scholarly journals Classical pilot-wave dynamics: The free particle

2021 ◽  
Vol 31 (3) ◽  
pp. 033136
Author(s):  
Matthew Durey ◽  
John W. M. Bush
Keyword(s):  
Free Particle ◽  
Wave Dynamics ◽  
Pilot Wave

scholarly journals Pilot-wave dynamics in a harmonic potential: Quantization and stability of circular orbits

2016 ◽  
Vol 93 (3) ◽  
Author(s):  
M. Labousse ◽  
A. U. Oza ◽  
S. Perrard ◽  
J. W. M. Bush
Keyword(s):  
Harmonic Potential ◽  
Circular Orbits ◽  
Wave Dynamics ◽  
Pilot Wave

scholarly journals Speed oscillations in classical pilot-wave dynamics

2020 ◽  
Vol 476 (2239) ◽  
pp. 20190884 ◽  
Author(s):  
Matthew Durey ◽  
Sam E. Turton ◽  
John W. M. Bush
Keyword(s):  
Dynamical System ◽  
Random Walk ◽  
Decay Rate ◽  
Wave Field ◽  
Theoretical Investigation ◽  
Parameter Space ◽  
Resonant Interaction ◽  
Wave Dynamics ◽  
Pilot Wave

We present the results of a theoretical investigation of a dynamical system consisting of a particle self-propelling through a resonant interaction with its own quasi-monochromatic pilot-wave field. We rationalize two distinct mechanisms, arising in different regions of parameter space, that may lead to a wavelike statistical signature with the pilot-wavelength. First, resonant speed oscillations with the wavelength of the guiding wave may arise when the particle is perturbed from its steady self-propelling state. Second, a random-walk-like motion may set in when the decay rate of the pilot-wave field is sufficiently small. The implications for the emergent statistics in classical pilot-wave systems are discussed.

scholarly journals Simulations of pilot-wave dynamics in a simple harmonic potential

2017 ◽  
Vol 2 (11) ◽  
Author(s):  
Kristin M. Kurianski ◽  
Anand U. Oza ◽  
John W. M. Bush
Keyword(s):  
Harmonic Potential ◽  
Wave Dynamics ◽  
Pilot Wave

scholarly journals Faraday pilot-wave dynamics in a circular corral

2020 ◽  
Vol 891 ◽  
Author(s):  
Matthew Durey ◽  
Paul A. Milewski ◽  
Zhan Wang
Keyword(s):  
Wave Dynamics ◽  
Pilot Wave ◽  
Image Position

scholarly journals Faraday pilot-wave dynamics: modelling and computation

2015 ◽  
Vol 778 ◽  
pp. 361-388 ◽  
Author(s):  
Paul A. Milewski ◽  
Carlos A. Galeano-Rios ◽  
André Nachbin ◽  
John W. M. Bush
Keyword(s):  
Fluid Model ◽  
Wave Theory ◽  
Realistic Model ◽  
Resonant Interaction ◽  
Wave System ◽  
Transient Wave ◽  
Wave Dynamics ◽  
Pilot Wave ◽  
Dynamics Modelling ◽  
Pilot Wave Theory

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. 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. We here develop a fluid model of pilot-wave hydrodynamics by coupling recent models of the droplet’s bouncing dynamics with a more realistic model of weakly viscous quasi-potential wave generation and evolution. 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.

scholarly journals The pilot-wave dynamics of walking droplets

2013 ◽  
Vol 25 (9) ◽  
pp. 091112 ◽  
Author(s):  
Daniel M. Harris ◽  
John W. M. Bush
Keyword(s):  
Wave Dynamics ◽  
Pilot Wave

Pilot-wave dynamics in a rotating frame: on the emergence of orbital quantization

2014 ◽  
Vol 744 ◽  
pp. 404-429 ◽  
Author(s):  
Anand U. Oza ◽  
Daniel M. Harris ◽  
Rodolfo R. Rosales ◽  
John W. M. Bush
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Stability Analysis ◽  
Rotation Rate ◽  
Wave Force ◽  
Rotating Frame ◽  
Wave Dynamics ◽  
Pilot Wave ◽  
Dynamic Constraint ◽  
The Stability

AbstractWe present the results of a theoretical investigation of droplets walking on a rotating vibrating fluid bath. The droplet’s trajectory is described in terms of an integro-differential equation that incorporates the influence of its propulsive wave force. Predictions for the dependence of the orbital radius on the bath’s rotation rate compare favourably with experimental data and capture the progression from continuous to quantized orbits as the vibrational acceleration is increased. The orbital quantization is rationalized by assessing the stability of the orbital solutions, and may be understood as resulting directly from the dynamic constraint imposed on the drop by its monochromatic guiding wave. 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.

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