具有随机重置和粘性边界的跑- tumble 粒子的再生理论
Renewal theory for a run-and-tumble particle with stochastic resetting and a sticky boundary
AI总结：
本文研究了具有随机重置和粘性边界的跑- tumble 粒子的再生理论，探讨了不同脱附协议对平均首次通过时间的影响。
摘要：
我们考虑一个受随机重置限制在半轴[0,∞)上的跑- tumble 粒子(RTP)，其在边界x=0处具有粘性。在介质中，RTP以恒定速率α>0在速度状态±v之间翻转，其中v>0，并随机重置到其初始位置和方向(x₀,k₀)∈(ℝ⁺,±)。当RTP到达目标x=0时，它会粘附到边界上进行随机等待时间，然后要么脱离并继续在介质中导航，或者(永久性)进入目标。这些事件是物理化学中粒子与部分反应表面吸附、脱附和吸收的类比。我们利用再生理论来描述粒子轨迹，基于连续的粘附事件，在两种不同的脱附协议下：通过重置到(x₀,k₀)和通过从x=0连续移动以速度+v。首先，我们推导了无吸收情况下的非平衡稳态(NESS)，并表征了边界处的积累。其次，我们计算了平均首次通过时间(MFPT)的统计特性。除了观察到MFPT通常对介质中重置的单峰依赖外，NESS和MFPT都强烈依赖于初始方向k₀和脱附协议。例如，如果初始方向朝向边界，我们发现由脱附诱导的重置协议可以比非重置脱附协议更有效地减少MFPT。我们还展示了如何匹配脱附动力学与介质中重置或翻转速率引入了在最小化吸附和吸收时间之间的权衡。在这种情况下，我们发现对于给定参数集，使吸收MFPT最小化的脱附协议几乎总是与当脱附和介质动力学不同时所偏好的相反。
英文摘要：
We consider a run-and-tumble particle (RTP) with stochastic resetting confined to the half line $[0,\infty)$ with a sticky boundary at $x=0$. In the bulk the RTP tumbles at a constant rate $α>0$ between velocity states $\pm v$ with $v>0$ and randomly resets to its initial position and orientation $(x_0,k_0)\in(\mathbb{R}^+,\pm)$. When the RTP reaches the target at $x=0$ it attaches to the boundary for a random waiting time before either detaching and continuing to navigate the bulk domain or (permanently) entering the target. These events are the analogs of adsorption, desorption, and absorption of a particle by a partially reactive surface in physical chemistry. We use renewal theory to characterize the particle trajectory in terms of successive binding events under two distinct desorption protocols: via resetting to $(x_0,k_0)$ and via continuous movement from $x=0$ with velocity $+v$. First we derive the nonequilibrum stationary state (NESS) in the case of no absorption and characterize the accumulation at the boundary. Second, we compute the mean first passage time (MFPT) statistics. In addition to observing the usual unimodal dependence of the MFPT on bulk resetting, both the NESS and MFPT strongly depend on the initial orientation $k_0$ and the desorption protocol. For instance, if the initial orientation is toward the boundary, we find that the desorption-induced resetting protocol can reduce the MFPT more effectively than the non-resetting desorption protocol. We also show how matching the desorption kinetics with the bulk resetting or tumbling rate introduces a trade-off between minimizing the adsorption and absorption times. In this setting we find that the desorption protocol which minimizes the absorption MFPT for a given set of parameters is almost always the opposite of that favored when desorption and bulk kinetics are not the same.
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