Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 157-164). / A decade ago, Yves Couder and coworkers discovered that millimetric droplets can walk on a vibrated fluid bath, and that these walking droplets or "walkers" display several features reminiscent of quantum particles. We first describe our experimental advances, that have allowed for a quantitative characterization of the system behavior, and guided the development of our accompanying theoretical models. We then detail our explorations of this rich dynamical system in several settings where the walker is confined, either by boundaries or an external force. Three particular cases are examined: a walker in a corral geometry, a walker in a rotating frame, and a walker passing through an aperture in a submerged barrier. In each setting, as the vibrational forcing is increased, progressively more complex trajectories arise. The manner in which multimodal statistics may emerge from the walker's chaotic dynamics is elucidated. / by Daniel Martin Harris. / Ph. D.
| Identifer | oai:union.ndltd.org:MIT/oai:dspace.mit.edu:1721.1/99068 |
| Date | January 2015 |
| Creators | Harris, Daniel Martin |
| Contributors | John W. M. Bush., Massachusetts Institute of Technology. Department of Mathematics., Massachusetts Institute of Technology. Department of Mathematics. |
| Publisher | Massachusetts Institute of Technology |
| Source Sets | M.I.T. Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 164 pages, application/pdf |
| Rights | M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission., http://dspace.mit.edu/handle/1721.1/7582 |
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