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

The hydraulic bump: The surface signature of a plunging jet

When a falling jet of fluid strikes a horizontal fluid layer, a hydraulic jump arises downstream of the point of impact provided a critical flow rate is exceeded. We here examine a phenomenon that arises below this jump threshold, a circular deflection of relatively small amplitude on the free surface, that we call the hydraulic bump. The form of the circular bump can be simply understood in terms of the underlying vortex structure and its height simply deduced with Bernoulli arguments. As the incoming flux increases, a breaking of axial symmetry leads to polygonal hydraulic bumps. The relation between this polygonal instability and that arising in the hydraulic jump is discussed. The coexistence of hydraulic jumps and bumps can give rise to striking nested structures with polygonal jumps bound within polygonal bumps. The absence of a pronounced surface signature on the hydraulic bump indicates the dominant influence of the subsurface vorticity on its instability

Efficient concepts for large erectable space structures

The status of Langley Research Center development of the nestable column concept is reviewed including results of member and truss component tests, and planned assembly studies. In addition, more recent studies of alternative member concepts are presented. Preliminary results on relative efficiency of several types of truss-type columns are compared and future test plans discussed

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

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

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

Visualizing SNP statistics in the context of linkage disequilibrium using LD-Plus

Summary: Often in human genetic analysis, multiple tables of single nucleotide polymorphism (SNP) statistics are shown alongside a Haploview style correlation plot. Readers are then asked to make inferences that incorporate knowledge across these multiple sets of results. To better facilitate a collective understanding of all available data, we developed a Ruby-based web application, LD-Plus, to generate figures that simultaneously display physical location of SNPs, binary SNP attributes (such as coding/non-coding or presence on genotyping platforms), common haplotypes and their frequencies and continuously scaled values (such as Fst, minor allele frequency, genotyping efficiency or P-values), all in the context of the D′ and r2 linkage disequilibrium structures. Combining these results into one comprehensive figure reduces dereferencing between figures and tables, and can provide unique insights into genetic features that are not clearly seen when results are partitioned across multiple figures and tables