齐次和非齐次间歇搜索策略的数值分析
Numerical analysis of homogeneous and inhomogeneous intermittent search strategies
摘要：
随机搜索是一个随机过程，表示粒子（表示为粒子）的随机运动，当它第一次到达（检测到）目标粒子或区域时终止。在间歇性搜索中，随机运动在两种或更多种运动模式之间交替，其中一种是非检测。一个示例是作为检测模式的缓慢扩散运动和作为非检测模式的快速定向弹道运动，这可以导致比纯扩散搜索快得多的检测。扩散模式和弹道模式之间的转换速率（和返回）以及弹道运动方向的概率分布定义了搜索策略。如果这些转移率和/或概率分布取决于搜索域内的空间坐标，则它是空间非均匀搜索策略，如果两者都是常数，则它是均匀搜索策略。在这里，我们研究的效率，衡量的平均首次通过时间，空间均匀和非均匀搜索策略的三个范式搜索问题：1）狭义逃逸问题，其中搜索器必须在搜索域的边界上找到一个小区域，2）反应动力学，其涉及在搜索域的内部检测不动的目标，3）反应逃逸问题，即扩散体首先需要找到一个扩散目标，然后才能通过边界上的一个狭窄区域逃逸。使用家庭的空间不均匀的搜索策略，部分动机的活细胞中的细胞骨架与中心体的空间组织，我们表明，他们几乎总是可以比均匀的策略更有效。
英文摘要：
A random search is a stochastic process representing the random motion of a particle (denoted as the searcher) that is terminated when it reaches (detects) a target particle or area the first time. In intermittent search the random motion alternates between two or more motility modes, one of which is non-detecting. An example is the slow diffusive motion as the detecting mode and fast, directed ballistic motion as the non-detecting mode, which can lead to much faster detection than a purely diffusive search. The transition rate between the diffusive and the ballistic mode (and back) together with the probability distribution of directions for the ballistic motion defines a search strategy. If these transition rates and/or probability distributions depend on the spatial coordinates within the search domain it is a spatially inhomogeneous search strategy, if both are constant, it is a homogeneous one. Here we study the efficiency, measured in terms of the mean first-passage time, of spatially homogeneous and inhomogeneous search strategies for three paradigmatic search problems: 1) the narrow escape problem, where the searcher has to find a small area on the boundary of the search domain, 2) reaction kinetics, which involves the detection of an immobile target in the interior of a search domain, and 3) the reaction-escape problem, where the searcher first needs to find a diffusive target before it can escape through a narrow region on the boundary. Using families of spatially inhomogeneous search strategies, partially motivated by the spatial organization of the cytoskeleton in living cells with a centrosome, we show that they can be made almost always more efficient than homogeneous strategies.
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