Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session L16: Drops: Bouncers and Walkers |
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Chair: Luiz Faria, MIT Room: D133/134 |
Monday, November 21, 2016 4:30PM - 4:43PM |
L16.00001: A model for Faraday pilot-waves over variable topography Luiz Faria In 2005 Yves Couder and co-workers discovered that droplets walking on a vibrating bath posses certain features previously thought to be exclusive to quantum systems. These millimetric droplets synchronize with their Faraday wavefield, creating a macroscopic pilot-wave system. In this talk we exploit the fact that the waves generated are nearly monochromatic and propose a hydrodynamic model capable of capturing the interaction between bouncing drops and a variable topography. We show that our model is able to reproduce some important experiments involving the drop-topography interaction, such as non-specular reflection and single-slit diffraction. [Preview Abstract] |
Monday, November 21, 2016 4:43PM - 4:56PM |
L16.00002: The chaotic interaction of two walkers Loic Tadrist, Naresh Samara, Peter Schlagheck, Tristan Gilet A droplet bouncing on a vertically vibrated bath may be propelled horizontally by the Faraday waves that it generates at each rebound. This association of a wave and a particle is called a walker. Ten years ago, Yves Couder and co-workers noted that the dynamical encounter of two walkers may lead to either scattered trajectories or orbital motion.\\ In this work, we investigate the interaction of two walkers more systematically. The walkers are launched towards each other with finely controlled initial conditions. Output trajectories are classified in four types: scattering, orbiting, wandering and complex. The interaction appears stochastic: the same set of initial parameters (to the measurement accuracy) can produce different outputs. Our analysis of the underlying chaos provides new insights on the stochastic nature of this experiment. [Preview Abstract] |
Monday, November 21, 2016 4:56PM - 5:09PM |
L16.00003: Snell's law and walking droplets John Bush, Giuseppe Pucci, Benjamin Aubin, Pierre-Thomas Brun, Luiz Faria Droplets walking on the surface of a vibrating bath have been shown to exhibit a number of quantum-like features. We here present the results of a combined experimental and theoretical investigation of such droplets crossing a linear step corresponding to a reduction in bath depth. When the step is sufficiently large, the walker reflects off the step; otherwise, it is refracted as it crosses the step. Particular attention is given to an examination of the regime in which the droplet obeys a form of Snell's Law, a behavior captured in accompanying simulations. Attempts to provide theoretical rationale for the dependence of the effective refractive index on the system parameters are described. [Preview Abstract] |
Monday, November 21, 2016 5:09PM - 5:22PM |
L16.00004: Diffraction and interference of walking drops Giuseppe Pucci, Daniel M. Harris, John W. M. Bush A decade ago, Yves Couder and Emmanuel Fort discovered a wave-particle association on the macroscopic scale: a drop can bounce~indefinitely on a vibrating bath of the same liquid and can be piloted by the~waves that it generates. These walking droplets~have~been shown to~exhibit several quantum-like features, including single-particle diffraction and interference.~Recently, the original~diffraction and interference experiments of Couder and Fort (Couder, Y. {\&} Fort, E.~\textit{Phys. Rev. Lett.}~\textbf{97}, 154101 (2006)) have been~revisited and contested~(Andersen, A.~\textit{et al. Phys. Rev. E}~\textbf{92}(1) 013006 (2015)). We~have~revisited~this system~using~an~improved~experimental set-up,~and~observed a~strong dependence of the behavior on system parameters, including drop size and vibrational~forcing. ~In both the single-~and the double-slit~geometries, the~diffraction pattern is dominated~by the interaction of the walking~droplet with a planar boundary.~Critically, in the~double-slit geometry, the walking droplet is influenced by both slits by virtue of its spatially~extended wave field. [Preview Abstract] |
Monday, November 21, 2016 5:22PM - 5:35PM |
L16.00005: Non-local features of a hydrodynamic pilot-wave system Andre Nachbin, Miles Couchman, John Bush A droplet walking on the surface of a vibrating fluid bath constitutes a pilot-wave system of the form envisaged for quantum dynamics by Louis de Broglie: a particle moves in resonance with its guiding wave field. We here present an examination of pilot-wave hydrodynamics in a confined domain. Specifically, we present a one-dimensional water wave model that describes droplets walking in single and multiple cavities. The cavities are separated by a submerged barrier, and so allow for the study of tunneling. They also highlight the non-local dynamical features arising due to the spatially-extended wave field. Results from computational simulations are complemented by laboratory experiments. [Preview Abstract] |
Monday, November 21, 2016 5:35PM - 5:48PM |
L16.00006: The energetics of bouncing droplets Sam Turton, Jan Molacek, John Bush We present the results of a theoretical investigation of the energetics of droplets bouncing on the surface of a vertically vibrating bath. We first assess the relative magnitudes of the kinetic, surface and gravitational potential energies of both the droplet and its wave field. We then seek to rationalize the transitions between the various bouncing and walking states that arise as the vibrational forcing is increased. Our results are compared with prior theoretical and experimental work. [Preview Abstract] |
Monday, November 21, 2016 5:48PM - 6:01PM |
L16.00007: The role of bouncing-phase variation for walking droplets Lucas Tambasco, Anand Oza, Luiz Faria, John Bush Experimental and theoretical studies of droplets walking on a vibrating bath show that the droplet’s impact phase depends on the driving acceleration. Experiments also show that this phase may change in the presence of boundaries or other walkers, indicating a dependence of phase on local wave amplitude. One expects that this phase variation may alter the stability of various dynamical states. We here introduce an integro-differential model for a walker's horizontal motion that accounts for the variability of impact phase, and use it to predict the stability of rectilinear walking and orbital solutions. Our model predictions are compared with those of previous constant-phase models and related to experiments whenever possible. [Preview Abstract] |
Monday, November 21, 2016 6:01PM - 6:14PM |
L16.00008: Walking droplets in confined domains Pedro S\'aenz, John Bush A millimetric liquid drop can walk spontaneously along the surface of a vibrating fluid bath, propelled by a resonant interaction with its own wave field. These walking droplets exhibit features previously thought to be exclusive to the microscopic quantum realm. We here explore experimentally the dynamics and statistics of this macroscopic wave-particle system in confined domains, or `corrals'. Particular attention is given to characterizing the influence of the corral geometry on the emergent probability distributions. The relation to analogous quantum systems (specifically, quantum corrals, the quantum mirage and scarring in Bose-Einstein condensates) is discussed. [Preview Abstract] |
Monday, November 21, 2016 6:14PM - 6:27PM |
L16.00009: Pairs of Bouncing Droplets Miles Couchman, Pierre Caldairou, Anand Oza, John Bush Multiple droplets bouncing on the surface of a vibrating fluid bath interact through the waves generated at each bounce. We here present the results of an experimental study of the behavior of two interacting droplets. As the driving acceleration of the bath is increased progressively, static bound states are found to destabilize into a variety of dynamical states including oscillating, orbiting, and ratcheting states. The type of instability depends on the droplet sizes and their separation distance. Attempts to provide theoretical rationale for the observed behavior are described. [Preview Abstract] |
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