发表机构
Imperial College London（帝国理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究二维有界域中边界诱导重置对单粒子扩散搜索的影响，利用更新理论、匹配渐近分析和格林函数计算平均首次通过时间，发现仅当重置点靠近目标时才能降低MFPT。
AI 中文摘要
大多数关于带重置的随机搜索过程的研究都集中在自发重置事件上，这些事件通常由泊松过程生成的随机时间序列触发。自发重置的一个主要后果是，在无界域中它会产生有限的平均首次通过时间（MFPT），从而得到一个最优重置率，使MFPT最小化。在有界域中，只要重置点离目标不太远，也可能出现最优重置率。近年来，人们对基于事件而非自发重置的兴趣日益增长，其中当达到特定阈值时触发重置。将阈值与物理上的非目标边界等同起来，就导致了所谓的边界诱导重置。在本文中，我们探讨了边界诱导重置对二维（2D）有界域Ω中单粒子扩散搜索的影响，该域包含一个或多个小的内部目标。内部目标边界完全吸收，而外部边界∂Ω是粘性的。也就是说，每当粒子到达∂Ω上的某一点时，它会附着在那里等待一个随机等待时间τ，之后立即重置到固定的内部点x₀∈Ω。利用更新理论、匹配渐近分析和格林函数，我们计算了被任一目标吸收的无条件MFPT，并将其与同一域上具有反射表面∂Ω且无重置的搜索过程的相应MFPT进行比较。我们表明，只有当搜索者的重置点x₀足够接近其中一个目标时，边界诱导重置才会相对于无重置情况降低MFPT。
英文摘要
Most studies of stochastic search processes with resetting focus on spontaneous resetting events that occur at a random sequence of times typically generated by a Poisson process. One of the major consequences of spontaneous resetting is that it yields a finite mean first passage time (MFPT) in unbounded domains, resulting in an optimal resetting rate that minimises the MFPT. An optimal resetting rate can also occur in bounded domains provided that the reset point is not too far from the target. Recently, there has been growing interest in event-based rather than spontaneous resetting, where resetting is triggered when a specific threshold is reached. Identifying the threshold with a physical non-target boundary then leads to so-called boundary-induced resetting. In this paper, we explore the effects of boundary-induced resetting on single-particle diffusive search in a two-dimensional (2D) bounded domain $Ω$ containing one or more small interior targets. The interior target boundaries are totally absorbing, whereas the exterior boundary $\partial Ω$ is sticky. That is, whenever the particle reaches a point on $\partial Ω$ it remains attached for a random waiting time $τ$ after which it immediately resets to a fixed interior point $\x_0\in Ω$. Using renewal theory, matched asymptotic analysis and Green's functions we calculate the unconditional MFPT for absorption by any of the targets and compare this with the corresponding MFPT of a search process on the same domain with a reflecting surface $\partial Ω$ and no resetting. We show that boundary-induced resetting only reduces the MFPT relative to the no resetting case if the searcher's reset point $\x_0$ is sufficiently close to one of the targets.
Comments25 pages, 10 figures
