Pilot-Wave Dynamics: Using Dynamic Mode Decomposition to characterize Bifurcations, Routes to Chaos and Emergent Statistics
| Title: | Pilot-Wave Dynamics: Using Dynamic Mode Decomposition to characterize Bifurcations, Routes to Chaos and Emergent Statistics |
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| Authors: | Kutz, J. Nathan, Nachbin, Andre, Baddoo, Peter J., Bush, John W. M. |
| Publication Year: | 2022 |
| Collection: | Mathematics Nonlinear Sciences Physics (Other) |
| Subject Terms: | Physics - Fluid Dynamics, Mathematics - Dynamical Systems, Nonlinear Sciences - Pattern Formation and Solitons |
| More Details: | We develop a data-driven characterization of the pilot-wave hydrodynamic system in which a bouncing droplet self-propels along the surface of a vibrating bath. We consider drop motion in a confined one-dimensional geometry, and apply the {\em Dynamic mode decomposition} (DMD) in order to characterize the evolution of the wave field as the bath's vibrational acceleration is increased progressively. DMD provides a regression framework for adaptively learning a best-fit linear dynamics model over snapshots of spatio-temporal data. The DMD characterization of the wave field yields a fresh perspective on the bouncing-droplet problem that forges valuable new links with the mathematical machinery of quantum mechanics. Moreover, it provides a low-rank characterization of the bifurcation structure of the pilot wave physics. Specifically, the analysis shows that as the vibrational acceleration is increased, the pilot-wave field undergoes a series of Hopf bifurcations that ultimately lead to a chaotic wave field. The established relation between the mean pilot-wave field and the droplet statistics allows us to characterize the evolution of the emergent statistics with increased vibrational forcing from the evolution of the pilot-wave field. We thus develop a numerical framework with the same basic structure as quantum mechanics, specifically a wave theory that predicts particle statistics. Comment: 12 pages, 10 figures |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2210.07097 |
| Accession Number: | edsarx.2210.07097 |
| Database: | arXiv |
| Description not available. |