Valani Rahil N, Slim Anja C, Paganin David M, Simula Tapio P, Vo Theodore
School of Physics and Astronomy, Monash University, Victoria 3800, Australia.
School of Mathematics, Monash University, Victoria 3800, Australia.
Phys Rev E. 2021 Jul;104(1-2):015106. doi: 10.1103/PhysRevE.104.015106.
A droplet bouncing on the surface of a vertically vibrating liquid bath can walk horizontally, guided by the waves it generates on each impact. This results in a self-propelled classical particle-wave entity. By using a one-dimensional theoretical pilot-wave model with a generalized wave form, we investigate the dynamics of this particle-wave entity. We employ different spatial wave forms to understand the role played by both wave oscillations and spatial wave decay in the walking dynamics. We observe steady walking motion as well as unsteady motions such as oscillating walking, self-trapped oscillations, and irregular walking. We explore the dynamical and statistical aspects of irregular walking and show an equivalence between the droplet dynamics and the Lorenz system, as well as making connections with the Langevin equation and deterministic diffusion.
在垂直振动的液池表面弹跳的液滴可以在它每次撞击时所产生的波的引导下水平移动。这就产生了一个自推进的经典粒子-波实体。通过使用具有广义波形的一维理论导波模型，我们研究了这个粒子-波实体的动力学。我们采用不同的空间波形来理解波振荡和空间波衰减在移动动力学中所起的作用。我们观察到了稳定的移动运动以及不稳定运动，如振荡移动、自陷振荡和不规则移动。我们探索了不规则移动的动力学和统计方面，并展示了液滴动力学与洛伦兹系统之间的等效性，以及与朗之万方程和确定性扩散的联系。
