gated target

We study the first hitting time statistics between a one-dimensional run-and-tumble particle and a target site that switches intermittently between visible and invisible phases. The two-state dynamics of the target is independent of the motion of the particle, which can be absorbed by the target only in its visible phase. We obtain the mean first hitting time when the motion takes place in a finite domain with reflecting boundaries. Considering the turning rate of the particle as a tuning parameter, we find that ballistic motion represents the best strategy to minimize the mean first hitting t…

带扩散的奔跑-翻滚粒子：边界局部时间与零扩散极限

Run-and-tumble particle with diffusion: boundary local times and the zero-diffusion limit

本文将带扩散的奔跑-翻滚粒子（RTP）在半直线边界上的随机微分方程理论从无扩散情形推广到含扩散情形，揭示零扩散极限的奇异性，并利用随机微积分和奇异摄动理论处理粘性与部分吸收边界，分析生存概率与首次通过时间密度。

有限尺寸一维非相互作用被动与主动系统中的电流涨落

Current fluctuations in finite-sized one-dimensional non-interacting passive and active systems

本文研究了有限一维盒子中非相互作用扩散粒子和run-and-tumble粒子的effusion问题，推导了边界流出粒子数涨落的解析结果，并证明了在有限系统中annealed和quenched涨落会在特定时间尺度后趋于一致。

近距离接触的粘性类型：吸收边界处的布朗运动

Close encounters of the sticky kind: Brownian motion at absorbing boundaries

本文构建了一维粘性布朗运动接触式模型，计算了粒子位置和占用时间的联合概率密度，以首次跨越随机阈值的占用时间定义吸收事件，并揭示了粘性RTP扩散极限与粘性BM的映射关系。