标题： 在行走液滴动力学中扩展液滴-波统计对应关系 显示英文标题

标题： Extending the Droplet-Wave Statistical Correspondence in Walking Droplet Dynamics

摘要： 行走液滴——在振动流体浴表面自我推进的毫米级油滴——表现出显著的涌现统计特性，这些特性仍然只部分被理解。 特别是，在各种实验中，观察到了液滴的统计分布与引导它的波场时间平均之间的稳健对应关系。 Durey、Milewski 和 Bush（2018）严格证明了在单个液滴在一个均匀且无限的流体浴中的情况下的这种对应关系，每个振动周期内有一次瞬时的液滴-浴相互作用。 他们还概述了该结果如何扩展到更一般的浴体拓扑结构，并且 Durey、Milewski 和 Wang（2020）的工作实现了这种针对圆形浴体的方法。 我们在本文中试图完成这个程序，严格将这种统计对应关系扩展到任意浴体拓扑结构、任意液滴-浴相互作用模型、多个液滴相互作用以及非共振的弹跳情况。 我们在一维几何结构的一滴和两滴系统中对这种对应关系进行了数值研究，并特别观察了时间平均波场如何区分相关和不相关的液滴对。 显示英文摘要

摘要： Walking droplets -- millimetric oil droplets that self-propel across the surface of a vibrating fluid bath -- exhibit striking emergent statistics that remain only partially understood. In particular, in a variety of experiments, a robust correspondence has been observed between the droplet's statistical distribution and the time-average of the wave field that guides it. Durey, Milewski, and Bush (2018) rigorously established such a correspondence in the case of a single droplet on a uniform, unbounded fluid bath, with a single, instantaneous droplet-bath impact during each vibration period. They also outlined how their result might extend to more general bath topography, and the work of Durey, Milewski, and Wang (2020) implemented such an approach for a circular bath. We attempt to complete this program in the present work, rigorously extending this statistical correspondence to account for arbitrary bath topography, arbitrary droplet-bath impact models, multiple droplet interactions, and non-resonant bouncing. We investigate this correspondence numerically in systems of one and two droplets in 1-D geometries, and particularly, we observe how the time-averaged wave field can distinguish between correlated and uncorrelated pairs of droplets.