The first passage search of a diffusing target (prey) by multiple searchers (predators) in confinement is an important problem in the stochastic process literature. While the analogous problem in open space has been studied in some detail, a systematic study in confined space is still lacking. In this paper, we study the first passage times for this problem in one, two, and three dimensions. Due to confinement, the survival probability of the target takes a form $\sim e^{-t/\tau }$ at large times $t$. The characteristic capture timescale $\tau$ associated with the rare capture events are rather challenging to measure. We use a computational algorithm that allows us to estimate $\tau$ with high accuracy. We study in detail the behavior of $\tau$ as a function of the system parameters, namely, the number of searchers $N$, the relative diffusivity $r$ of the target with respect to the searcher, and the system size. We find that $\tau$ deviates from the $\sim 1/N$ scaling seen in the case of a static target, and this deviation varies continuously with $r$ and the spatial dimensions.

中文翻译：

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在密闭空间中被多个捕食者捕获扩散性猎物

第一通道搜索漫射目标（猎物）通过在多个搜索者（食肉动物）的限制是在随机过程文献的一个重要问题。尽管已经对开放空间中的类似问题进行了详细研究，但仍缺乏对受限空间的系统研究。在本文中，我们从一个维度，两个维度和三个维度研究该问题的首次通过时间。由于局限性，目标的生存概率采用以下形式$〜{Ë}^{-Ť/\tau }$ 在很多时候 $Ť$。该特性捕获时间尺度$\tau$与罕见捕获事件相关联的测量非常具有挑战性。我们使用一种计算算法，可以估算$\tau$精度高。我们详细研究了$\tau$ 作为系统参数的函数，即搜索者的数量 $ñ$，相对扩散率 $\mathrm{[R}$目标相对于搜索者的数量以及系统大小。我们发现$\tau$ 偏离 $〜\mathrm{1个}/ñ$ 在静态目标的情况下会看到缩放比例，并且此偏差会随着 $\mathrm{[R}$ 和空间尺寸。