Pilot-wave hydrodynamics

Yves Couder, Emmanuel Fort, and coworkers recently discovered that a millimetric droplet sustained on the surface of a vibrating fluid bath may self-propel through a resonant interaction with its own wave field. This article reviews experimental evidence indicating that the walking droplets exhibit certain features previously thought to be exclusive to the microscopic, quantum realm. It then reviews theoretical descriptions of this hydrodynamic pilot-wave system that yield insight into the origins of its quantumlike behavior. Quantization arises from the dynamic constraint imposed on the droplet by its pilot-wave field, and multimodal statistics appear to be a feature of chaotic pilot-wave dynamics. I attempt to assess the potential and limitations of this hydrodynamic system as a quantum analog. This fluid system is compared to quantum pilot-wave theories, shown to be markedly different from Bohmian mechanics and more closely related to de Broglie’s original conception of quantum dynamics, his double-solution theory, and its relatively recent extensions through researchers in stochastic electrodynamics.National Science Foundation (U.S.) (Grant CBET-0966452)National Science Foundation (U.S.) (Grant CMMI-1333242)MIT-France ProgramMIT-Brazil Progra

The aerodynamics of the beautiful game

We consider the aerodynamics of football, specifically, the interaction between a ball in flight and the ambient air. Doing so allows one to account for the characteristic range and trajectories of balls in flight, as well as their anomalous deflections as may be induced by striking the ball either with or without spin. The dynamics of viscous boundary layers is briefly reviewed, its critical importance on the ball trajectories highlighted. The Magnus effect responsible for the anomalous curvature of spinning balls is seen to depend critically on the surface roughness of the ball, the sign of the Magnus force reversing for smooth balls. The origins of the fluttering of balls struck with nearly no spin is also discussed. Particular attention is given to categorizing and providing aerodynamic rationale for the various free kick styles

A hydrodynamic analog of interaction-free measurement

Interaction-free measurement allows for quantum particles to detect objects along paths they never traveled. As such, it represents one of the most beguiling of quantum phenomena. Here, we present a classical analog of interaction-free measurement using the hydrodynamic pilot-wave system, in which a droplet self-propels across a vibrating fluid surface, guided by a wave of its own making. We argue that existing rationalizations of interaction-free quantum measurement in terms of particles being guided by wave forms allow for a classical description manifest in our hydrodynamic system, wherein the measurement is decidedly not interaction-free

Interfacial propulsion by directional adhesion

The rough integument of water-walking arthropods is well-known to be responsible for their water-repellency [1], [2], [3] and [4]; however, water-repellent surfaces generally experience reduced traction at an air–water interface [5], [6], [7] and [8]. A conundrum then arises as to how such creatures generate significant propulsive forces while retaining their water-repellency. We here demonstrate through a series of experiments that they do so by virtue of the detailed form of their integument; specifically, their tilted, flexible hairs interact with the free surface to generate directionally anisotropic adhesive forces that facilitate locomotion. We thus provide new rationale for the fundamental topological difference in the roughness on plants and water-walking arthropods, and suggest new directions for the design and fabrication of unidirectional superhydrophobic surfaces

The Clapping Book

A steady horizontal air stream flows across a book clamped at its downstream end. Pages lift off to form a growing bent stack whose shape is determined by the torques associated with aerodynamic forces, weight and elastic resistance to bending. As more pages lift off to join the bent stack, the increasing importance of bending rigidity to dynamic pressure eventually causes the book to clap shut. The process restarts, and self-sustained oscillations emerge. [Fluid dynamics video]Comment: 1 page, Video submission for the 26th Annual Gallery of Fluid Motion (American Physical Society). Videos available from http://ecommons.library.cornell.edu/bitstream/1813/11473/2/GFM_clapping_reis_mpeg1.mpg low (mpeg-1) and http://ecommons.library.cornell.edu/bitstream/1813/11473/3/GFM_clapping_reis_mpeg2.mpg high (mpeg-2) resolutio

Generating uniaxial vibration with an electrodynamic shaker and external air bearing

Electrodynamic shakers are widely used in experimental investigations of vibrated fluids and granular materials. However, they are plagued by undesirable internal resonances that can significantly impact the quality of vibration. In this work, we measure the performance of a typical shaker and characterize the influence that a payload has on its performance. We present the details of an improved vibration system based on a concept developed by Goldman (2002) which consists of a typical electrodynamic shaker with an external linear air bearing to more effectively constrain the vibration to a single axis. The principal components and design criteria for such a system are discussed. Measurements characterizing the performance of the system demonstrate considerable improvement over the unmodified test shaker. In particular, the maximum inhomogeneity of the vertical vibration amplitude is reduced from approximately 10 percent to 0.1 percent; moreover, transverse vibrations were effectively eliminated.National Science Foundation (U.S.) (CBET-0966452)National Science Foundation (U.S.) (CMMI-1333242)National Science Foundation (U.S.). Graduate Research Fellowship Progra

Superradiant droplet emission from parametrically excited cavities

Superradiance occurs when a collection of atoms exhibits 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 wavefield, 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. We further show that the amplified emission rate varies sinusoidally with distance between the cavities, thus demonstrating a hydrodynamic phenomenon that captures the essential features of superradiance in optical systems

Simulations of pilot-wave dynamics in a simple harmonic potential

We present the results of a numerical investigation of droplets walking in a harmonic potential on a vibrating fluid bath. The droplet's trajectory is described by an integro-differential equation, which is simulated numerically in various parameter regimes. We produce a regime diagram that summarizes the dependence of the walker's behavior on the system parameters for a droplet of fixed size. At relatively low vibrational forcing, a number of periodic and quasiperiodic trajectories emerge. In the limit of large vibrational forcing, the walker's trajectory becomes chaotic, but the resulting trajectories can be decomposed into portions of unstable quasiperiodic states.National Science Foundation (U.S.) (Grant CMMI-1333242)National Science Foundation (U.S.) (Grant DMS-1614043

A low-cost, precise piezoelectric droplet-on-demand generator

We present the design of a piezoelectric droplet-on-demand generator capable of producing droplets of highly repeatable size ranging from 0.5 to 1.4 mm in diameter. The generator is low cost and simple to fabricate. We demonstrate the manner in which droplet diameter can be controlled through variation of the piezoelectric driving waveform parameters, outlet pressure, and nozzle diameter.National Science Foundation (U.S.) (Grants CBET-0966452 and CMMI-1333242)National Science Foundation (U.S.) (Fellowship