2014/08/26 by Matthieu Labousse, Stéphane Perrard
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Attractor #Classical mechanics #Dissipation #Hamiltonian (control theory) #Harmonic oscillator #Mathematical analysis #Mathematics #Mechanics #Micro and Nano Robotics #Orbital Angular Momentum in Optics #Physics #Quantum mechanics #Rayleigh scattering #Rayleigh wave #Simple harmonic motion #Statistical physics #Wave propagation #physics.class-ph #physics.flu-dyn
paper · pdf · doi:10.1103/physreve.90.022913
published as Physical Review E, 90, 022913 (2014) · 10 pages, 6 figures
openalex publication_date 2014/08/26 · arxiv created 2014/08/31 · arxiv updated 2014/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.