Despite major advances in the understanding of the formation and dynamics of nanoclusters in the past decades, theoretical bases for the control of their shape are still lacking. We investigate strategies for driving fluctuating few-particle clusters to an arbitrary target shape in minimum time with or without an external field. This question is recast into a first passage problem, solved numerically, and discussed within a high temperature expansion. Without field, large-enough low-energy target shapes exhibit an optimal temperature at which they are reached in minimum time. We then compute the optimal way to set an external field to minimize the time to reach the target, leading to a gain of time that grows when increasing cluster size or decreasing temperature. This gain can shift the optimal temperature or even create one. Our results could apply to clusters of atoms at equilibrium, and colloidal or nanoparticle clusters under thermo- or electrophoresis.

中文翻译：

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控制有和没有宏观场的小星团的形状

尽管在过去几十年中对纳米团簇的形成和动力学的理解取得了重大进展，但仍缺乏控制其形状的理论基础。我们研究了在有或没有外部场的情况下在最短的时间内将波动的小粒子簇驱动到任意目标形状的策略。这个问题被改写为第一个通道问题，用数值求解，并在高温膨胀中讨论。在没有场的情况下，足够大的低能量目标形状表现出在最短时间达到它们的最佳温度。然后，我们计算设置外部场以最小化到达目标的时间的最佳方法，从而在增加集群大小或降低温度时增加时间增益。这种增益可以改变最佳温度，甚至创造一个。