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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 dynamic mode decomposition (DMD) in order to characterize the evolution of the wave field as the bath’s vibrational acceleration is increased progressively. Dynamic mode decomposition provides a regression framework for adaptively learning a best-fit linear dynamics model over snapshots of spatiotemporal data. Thus, DMD reduces the complex nonlinear interactions between pilot waves and droplet to a low-dimensional linear superposition of DMD modes characterizing the wave field. In particular, it provides a low-dimensional characterization of the bifurcation structure of the pilot-wave physics, wherein the excitation and recruitment of additional modes in the linear superposition models the bifurcation sequence. This DMD characterization yields a fresh perspective on the bouncing-droplet problem that forges valuable new links with the mathematical machinery of quantum mechanics. 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.
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Extracting Spatial–Temporal Coherent Patterns in Geomagnetic Secular Variation Using Dynamic Mode Decomposition
Abstract Rapid growth of magnetic‐field observations through SWARM and other satellite missions motivate new approaches to analyze it. Dynamic mode decomposition (DMD) is a method to recover spatially coherent motion with a periodic time dependence. We use this method to simultaneously analyze the geomagnetic radial field and its secular variation from CHAOS‐7 at high latitudes. A total of five modes are permitted by noise levels in the observations. One mode represents a slowly evolving background state, whereas the other four modes describe a pair of waves; each wave is comprised of a complex DMD mode and its complex conjugate. The waves have periods ofT1 = 19.1 andT2 = 58.4 years and quality factors ofQ1 = 11.0 andQ2 = 4.6, respectively. A 60‐year wave is consistent with previous predictions for zonal waves in a stratified fluid. The 20‐year wave is also consistent with previous reports at high latitudes, although its nature is less clear.
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- Award ID(s):
- 2214244
- PAR ID:
- 10400522
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Geophysical Research Letters
- Volume:
- 50
- Issue:
- 5
- ISSN:
- 0094-8276
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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