论文标题
并行随机目标搜索的最佳搜索器分布
Optimal Searcher Distribution for Parallel Random Target Searches
论文作者
论文摘要
我们考虑一个问题，即使用$ n $独立的随机步行者在有限的$ d $维域中找到一个目标，当时在目标位置上的部分信息作为概率分布。当$ n $很大时，首先时间的时间敏感地取决于初始搜索器的分布，该分布引用了最佳搜索器分布的问题，该问题是最小化的第一个流程时间。在这里，我们通过分析得出最佳分布的方程，并探索其限制表达式。如果目标体积可以忽略，则最佳分布与目标分布成正比至三分之一的功率。如果我们考虑有限量的目标，并且在大$ n $限制中不能忽略搜索者初始重叠的概率，则最佳分布对目标分布的依赖性很弱，这是目标分布的对数。使用Langevin Dynamics模拟，我们在数值中证明了我们在一维和二维中的预测。
We consider a problem of finding a target located in a finite $d$-dimensional domain, using $N$ independent random walkers, when partial information on the target location is given as a probability distribution. When $N$ is large, the first-passage time sensitively depends on the initial searcher distribution, which invokes the question of what is the optimal searcher distribution that minimizes the first-passage time. Here, we analytically derive the equation for the optimal distribution and explore its limiting expressions. If the target volume can be ignored, the optimal distribution is proportional to the target distribution to the power of one-third. If we consider a target of a finite volume and the probability of initial overlapping of searchers with the target cannot be ignored in the large $N$ limit, the optimal distribution has a weak dependence on the target distribution, given as a logarithm of the target distribution. Using Langevin dynamics simulations, we numerically demonstrate our predictions in one- and two-dimensions.
