Classical pilot-wave dynamics: the free particle

Durey, M. and Bush, J. W.M. (2021) Classical pilot-wave dynamics: the free particle. Chaos: An Interdisciplinary Journal of Nonlinear Science, 31(3), 033136. (doi: 10.1063/5.0039975) (PMID:33810713)

Abstract

We present the results of a theoretical investigation into the dynamics of a vibrating particle propelled by its self-induced wave field. Inspired by the hydrodynamic pilot-wave system discovered by Yves Couder and Emmanuel Fort, the idealized pilot-wave system considered here consists of a particle guided by the slope of its quasi-monochromatic “pilot” wave, which encodes the history of the particle motion. We characterize this idealized pilot-wave system in terms of two dimensionless groups that prescribe the relative importance of particle inertia, drag and wave forcing. Prior work has delineated regimes in which self-propulsion of the free particle leads to steady or oscillatory rectilinear motion; it has further revealed parameter regimes in which the particle executes a stable circular orbit, confined by its pilot wave. We here report a number of new dynamical states in which the free particle executes self-induced wobbling and precessing orbital motion. We also explore the statistics of the chaotic regime arising when the time scale of the wave decay is long relative to that of particle motion and characterize the diffusive and rotational nature of the resultant particle dynamics. We thus present a detailed characterization of free-particle motion in this rich two-parameter family of dynamical systems.

• Item Type: Articles
• Additional Information: The authors gratefully acknowledge the NSF for financial support through Grant No. CMMI-1727565.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Durey, Dr Matthew
• Authors: Durey, M., and Bush, J. W.M.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Chaos: An Interdisciplinary Journal of Nonlinear Science
• Publisher: American Institute of Physics
• ISSN: 1054-1500
• ISSN (Online): 1089-7682
• Published Online: 12 March 2021
• Copyright Holders: Copyright © 2021 The Authors
• First Published: First published in Chaos: An Interdisciplinary Journal of Nonlinear Science 31(3): 033136
• Publisher Policy: Reproduced under a Creative Commons License