多粒子搜索中依赖于到达次序的最优重置

中文摘要 AI 辅助

在许多软物质和生物系统中，任务完成依赖于多个搜索者的累积到达，而非单个先锋的速度。因此，完成动力学不仅由首次到达决定，还由首次通过时间的完整有序序列决定。在此，我们确定了随机重置如何针对所有到达次序优化这些有序到达。我们为非相互作用的布朗搜索者构建了一个精确的有限$N$参考，并获得了平均有序首次通过时间$\langle T_{(k)} \rangle$及其最优重置率$r_k^*$。对于具有相同初始条件的搜索者，$r_k^*$随到达次序单调增加，并且随着种群规模的增大，趋近于已知的大$N$分位数极限，在该极限中，仅当临界次序分数$\phi_c \simeq 0.412$以上时才出现有限最优值。空间异质性定性重组了这一序列，即使没有粒子相互作用，也将其最大值从后期次序转移到早期次序。然后，我们将此基线与非平衡布朗胶体实验、相互作用的活性布朗粒子以及具有持久环境记忆的集体自趋化搜索进行比较。在这些系统中，对重置的敏感性随到达次序强烈增加，而相对于适当的非相互作用参考的偏差揭示了直接相互作用、有限返回开销和环境记忆的影响。我们的结果表明，多粒子搜索中的最优重置由所需的完成次序决定，并且必须相对于协议和几何匹配的基线进行评估。

英文摘要

In many soft-matter and biological systems, task completion relies on the cumulative arrival of multiple searchers rather than the speed of a single pioneer. The completion kinetics are therefore set not only by the first arrival, but by the full ordered sequence of first-passage times. Here, we determine how stochastic resetting optimizes these ordered arrivals for all arrival ranks. We construct an exact finite-$N$ reference for non-interacting Brownian searchers and obtain the mean ordered first-passage time $\langle T_{(k)} \rangle$ and its optimal resetting rate $r_k^*$. For searchers with identical initial conditions, $r_k^*$ increases monotonically with arrival rank and, with increasing population size, approaches the known large-$N$ quantile limit where a finite optimum appears only above a critical rank fraction $ϕ_c \simeq 0.412$. Spatial heterogeneity qualitatively reorganizes this sequence, shifting its maximum from late to early ranks even without particle interactions. We then compare this baseline with Brownian colloid experiments, interacting active Brownian particles, and a collective autochemotactic search with persistent environmental memory. Across these systems, sensitivity to resetting increases strongly with arrival rank, while deviations from appropriate non-interacting references reveal the influence of direct interactions, finite return overhead, and environmental memory. Our results show that optimal resetting in multiparticle search is governed by the required completion rank and must be evaluated relative to protocol- and geometry-matched baselines.

发表机构

• The Raymond and Beverley School of Chemistry, Tel Aviv University（特拉维夫大学雷蒙德和贝弗利化学学院）
• The Raymond and Beverley School of Physics & Astronomy, Tel Aviv University（特拉维夫大学雷蒙德和贝弗利物理与天文学院）

机构由 AI 辅助整理，请以论文原文为准。