Standard map-like models for single and multiple walkers in an annular cavity

TL;DR

This paper introduces standard map-inspired models for single and multiple walking droplets in an annular cavity, achieving qualitative and quantitative agreement with experiments and predicting new behaviors.

Contribution

It presents novel dynamical models based on the standard map for walking droplets, validated against experimental data and analyzed through bifurcation theory.

Findings

Models replicate experimental complex dynamics

Predictions include unobserved droplet behaviors

Analysis confirms chaotic and bifurcation phenomena

Abstract

Recent experiments on walking droplets in an annular cavity showed the existence of complex dynamics including chaotically changing velocity. This article presents models, influenced by the kicked rotator/standard map, for both single and multiple droplets. The models are shown to achieve both qualitative and quantitative agreement with the experiments, and makes predictions about heretofore unobserved behavior. Using dynamical systems techniques and bifurcation theory, the single droplet model is analyzed to prove dynamics suggested by the numerical simulations.