Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session E34: Drops VI: Bouncing Drops |
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Chair: David Hu, Georgia Institute of Technology Room: 405 |
Sunday, November 24, 2013 4:45PM - 4:58PM |
E34.00001: Droplets walking in a rotating frame: from quantized orbits to wavelike statistics Daniel M. Harris, John W.M. Bush We present the results of an experimental investigation of a droplet walking on the surface of a vibrating rotating fluid bath. Particular attention is given to demonstrating that the stable quantized orbits reported by Fort et al. (PNAS, 2010) arise only for a finite range of vibrational forcing, above which chaotic trajectories with wavelike statistics arise. We first present a detailed characterization of the emergence of orbital quantization, and then examine the system behavior at higher driving amplitudes. As the vibrational forcing is increased progressively, stable circular orbits are succeeded by wobbling orbits with, in turn, stationary and drifting orbital centers. Subsequently, there is a transition to wobble-and-leap dynamics, in which wobbling of increasing amplitude about a stationary center is punctuated by the orbital center leaping approximately half a Faraday wavelength. Finally, in the limit of high vibrational forcing, irregular chaotic trajectories emerge, characterized by a wavelike statistical behavior that reflects the persistent dynamic influence of the unstable orbital states. [Preview Abstract] |
Sunday, November 24, 2013 4:58PM - 5:11PM |
E34.00002: Pilot-wave dynamics in a rotating frame: on the emergence of orbital quantization Anand Oza, Daniel Harris, Rodolfo Rosales, John Bush We present the results of a theoretical investigation of droplets walking on a rotating vibrating fluid bath. The droplet's trajectory is described in terms of an integro-differential equation that incorporates the influence of its propulsive wave force. Predictions for the dependence of the orbital radius on the bath's rotation rate compare favorably with experimental data and capture the progression from continuous to quantized orbits as the vibrational acceleration is increased. The orbital quantization is rationalized by assessing the stability of the orbital solutions, and may be understood as resulting directly from the dynamic constraint imposed on the drop by its monochromatic guiding wave. The stability analysis also predicts the existence of wobbling orbital states reported in recent experiments, and the virtual absence of stable orbits in the limit of large vibrational forcing. [Preview Abstract] |
Sunday, November 24, 2013 5:11PM - 5:24PM |
E34.00003: Quantization of a particle guided by its own pilot-wave St\'ephane Perrard, Matthieu Labousse, Emmanuel Fort, Yves Couder The association of a particle and a wave can be obtained even at a macroscopic scale, using a simple experimental set up. A liquid bath is set into vertical oscillation so that any drop deposit on it has never the time to break the air layer under it. The drop is always ejected from the bath by the vibration and can then live for hours. The impact generates waves at the surface of the bath which can propel the drop. It becomes a walker, the self-propelled entity formed by a bouncing droplet and its associated surface wave. This system has already shown surprising wave-particle duality as single particle diffraction or Bohr-Sommerfeld quantization of level when the drop is submitted to a transverse force. We now study its motion when the walker is submitted to a central force, which can be tuned at will. In particular, I will present our results in the case of a 2D harmonic potential well. In the case of a strong coupling between the waves and the bouncing drop, the walker exhibit a discrete set of state where the angular momentum and the spatial extend of each level are quantized. Disordered trajectories also appear, as an intermittency between the pure eigenmodes through transitions between them. [Preview Abstract] |
Sunday, November 24, 2013 5:24PM - 5:37PM |
E34.00004: ``Quantum" interference with bouncing drops Tomas Bohr, Anders Andersen, Jacob Madsen, Christian Reichelt, Benny Lautrup, Clive Ellegaard, Mogens Levinsen In a series of recent papers (most recently D. Harris, J. Moukhtar, E. Fort, Y. Couder and J. Bush, Phys. Rev. E {\bf 88}, 011001(R) (2013)) Yves Couder and collaborators have explored the dynamics of walking drops on the surface of a vibrated bath of silicon oil and have demonstrated a close analogy to quantum phenomena. The bouncing drop together with the surface wave that it excites seems to be very similar to the pilot wave envisaged by de Broglie for quantum particles. In particular, Couder and Fort (Phys. Rev. Lett. {\bf 97}, 154101 (2006)) have studied a double slit experiment with walking drops, where an interference pattern identical to the quantum version is found even though it is possible to follow the orbits of the drops and unambigously determine which slit it goes through, something which in quantum mechanics would be ruled out by the Heisenberg uncertainly relations. We have repeated the experiment and present a somewhat more complicated picture. Theoretically, we study a Schr{\"o}dinger equation with a source term originating from a localised ``particle" being simultaneously guided by the wave. We present simple solutions to such a field theory and discuss the fundamental difficulties met by such a theory in order to comply with quantum mechanics. [Preview Abstract] |
Sunday, November 24, 2013 5:37PM - 5:50PM |
E34.00005: The hydrodynamic boost factor for walking droplets John Bush, Anand Oza, Jan Molacek It has recently been demonstrated that droplets walking on a vibrating fluid bath exhibit several dynamical features previously thought to be peculiar to the microscopic realm. Such ``walkers,'' consisting of droplet plus guiding wave field, are spatially extended objects. We here examine the dependence of the walker mass and momentum on its velocity. Doing so indicates that in certain parameter regimes, the walker dynamics may be described in terms of the inviscid mechanics of a particle with a speed-dependent mass. Drawing an analogy with relativistic mechanics, we define a hydrodynamic boost factor for these walking droplets, consideration of which provides rationale for the anomalous radii of walkers executing circular orbits. [Preview Abstract] |
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