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Information stored in Faraday waves: the origin of a path memory

Published online by Cambridge University Press:  25 March 2011

ANTONIN EDDI ,
ERIC SULTAN ,
JULIEN MOUKHTAR ,
EMMANUEL FORT ,
MAURICE ROSSI  and
YVES COUDER
ANTONIN EDDI*
Affiliation:
Laboratoire Matières et Systèmes Complexes, Université Paris Diderot and CNRS, UMR 7057, Bâtiment Condorcet, 10 rue Alice Domon et Léonie Duquet, 75013 Paris, France
ERIC SULTAN
Affiliation:
Laboratoire FAST, Université Pierre et Marie Curie, Université Paris-Sud and CNRS, UMR 7608, Bâtiment 502, Campus Universitaire, 91405 Orsay, France
JULIEN MOUKHTAR
Affiliation:
Laboratoire Matières et Systèmes Complexes, Université Paris Diderot and CNRS, UMR 7057, Bâtiment Condorcet, 10 rue Alice Domon et Léonie Duquet, 75013 Paris, France
EMMANUEL FORT
Affiliation:
Institut Langevin, ESPCI ParisTech, Université Paris Diderot and CNRS, UMR 7587, 10 rue Vauquelin, 75231 Paris CEDEX 05, France
MAURICE ROSSI
Affiliation:
Institut Jean Le Rond D'Alembert, Université Pierre et Marie Curie and CNRS, UMR 7190, 4 Place Jussieu, 75252 Paris CEDEX 05, France
YVES COUDER
Affiliation:
Laboratoire Matières et Systèmes Complexes, Université Paris Diderot and CNRS, UMR 7057, Bâtiment Condorcet, 10 rue Alice Domon et Léonie Duquet, 75013 Paris, France
*
†Email address for correspondence: antonin.eddi@univ-paris-diderot.fr
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Abstract

On a vertically vibrating fluid interface, a droplet can remain bouncing indefinitely. When approaching the Faraday instability onset, the droplet couples to the wave it generates and starts propagating horizontally. The resulting wave–particle association, called a walker, was shown previously to have remarkable dynamical properties, reminiscent of quantum behaviours. In the present article, the nature of a walker's wave field is investigated experimentally, numerically and theoretically. It is shown to result from the superposition of waves emitted by the droplet collisions with the interface. A single impact is studied experimentally and in a fluid mechanics theoretical approach. It is shown that each shock emits a radial travelling wave, leaving behind a localized mode of slowly decaying Faraday standing waves. As it moves, the walker keeps generating waves and the global structure of the wave field results from the linear superposition of the waves generated along the recent trajectory. For rectilinear trajectories, this results in a Fresnel interference pattern of the global wave field. Since the droplet moves due to its interaction with the distorted interface, this means that it is guided by a pilot wave that contains a path memory. Through this wave-mediated memory, the past as well as the environment determines the walker's present motion.

JFM classification

Drops and Bubbles: Drops Waves/Free-surface Flows: Faraday waves Nonlinear Dynamical Systems: Pattern formation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 674 , 10 May 2011 , pp. 433 - 463
Copyright
Copyright © Cambridge University Press 2011

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