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This study explores a theoretical vibrating particle system, revealing new wobbling and precessing orbital motions. The research characterizes complex dynamics in a two-parameter system, offering insights into pilot-wave phenomena.

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Area of Science:

  • Physics
  • Fluid Dynamics
  • Nonlinear Dynamics

Background:

  • Inspired by Couder and Fort's hydrodynamic pilot-wave systems.
  • Focuses on an idealized system of a particle guided by its self-induced wave field.
  • The pilot wave encodes the particle's motion history.

Purpose of the Study:

  • To theoretically investigate the dynamics of a vibrating particle propelled by its self-induced wave field.
  • To characterize the system using dimensionless groups.
  • To identify new dynamical states and explore chaotic regimes.

Main Methods:

  • Theoretical investigation of a particle-wave interaction model.
  • Characterization using two dimensionless parameters.
  • Analysis of particle inertia, drag, and wave forcing.

Main Results:

  • Identified regimes of steady, oscillatory, and circular orbital motion.
  • Discovered new self-induced wobbling and precessing orbital dynamics.
  • Characterized chaotic regimes and the diffusive/rotational nature of particle dynamics.

Conclusions:

  • The idealized pilot-wave system exhibits rich dynamics across a two-parameter space.
  • New orbital and chaotic states expand the understanding of self-propelled particle systems.
  • Provides a detailed characterization of free-particle motion in this theoretical framework.