Walking Droplets Through the Lens of Dynamical Systems

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.

arXiv comment19 pages, 12 figures

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• Superwalking droplets
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• Interaction of two walkers: Wave-mediated energy and force
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• Standard map-like models for single and multiple walkers in an annular cavity
• Trajectory eigenmodes of an orbiting wave source

Cited by in corpus (8)

• Unsteady dynamics of a classical particle-wave entity
• Lorenz-like systems emerging from an integro-differential trajectory equation of a one-dimensional wave-particle entity
• Pseudo-laminar chaos from on-off intermittency
• Quantum-like behavior of an active particle in a double-well potential
• Crises and chaotic scattering in hydrodynamic pilot-wave experiments
• Damped-driven system of bouncing droplets leading to deterministic diffusive behavior
• The invariant measure of a walking droplet in hydrodynamic pilot-wave theory
• Multi-bounce resonances in the interaction of walking droplets