Dynamics, emergent statistics, and the mean-pilot-wave potential of walking droplets
Name
1.5030639.pdf
Description
Published version
Size
4.62 MB
Format
Adobe PDF
Checksum (MD5)
c6f313abc34d6101ac970fbaa527566d
Author(s)
Durey, Matthew
Milewski, Paul A.
Bush, John W. M.
Date Issued
September 2018
Journal
Chaos: An Interdisciplinary Journal of Nonlinear Science
Publisher
American Institute of Physics
Citation
Durey, Matthew et al. "Dynamics, emergent statistics, and the mean-pilot-wave potential of walking droplets." Chaos: An Interdisciplinary Journal of Nonlinear Science 28, 9 (September 2018): 096108 © 2018 Author(s).
Version
Final published version
Abstract
A millimetric droplet may bounce and self-propel on the surface of a vertically vibrating bath, where its horizontal "walking" motion is induced by repeated impacts with its accompanying Faraday wave field. For ergodic long-time dynamics, we derive the relationship between the droplet's stationary statistical distribution and its mean wave field in a very general setting. We then focus on the case of a droplet subjected to a harmonic potential with its motion confined to a line. By analyzing the system's periodic states, we reveal a number of dynamical regimes, including those characterized by stationary bouncing droplets trapped by the harmonic potential, periodic quantized oscillations, chaotic motion and wavelike statistics, and periodic wave-trapped droplet motion that may persist even in the absence of a central force. We demonstrate that as the vibrational forcing is increased progressively, the periodic oscillations become chaotic via the Ruelle-Takens-Newhouse route. We rationalize the role of the local pilot-wave structure on the resulting droplet motion, which is akin to a random walk. We characterize the emergence of wavelike statistics influenced by the effective potential that is induced by the mean Faraday wave field.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution 4.0 International license
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DOI of Published Version
https://doi.org/10.1063/1.5030639
