一维、二维和三维最优间歇搜索策略的鲁棒性
Robustness of optimal intermittent search strategies in dimension 1, 2 and 3
摘要：
各种尺度的搜索问题都涉及到一个机器人，无论它是反应前的分子还是觅食的动物，它都会进行间歇性的运动。在这里，我们分析了一个通用模型的基础上，这种类型的间歇性运动，其中的间歇性交替阶段的慢动作允许检测，和快速运动的阶段没有检测。我们提出了完整和系统的结果，不同的建模假设的检测机制在空间维度1，2和3。我们的研究完成并扩展了我们最近的信[Loverdo { \it et al.} Nature Physics { \bf 4}，134（2008）]，并给出了必要的计算细节。此外，提出了一种新的检测阶段的建模。我们表明，平均目标检测时间可以最小化作为一个函数的平均持续时间的每个阶段在维度1，2和3。重要的是，这种最优策略不依赖于缓慢检测阶段的建模细节，这表明我们的结果具有鲁棒性。我们相信，这种系统的分析可以作为基础，定量研究各种真正的搜索问题，涉及间歇性行为。
英文摘要：
Search problems at various scales involve a searcher, be it a molecule before reaction or a foraging animal, which performs an intermittent motion. Here we analyze a generic model based on such type of intermittent motion, in which the searcher alternates phases of slow motion allowing detection, and phases of fast motion without detection. We present full and systematic results for different modeling hypotheses of the detection mechanism in space dimension 1, 2 and 3. Our study completes and extends the results of our recent letter [Loverdo {\it et al.} Nature Physics {\bf 4}, 134 (2008)] and gives the necessary calculation details. In addition, a new modeling of the detection phase is presented. We show that the mean target detection time can be minimized as a function of the mean duration of each phase in dimension 1, 2 and 3. Importantly, this optimal strategy does not depend on the details of the modeling of the slow detection phase, which shows the robustness of our results. We believe that this systematic analysis can be used as a basis to study quantitatively various real search problems involving intermittent behaviors.
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