Multi-bounce resonances in the interaction of walking droplets

Abstract

Discrete dynamical models of walking droplets ("walkers") have allowed swift numerical experiments revealing heretofore unobserved quantum statistics and related behaviors in a classical hydrodynamic system. We present evidence that one such model of walking droplets exhibits the empirically elusive $n$-bounce resonances that are traditionally seen in the scattering of solitary waves governed by covariant nonlinear field theories with polynomial self-interaction. A numerical investigation of the chosen model of interacting walking droplets reveals a fractal structure of resonances in the velocity in--velocity out diagram, much like the usual maps constructed for collisions of solitary waves. We suggest avenues for further theoretical analysis of walker collisions, which may connect this discrete model to the field-theoretic setting, as well as directions towards new experimental realizations $n$-bounce resonances.

13 pages, 5 figures. v2: minor updates, accepted for publication in a Special Issue of Mechanics Research Communications. This paper is dedicated to the memory of our friend, mentor, and colleague, Denis Blackmore. Skål

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