A trajectory equation for walking droplets : hydrodynamic pilot-wave theory
Name
890211673-MIT.pdf
Description
Full printable version
Size
8.51 MB
Format
Adobe PDF
Checksum (MD5)
24611fadbfa82a738a952ec7f9fda044
Author(s)
Oza, Anand Uttam
Advisor(s)
John W. M. Bush and Rodolfo R. Rosales.
Date Issued
2014
Publisher
Massachusetts Institute of Technology
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. The orbital quantization is rationalized 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 give rise to a coherent statistical behavior with wave-like features. We characterize the progression from quantized orbits to chaotic dynamics as the vibrational forcing is increased progressively. We then describe the dynamics of a weakly-accelerating walker in terms of its wave-induced added mass, which provides rationale for the anomalously large orbital radii observed in experiments.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.
65
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 185-189).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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