论文标题
在扩散搜索和捕获下的目标竞争资源竞争
Target competition for resources under diffusive search-and-capture
论文作者
论文摘要
在本文中，我们使用渐近分析来确定$ n $ n $小的内部目标中每个界限内的稳态平均资源数量。资源的积累是基于多轮搜索事件的；每当搜索者找到目标时，它都会将资源数据包提供到目标，之后它逃脱并返回其初始位置（捕获后重置）。然后，将搜索者与货物相互补充，并在随机延迟后启动新的搜索过程。假设资源的积累是由于退化而平衡的，则可以在资源分布的时刻获得一般表达。我们使用它来表明目标中的平均资源数量与其有效的“形状电容”成正比。然后，我们将分析扩展到扩散搜索的情况，并在捕获前使用随机重置，其中搜索者的位置在随机的时间序列上重置为其初始位置，该序列在统计学上独立于持续的搜索过程，与捕获后重置时间的顺序相反。
In this paper we use asymptotic analysis to determine the steady-state mean number of resources in each of $N$ small interior targets within a three-dimensional bounded domain. The accumulation of resources is based on multiple rounds of search-and-capture events; whenever a searcher finds a target it delivers a resource packet to the target, after which it escapes and returns to its initial position (resetting after capture). The searcher is then resupplied with cargo and a new search process is initiated after a random delay. Assuming that the accumulation of resources is counterbalanced by degradation, one can derive general expressions for the moments of the resource distribution. We use this to show that the mean number of resources in a target is proportional to its effective "shape capacitance." We then extend the analysis to the case of diffusive search with stochastic resetting before capture, where the position of the searcher is reset to its initial position at a random sequence of times that is statistically independent of the ongoing search process, in contrast to the sequence of resetting times after capture.
