Exotic orbits of two interacting wave sources

Protière, Suzie; Bohn, Steffen; Couder, Y.

doi:10.1103/physreve.78.036204

Cited by 43 publications

(42 citation statements)

References 19 publications

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“…In future work, one may apply the methodology of Durey and Milewski [26] followed here to the chaotic trajectories of walkers under the influence of a Coriolis force [12,23,39] with a view to seeking a similar double quantization in that system. A broader exploration of pilot-wave systems with different external forces and geometries should yield a better understanding of the emergent statistics of chaotic pilot-wave dynamics.…”

Section: Discussionmentioning

confidence: 99%

Simulations of pilot-wave dynamics in a simple harmonic potential

2017

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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 integrodifferential 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.

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Section: Discussionmentioning

confidence: 99%

Simulations of pilot-wave dynamics in a simple harmonic potential

2017

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“…Experiments conducted over the past eight years have revealed that the resulting "path memory" is responsible for the complex walker dynamics and their quantum-like behavior [29]. Multiple walkers may interact with each other through their wave fields and thus exhibit interesting coherent behavior [26,28,55,30].…”

Section: Introductionmentioning

confidence: 99%

A trajectory equation for walking droplets: hydrodynamic pilot-wave theory

2013

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Yves Couder and coworkers have demonstrated that millimetric droplets walking on a vibrating fluid bath exhibit several features previously thought to be peculiar to the microscopic quantum realm, including single-particle diffraction, tunneling, quantized orbits, and wave-like statistics in a corral. We here develop an integro-differential trajectory equation for these walking droplets with a view to gaining insight into their subtle dynamics. The orbital quantization is rationalized by assessing the stability of the orbital solutions. The stability analysis also predicts the existence of wobbling orbital states reported in recent experiments, and the absence of stable orbits in the limit of large vibrational forcing. In this limit, the complex walker dynamics give rise to a coherent statistical behavior with wave-like features. We characterize the progression from quantized orbits to chaotic dynamics as the vibrational forcing is increased progressively. We then describe the dynamics of a weakly-accelerating walker in terms of its wave-induced added mass, which provides rationale for the anomalously large orbital radii observed in experiments.

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“…We proceed by investigating the interaction between a pair of walkers, as was examined experimentally by Protière et al (2006), Protière et al (2008) and Eddi et al (2012). We confine our attention to two special cases, where the walkers are initially antiparallel and parallel.…”

Section: Two-particle Interactionmentioning

confidence: 99%

“…We confine our attention to two special cases, where the walkers are initially antiparallel and parallel. Protière et al (2008) report that when the walkers are initially antiparallel, and so approach each other, they may either scatter or lock into orbit, depending on their relative bouncing phase, and the perpendicular distance between their original paths, the so-called impact parameter, d I .…”

Section: Two-particle Interactionmentioning

confidence: 99%

Faraday pilot-wave dynamics: modelling and computation

et al. 2015

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A millimetric droplet bouncing on the surface of a vibrating fluid bath can self-propel by virtue of a resonant interaction with its own wave field (Couder et al. 2005a;Protière et al. 2006). This system represents the first known example of a pilot-wave system of the form envisaged by Louis de Broglie in his double-solution pilot-wave theory (de Broglie 1930(de Broglie , 1956(de Broglie , 1987. We here develop a numerical model of pilot-wave hydrodynamics by coupling recent models of the droplet's bouncing dynamics (Moláček & Bush 2013a,b) with a more realistic model of weakly viscous wave generation and evolution. (Lamb 1932;Dias et al. 2008). The resulting model is the first to capture a number of features reported in experiment, including the rapid transient wave generated during impact, the Doppler effect, and walker-walker interactions.

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Exotic orbits of two interacting wave sources

Cited by 43 publications

References 19 publications

Simulations of pilot-wave dynamics in a simple harmonic potential

Simulations of pilot-wave dynamics in a simple harmonic potential

A trajectory equation for walking droplets: hydrodynamic pilot-wave theory

Faraday pilot-wave dynamics: modelling and computation

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