曲面流形上微型游泳者的最优导航策略
Optimal navigation strategies for microswimmers on curved manifolds
摘要：
对于在流体流中移动的微生物来说，找到到达所需目的地的最快路径是一项至关重要的任务。我们研究这个问题，通过建立一个分析的形式主义过阻尼microswimmer弯曲流形和任意流。我们表明，该解决方案对应于一个Randers度量，这是一个不对称的芬斯勒度量，反映了问题的不可逆性的测地线。使用球面的例子，我们证明了游泳者的表现，遵循这一“兰德斯政策”总是击败一个更直接的政策。对等时线形状的研究揭示了自相交、尖点和突然的非线性效应等特征。我们的工作为广义广义相对论中的微泳物理和测地线提供了一个联系。
英文摘要：
Finding the fastest path to a desired destination is a vitally important task for microorganisms moving in a fluid flow. We study this problem by building an analytical formalism for overdamped microswimmers on curved manifolds and arbitrary flows. We show that the solution corresponds to the geodesics of a Randers metric, which is an asymmetric Finsler metric that reflects the irreversible character of the problem. Using the example of a spherical surface, we demonstrate that the swimmer performance that follows this "Randers policy" always beats a more direct policy. A study of the shape of isochrones reveals features such as self-intersections, cusps, and abrupt nonlinear effects. Our work provides a link between microswimmer physics and geodesics in generalizations of general relativity.
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