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A droplet bouncing on the surface of a vertically vibrating liquid bath can walk horizontally, guided by the waves it generates on each impact. This results in a self-propelled classical particle-wave entity. By using a one-dimensional…

Fluid Dynamics · Physics 2021-07-14 Rahil N. Valani , Anja C. Slim , David M. Paganin , Tapio P. Simula , Theodore Vo

Pilot-wave hydrodynamics concerns the dynamics of 'walkers,' droplets walking on a vibrating bath, and has provided the basis for the burgeoning field of hydrodynamic quantum analogs. We here explore a theoretical model of pilot-wave…

Fluid Dynamics · Physics 2025-01-22 Bauyrzhan K. Primkulov , Davis J. Evans , Joel B. Been , John W. M. Bush

A classical wave-particle entity in the form of a millimetric walking droplet can emerge on the free surface of a vertically vibrating liquid bath. Such wave-particle entities have been shown to exhibit hydrodynamic analogs of quantum…

Chaotic Dynamics · Physics 2022-01-19 Rahil N. Valani

We report a new type of fluid-based driven dissipative oscillator system consisting of a lattice of millimetric fluid droplets bouncing on a vertically vibrating liquid bath and bound within an annular ring. We characterize the system…

Soft Condensed Matter · Physics 2020-10-27 Stuart J. Thomson , Miles M. P. Couchman , John W. M. Bush

We study the phenomenon of the "walking droplet", by means of numerical fluid dynamics simulations using the Smoothed Particle Hydrodynamics numerical method. This phenomenon occurs when a millimetric drop is released on the surface of an…

Fluid Dynamics · Physics 2017-08-17 Diego Molteni , Enrico Vitanza , Onofrio Rosario Battaglia

We aim to describe a droplet bouncing on a vibrating bath using a simple and highly versatile model inspired from quantum mechanics. Close to the Faraday instability, a long-lived surface wave is created at each bounce, which serves as a…

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…

Soft Condensed Matter · Physics 2023-05-25 Adrien Hélias , Matthieu Labousse

A droplet bouncing on the surface of a vibrating liquid bath can move horizontally guided by the wave it produces on impacting the bath. The wave itself is modified by the environment, and thus the interactions of the moving droplet with…

Fluid Dynamics · Physics 2019-07-19 Rahil N. Valani , Anja C. Slim

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…

Chaotic Dynamics · Physics 2023-11-06 George Zhang , Ivan C. Christov , Aminur Rahman

We present a deep-learning based tracking objects of interest in walking droplet and granular intruder experiments. In a typical walking droplet experiment, a liquid droplet, known as \textit{walker}, propels itself laterally on the free…

Computer Vision and Pattern Recognition · Computer Science 2023-11-17 Erdi Kara , George Zhang , Joseph J. Williams , Gonzalo Ferrandez-Quinto , Leviticus J. Rhoden , Maximilian Kim , J. Nathan Kutz , Aminur Rahman

When a liquid droplet impacts a vibrated micro-structured surface with asymmetric topology, the liquids perform a horizontal motion during its bouncing. The moving effect is observed when the liquid is in contact with a low surface energy…

Fluid Dynamics · Physics 2020-09-10 Dinh-Tuan Phan , Hao Yu , Tuan Tran

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,…

Fluid Dynamics · Physics 2020-11-18 Aminur Rahman , Denis Blackmore

A bouncing droplet on a vibrated bath can couple to the waves it generates, so that it becomes a propagative walker. Its propulsion at constant velocity means that a balance exists between the permanent input of energy provided by the…

Classical Physics · Physics 2014-09-02 Matthieu Labousse , Stéphane Perrard

Deformed droplets are ubiquitous in various industrial applications, such as inkjet printing, lab-on-a-chip devices, and spray cooling, and can fundamentally affect the involved applications both favorably and unfavorably. Here, we employ…

We experimentally investigate the dynamics of synthetic active particles composed of gravitationally bouncing, superwalking droplets confined within an annular fluid bath. Driven by a topologically pumping dual-frequency waveform, the…

Fluid Dynamics · Physics 2025-12-19 Rudra Sekhri , Rahil N. Valani , Tapio Simula

Walking droplets -- millimetric oil droplets that self-propel across the surface of a vibrating fluid bath -- exhibit striking emergent statistics that remain only partially understood. In particular, in a variety of experiments, a robust…

Fluid Dynamics · Physics 2026-01-28 Skyler Mao , David Darrow

A millimetric bouncing droplet sustained on a vibrating bath becomes a moving wave source (particle) through periodically interacting with the local wave field it generates during the droplet-bath impact. By virtue of such particle-wave…

Fluid Dynamics · Physics 2021-08-25 Jianbo Tang , Xi Zhao , Jing Liu

A classical wave-particle entity (WPE) can be realized experimentally as a droplet walking on the free surface of a vertically vibrating liquid bath, with the droplet's horizontal walking motion guided by its self-generated wave field.…

Dynamical Systems · Mathematics 2023-04-18 Joshua Perks , Rahil Valani

Swimming droplets are a class of active particles whose motility changes as a function of time due to shrinkage and self-avoidance of their trail. Here we combine experiments and theory to show that our non-Markovian droplet (NMD) model,…

Soft Condensed Matter · Physics 2024-05-17 Wenjun Chen , Adrien Izzet , Ruben Zakine , Eric Clément , Eric Vanden-Eijnden , Jasna Brujic

The interaction of 'walking droplets' and capillary waves in a weakly subcritical Faraday wave experiment has been studied as a hydrodynamic analog to Bohmian quantum mechanics (see "Hydrodynamic Quantum Analogs", J. Bush and A. Oza, Rep.…

Fluid Dynamics · Physics 2025-12-02 Emily Dunn , Bavand Keshavarz , Earl Dowell
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