Walking Droplets Through the Lens of Dynamical Systems

TL;DR

This paper reviews the recent progress in understanding walking droplets on vibrating fluid baths using Dynamical Systems Theory, highlighting complex nonlinear behaviors and connections to quantum phenomena, and proposing future research directions.

Contribution

It provides a comprehensive overview of how dynamical systems analysis can elucidate the complex behaviors of walking droplets and outlines unresolved questions in the field.

Findings

Identification of nonlinear dynamics in walking droplet models

Connections drawn between fluidic experiments and quantum mechanics

Outline of open problems for future dynamical systems research

Abstract

Over the past decade the study of fluidic droplets bouncing and skipping (or ``walking'') on a vibrating fluid bath has gone from an interesting experiment to a vibrant research field. The field exhibits challenging fluids problems, potential connections with quantum mechanics, and complex nonlinear dynamics. We detail advancements in the field of walking droplets through the lens of Dynamical Systems Theory, and outline questions that can be answered using dynamical systems analysis. The article begins by discussing the history of the fluidic experiments and their resemblance to quantum experiments. With this physics backdrop, we paint a portrait of the complex nonlinear dynamics present in physical models of various walking droplet systems. Naturally, these investigations lead to even more questions, and some unsolved problems that are bound to benefit from rigorous Dynamical Systems Analysis are outlined.