The stability of bound states in pilot-wave hydrodynamics
Name
1191254481-MIT.pdf
Size
34.77 MB
Format
Adobe PDF
Checksum (MD5)
13cd6ad76024d5075c72f1911ec1ccfe
Author(s)
Couchman, Miles Meissner Paasikivi.
Advisor(s)
John W. M. Bush.
Date Issued
2020
Publisher
Massachusetts Institute of Technology
Abstract
Millimetric droplets bouncing on the surface of a vertically vibrating fluid bath may self-propel through a resonant interaction with their own wavefield, displaying behaviors previously thought to be exclusive to the microscopic quantum realm. We investigate the stability of quantized bound states comprised of multiple droplets interacting through their shared wavefield, using an integrated experimental and theoretical approach. We consider the behavior of droplet pairs, rings, and chains as the bath's vibrational acceleration is increased progressively, and uncover a rich variety of dynamical states including periodic oscillations and traveling waves. The instability observed is dependent on the droplet number and size, and whether the drops are bouncing in- or out-of-phase relative to their neighbors. We develop a new theoretical model that accounts for the coupling between a drop's horizontal and vertical motion, enabling us to rationalize the majority of our experimental findings. We thus demonstrate that variations in a drop's impact phase with the bath have a critical influence on the stability of bouncing-droplet bound states. Our work provides insight into the complex interactions and collective motions that arise in bouncing-droplet aggregates, and forges new mathematical links with extant models of microscopic physics.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020
Cataloged from the official PDF of thesis.
Includes bibliographical references (pages 185-195).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided.
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