Pilot-wave dynamics: Using dynamic mode decomposition to characterize bifurcations, routes to chaos, and emergent statistics.

We develop a data-driven characterization of the pilot-wave hydrodynamic system in which a bouncing droplet self-propels along the surface of a vibrating bath. We consider drop motion in a confined one-dimensional geometry and apply the dynamic mode decomposition (DMD) in order to characterize the evolution of the wave field as the bath's vibrational acceleration is increased progressively. Dynamic mode decomposition provides a regression framework for adaptively learning a best-fit linear dynamics model over snapshots of spatiotemporal data.

Superradiant Droplet Emission from Parametrically Excited Cavities.

Superradiance occurs when a collection of atoms exhibits a cooperative, spontaneous emission of photons at a rate that exceeds that of its component parts. Here, we reveal a similar phenomenon in a hydrodynamic system consisting of a pair of vibrationally excited cavities, coupled through their common wave field, that spontaneously emit droplets via interfacial fracture. We show that the droplet emission rate of two coupled cavities is higher than the emission rate of two isolated cavities.

Emergent order in hydrodynamic spin lattices.

Macroscale analogues of microscopic spin systems offer direct insights into fundamental physical principles, thereby advancing our understanding of synchronization phenomena and informing the design of novel classes of chiral metamaterials. Here we introduce hydrodynamic spin lattices (HSLs) of 'walking' droplets as a class of active spin systems with particle-wave coupling. HSLs reveal various non-equilibrium symmetry-breaking phenomena, including transitions from antiferromagnetic to ferromagnetic order that can be controlled by varying the lattice geometry and system rotation.

A guideline to limit indoor airborne transmission of COVID-19.

The current revival of the American economy is being predicated on social distancing, specifically the Six-Foot Rule, a guideline that offers little protection from pathogen-bearing aerosol droplets sufficiently small to be continuously mixed through an indoor space. The importance of airborne transmission of COVID-19 is now widely recognized. While tools for risk assessment have recently been developed, no safety guideline has been proposed to protect against it.

Classical pilot-wave dynamics: The free particle.

We present the results of a theoretical investigation into the dynamics of a vibrating particle propelled by its self-induced wave field. Inspired by the hydrodynamic pilot-wave system discovered by Yves Couder and Emmanuel Fort, the idealized pilot-wave system considered here consists of a particle guided by the slope of its quasi-monochromatic "pilot" wave, which encodes the history of the particle motion. We characterize this idealized pilot-wave system in terms of two dimensionless groups that prescribe the relative importance of particle inertia, drag and wave forcing.

Hydrodynamic quantum analogs.

The walking droplet system discovered by Yves Couder and Emmanuel Fort presents an example of a vibrating particle self-propelling through a resonant interaction with its own wave field. It provides a means of visualizing a particle as an excitation of a field, a common notion in quantum field theory. Moreover, it represents the first macroscopic realization of a form of dynamics proposed for quantum particles by Louis de Broglie in the 1920s.

Speed oscillations in classical pilot-wave dynamics.

We present the results of a theoretical investigation of a dynamical system consisting of a particle self-propelling through a resonant interaction with its own quasi-monochromatic pilot-wave field. We rationalize two distinct mechanisms, arising in different regions of parameter space, that may lead to a wavelike statistical signature with the pilot-wavelength. First, resonant speed oscillations with the wavelength of the guiding wave may arise when the particle is perturbed from its steady self-propelling state.

Predictability in a hydrodynamic pilot-wave system: Resolution of walker tunneling.

A walker is a macroscopic coupling of a droplet and a capillary wave field that exhibits several quantumlike properties. In 2009, Eddi et al. [Phys.

A new wrinkle on liquid sheets: Turning the mechanism of viscous bubble collapse upside down.

Viscous bubbles are prevalent in both natural and industrial settings. Their rupture and collapse may be accompanied by features typically associated with elastic sheets, including the development of radial wrinkles. Previous investigators concluded that the film weight is responsible for both the film collapse and wrinkling instability.

A hydrodynamic analog of Friedel oscillations.

We present a macroscopic analog of an open quantum system, achieved with a classical pilot-wave system. Friedel oscillations are the angstrom-scale statistical signature of an impurity on a metal surface, concentric circular modulations in the probability density function of the surrounding electron sea. We consider a millimetric drop, propelled by its own wave field along the surface of a vibrating liquid bath, interacting with a submerged circular well.

Dynamics, emergent statistics, and the mean-pilot-wave potential of walking droplets.

A millimetric droplet may bounce and self-propel on the surface of a vertically vibrating bath, where its horizontal "walking" motion is induced by repeated impacts with its accompanying Faraday wave field. For ergodic long-time dynamics, we derive the relationship between the droplet's stationary statistical distribution and its mean wave field in a very general setting. We then focus on the case of a droplet subjected to a harmonic potential with its motion confined to a line.

Exploring orbital dynamics and trapping with a generalized pilot-wave framework.

We explore the effects of an imposed potential with both oscillatory and quadratic components on the dynamics of walking droplets. We first conduct an experimental investigation of droplets walking on a bath with a central circular well. The well acts as a source of Faraday waves, which may trap walking droplets on circular orbits.

Introduction to focus issue on hydrodynamic quantum analogs.

Hydrodynamic quantum analogs is a nascent field initiated in 2005 by the discovery of a hydrodynamic pilot-wave system [Y. Couder, S. Protière, E.

The interaction of a walking droplet and a submerged pillar: From scattering to the logarithmic spiral.

Millimetric droplets may walk across the surface of a vibrating fluid bath, propelled forward by their own guiding or "pilot" wave field. We here consider the interaction of such walking droplets with a submerged circular pillar. While simple scattering events are the norm, as the waves become more pronounced, the drop departs the pillar along a path corresponding to a logarithmic spiral.

Walking droplets in a circular corral: Quantisation and chaos.

A millimetric liquid droplet may walk across the surface of a vibrating liquid bath through a resonant interaction with its self-generated wavefield. Such walking droplets, or "walkers," have attracted considerable recent interest because they exhibit certain features previously believed to be exclusive to the microscopic, quantum realm. In particular, the intricate motion of a walker confined to a closed geometry is known to give rise to a coherent wave-like statistical behavior similar to that of electrons confined to quantum corrals.

Hydrodynamic spin states.

We present the results of a theoretical investigation of hydrodynamic spin states, wherein a droplet walking on a vertically vibrating fluid bath executes orbital motion despite the absence of an applied external field. In this regime, the walker's self-generated wave force is sufficiently strong to confine the walker to a circular orbit. We use an integro-differential trajectory equation for the droplet's horizontal motion to specify the parameter regimes for which the innermost spin state can be stabilized.

The onset of chaos in orbital pilot-wave dynamics.

We present the results of a numerical investigation of the emergence of chaos in the orbital dynamics of droplets walking on a vertically vibrating fluid bath and acted upon by one of the three different external forces, specifically, Coriolis, Coulomb, or linear spring forces. As the vibrational forcing of the bath is increased progressively, circular orbits destabilize into wobbling orbits and eventually chaotic trajectories. We demonstrate that the route to chaos depends on the form of the external force.

Drop impact and capture on a thin flexible fiber.

When a drop impacts a thin fiber, a critical impact speed can be defined, below which the drop is entirely captured by the fiber, and above which the drop pinches-off and fractures. We discuss here the capture dynamics of both inviscid and viscous drops on flexible fibers free to deform following impact. We characterize the impact-induced elongation of the drop thread for both high and low viscosity drops, and show that the capture dynamics depends on the relative magnitudes of the bending time of the fiber and deformation time of the drop.

The cocktail boat.

We describe the inspiration, development, and deployment of a novel cocktail device modeled after a class of water-walking insects. Semi-aquatic insects like Microvelia and Velia evade predators by releasing a surfactant that quickly propels them across the water. We exploit an analogous propulsion mechanism in the design of an edible cocktail boat.

Capillary instability on an elastic helix.

We present the results of a combined experimental and theoretical investigation of the capillary instability of an elastic helical thread bound within a fluid. The influence of the thread's elastic energy on the classic Rayleigh-Plateau instability is elucidated. The most unstable wavelength can be substantially increased by the influence of the helical coil.

Biomimicry and the culinary arts.

We present the results of a recent collaboration between scientists, engineers and chefs. Two particular devices are developed, both inspired by natural phenomena reliant on surface tension. The cocktail boat is a drink accessory, a self-propelled edible boat powered by alcohol-induced surface tension gradients, whose propulsion mechanism is analogous to that employed by a class of water-walking insects.

Wavelike statistics from pilot-wave dynamics in a circular corral.

Bouncing droplets can self-propel laterally along the surface of a vibrated fluid bath by virtue of a resonant interaction with their own wave field. The resulting walking droplets exhibit features reminiscent of microscopic quantum particles. Here we present the results of an experimental investigation of droplets walking in a circular corral.

Optimal concentrations in transport systems.

Many biological and man-made systems rely on transport systems for the distribution of material, for example matter and energy. Material transfer in these systems is determined by the flow rate and the concentration of material. While the most concentrated solutions offer the greatest potential in terms of material transfer, impedance typically increases with concentration, thus making them the most difficult to transport.

The hummingbird's tongue: a self-assembling capillary syphon.

We present the results of a combined experimental and theoretical investigation of the dynamics of drinking in ruby-throated hummingbirds. In vivo observations reveal elastocapillary deformation of the hummingbird's tongue and capillary suction along its length. By developing a theoretical model for the hummingbird's drinking process, we investigate how the elastocapillarity affects the energy intake rate of the bird and how its open tongue geometry reduces resistance to nectar uptake.

The fine art of surfacing: its efficacy in broadcast spawning.

Many organisms reproduce by releasing gametes into the surrounding fluid. For some such broadcast spawners, gametes are positively or negatively buoyant, and, as a result, fertilization occurs on a two-dimensional surface rather than in the bulk of the air or water. We here rationalize this behaviour by considering the encounter rates of gametes on the surface and in the fluid bulk.