Spring 2015
Seminars are held on Mondays from 1:30 - 2:30PM in Cullimore Hall, Room 611, unless noted otherwise. For questions about the seminar schedule, please contact David Shirokoff.
Date: April 6, 2014
Speaker: Anand Oza
Courant Institute of Mathematical Sciences,
New York University
Title: "A Trajectory Equation for Walking Droplets: Hydrodynamic Pilot-Wave Theory"
Abstract:
Yves Couder and coworkers have demonstrated that millimetric droplets walking on a vibrating fluid bath exhibit several features previously thought to be peculiar to the microscopic quantum realm, including single-particle diffraction, tunneling, quantized orbits, and wave-like statistics in a corral. We here develop an integro-differential trajectory equation for these walking droplets with a view to gaining insight into their subtle dynamics. We then rationalize the emergence of orbital quantization in a rotating frame by assessing the stability of the orbital solutions. 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. In this limit, the complex walker dynamics gives rise to a coherent statistical behavior with wave-like features.