Faraday wave-droplet dynamics: discrete-time analysis
Faraday wave-droplet dynamics: discrete-time analysis
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DOI：
10.1017/jfm.2017.235
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发表时间：
2017-06-25
影响因子：
3.7
通讯作者：
Milewski, Paul A.
中科院分区：
文献类型：
--
作者：
Durey, Matthew;Milewski, Paul A.
由于与波场的推进性相互作用，液滴可能在同一流体的垂直振动槽的表面上“行走”。这种流体动力导波系统表现出许多以前认为只存在于量子领域的动力学。从第一性原理出发，我们推导了离散时间流体模型，其中浴液-液滴相互作用被建模为瞬时的。通过分析系统不动点的稳定性，我们解释了行走液滴的动力学，并捕获了多液滴相互作用的量化。研究了谐波势中的圆形轨道，通过系统的统计分析得到了混沌轨道的双量子化。
A droplet may 'walk' across the surface of a vertically vibrating bath of the same fluid, due to the propulsive interaction with its wave field. This hydrodynamic pilot-wave system exhibits many dynamics previously believed to exist only in the quantum realm. Starting from first principles, we derive a discrete-time fluid model, whereby the bath-droplet interactions are modelled as instantaneous. By analysing the stability of the fixed points of the system, we explain the dynamics of a walking droplet and capture the quantisations for multiple-droplet interactions. Circular orbits in a harmonic potential are studied, and a double quantisation of chaotic trajectories is obtained through systematic statistical analysis.