论文标题
在弯曲流形上的微武器的最佳导航策略
Optimal navigation strategies for microswimmers on curved manifolds
论文作者
论文摘要
找到通往所需目的地的最快路径是微生物在流体流动中移动的至关重要的任务。我们通过在弯曲的歧管和任意流中建立过度阻尼的微武者来研究这个问题。我们表明该解决方案对应于Randers度量的大地测量学，这是一个不对称的Finsler指标，反映了问题的不可逆转特征。以球形表面为例，我们证明了遵循此“兰德斯政策”的游泳运动员始终击败了更直接的政策。对等异源形状的研究揭示了诸如自相互作用，尖和突然非线性效应之类的特征。我们的工作在广义相对论的概括中提供了微观机构物理学与大地测量学之间的联系。
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.
