Statistical self-organization of a gas of interacting walking drops in a confining potential

TL;DR

This paper explores the collective behavior of many walking drops on a fluid surface, revealing self-organized structures and wave-mediated interactions that persist despite individual trajectory randomness.

Contribution

It introduces a numerical study of a large ensemble of walking drops, demonstrating emergent order and wave-based interactions in a confined, active matter system.

Findings

Ordered internal structure remains invariant to parameter changes

Wave symmetry underpins non-stationary self-organization

Oscillatory pair potentials lead to collective active states

Abstract

A drop bouncing on a vertically-vibrated surface may self-propel forward by standing waves and travels along a fluid interface. This system called walking drop forms a non-quantum wave-particle association at the macroscopic scale. The dynamics of one particle has triggered many investigations and has resulted in spectacular experimental results in the last decade. We investigate numerically the dynamics of a gas of walkers, i.e. a large number of walking drops evolving on a unbounded fluid interface in the presence of a confining potential acting on the particles. We show that even if the individual trajectories are erratic, the system presents well-defined ordered internal structure that remains invariant to parameter variations such as the number of drops, the memory time and the bath radius. We rationalize such non-stationary self-organization in terms of the symmetry of the waves and show that oscillatory pair potentials form a wavy collective state of active matter.