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Non-Hamiltonian features of a classical pilot-wave dynamics

Abstract : A bouncing droplet on a vibrated bath can couple to the waves it generates, so that it becomes a propagative walker. Its propulsion at constant velocity means that a balance exists between the permanent input of energy provided by the vibration and the dissipation. Here we seek a simple theoretical description of the resulting non-Hamiltonian dynamics with a walker immersed in a harmonic potential well. We demonstrate that the interaction with the recently emitted waves can be modeled by a Rayleigh-type friction. The Rayleigh oscillator has well defined attractors. The convergence toward them and their stability is investigated through an energetic approach and a linear stability analysis. These theoretical results provide a description of the dynamics in excellent agreement with the experimental data. It is thus a basic framework for further investigations of wave-particle interactions when memory effects are included.
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Contributor : Matthieu Labousse <>
Submitted on : Saturday, August 30, 2014 - 10:09:36 PM
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Matthieu Labousse, Stéphane Perrard. Non-Hamiltonian features of a classical pilot-wave dynamics. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2014, 90, pp.022913. ⟨10.1103/PhysRevE.90.022913⟩. ⟨hal-01059409⟩

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