Onset of chaos in orbital pilot-wave dynamics

Posted by on Jan 15, 2017 in Bibliography, Core Bibliography, Numerical Simulation | 0 comments

Abstract  : We examine the orbital dynamics of droplets self-propelling along the surface of a vibrating bath. Circular orbital motion may arise when the walking droplet is subjected to one of three external force fields, the Coriolis force, a simple harmonic force, and a Coulomb force. Particular attention is given to a theoretical characterization of the onset of chaos that accompanies the destabilization of such circular orbits.

Tambasco, L., Harris, D., Oza, A., Rosales, R., & Bush, J. (2015, November). Onset of chaos in orbital pilot-wave dynamics. In APS Meeting Abstracts.

Onset of Chaos Numerical

 

Paper available on researchgate.net/ (Requires free login)

Read More

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

Posted by on Jul 7, 2014 in Bibliography, Core Bibliography | 0 comments

Oza, A. U., Harris, D. M., Rosales, R. R., & Bush, J. W. (2014). Pilot-wave dynamics in a rotating frame: on the emergence of orbital quantization. Journal of Fluid Mechanics, 744, 404-429.

We 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

http://math.mit.edu/~auoza/JFM_2.pdf

Read More

A trajectory equation for walking droplets: hydrodynamic pilot-wave theory

Posted by on Dec 13, 2013 in Bibliography, Core Bibliography, Numerical Simulation | 0 comments

Oza, A. U., Rosales, R. R., & Bush, J. W. (2013). A trajectory equation for walking droplets: hydrodynamic pilot-wave theory. Journal of Fluid Mechanics,737, 552-570.

 

http://math.mit.edu/~bush/wordpress/wp-content/uploads/2013/12/ORB-JFM.pdf

 

Integro-differential equation describing the horizontal motion of a walking droplet

Stability to perturbations

Read More