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Bouncing walking droplets possess fascinating properties due to their peculiar wave/particule interaction. In order to study such walkers in a 1d system, we considered the case of one or more droplets in an annular cavity. We show that, in…

Fluid Dynamics · Physics 2015-11-04 B. Filoux , M. Hubert , N. Vandewalle

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 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

A bouncing droplet, self-propelled by its interaction with the waves it generates, forms a classical wave-particle association called a "walker." Previous works have demonstrated that the dynamics of a single walker is driven by its global…

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

Until recently, wave-particle duality has been thought of as quantum principle without a counterpart in classical physics. This belief was challenged after (i) finding that average dynamics of a classical particle in strong inhomogeneous…

Quantum Physics · Physics 2015-06-03 Alexander Y. Davydov

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

Damped-driven systems are ubiquitous in science, however the damping and driving mechanisms are often quite convoluted. This manuscript presents an experimental and theoretical investigation of a fluidic droplet on a vertically vibrating…

Fluid Dynamics · Physics 2023-09-12 Aminur Rahman

We consider the dynamics of a droplet on a vibrating fluid bath. This hydrodynamic quantum analog system is shown to elicit the canonical behavior of damped-driven systems, including a period doubling route to chaos. By approximating the…

Dynamical Systems · Mathematics 2022-11-10 Aminur Rahman , J. Nathan Kutz

Recently discrete dynamical models of walking droplet dynamics have allowed for fast numerical simulations of their horizontal chaotic motion and consequently the long-time statistical distribution of the droplet position. We develop a…

Dynamical Systems · Mathematics 2023-02-03 Gonzalo Ferrandez Quinto , Aminur Rahman

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 Kapitza-Dirac effect is the diffraction of quantum particles by a standing wave of light. We here report an analogous phenomenon in pilot-wave hydrodynamics, wherein droplets walking across the surface of a vibrating liquid bath are…

A classical wave-particle entity (WPE) can materialize as a millimeter-sized droplet walking horizontally on the free surface of a vertically vibrating liquid bath. This WPE comprises a particle (droplet) that shapes its environment by…

Fluid Dynamics · Physics 2023-08-08 Rahil N. Valani

Active particles are non-equilibrium entities that uptake energy and convert it into self-propulsion. A dynamically rich class of inertial active particles having features of wave-particle coupling and wave memory are walking/superwalking…

Soft Condensed Matter · Physics 2026-03-03 Rahil N. Valani , David M. Paganin

The concept of walking wave is introduced from classical relativistic positions. One- and three-dimensional walking waves considered with their wave equations and dispersion equations. It is shown that wave characteristics (de Broglie's and…

General Physics · Physics 2012-05-03 A. V. Goryunov

A recent surge of discoveries has sparked significant interest in active systems where a particle moves autonomously in resonance with its self-generated wave field, leading to notable wave-mediated effects including new propulsion…

Soft Condensed Matter · Physics 2026-05-26 Austin M. Blitstein , Rodolfo R. Rosales , Pedro J. Sáenz

Inspired by bouncing drop experiments that revealed how macroscopic systems can exhibit wave-particle properties previously thought to be exclusive to quantum systems, we introduce here a new wave-particle system based on internal gravity…

Fluid Dynamics · Physics 2025-05-16 Simon Gsell , Patrice Le Gal

We study the dynamical properties of an active particle subject to a swimming speed explicitly depending on the particle position. The oscillating spatial profile of the swim velocity considered in this paper takes inspiration from…

Soft Condensed Matter · Physics 2022-03-15 Lorenzo Caprini , Umberto Marini Bettolo Marconi , René Wittmann , Hartmut Löwen

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

A growing number of dynamical situations involve the coupling of particles or singularities with physical waves. In principle these situations are very far from the wave-particle duality at quantum scale where the wave is probabilistic by…

Quantum Physics · Physics 2014-02-07 Stéphane Perrard , Matthieu Labousse , Marc Miskin , Emmanuel Fort , Yves Couder