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Pilot-wave dynamics: Using dynamic mode decomposition to characterize bifurcations, routes to chaos, and emergent
J Nathan Kutz1, André Nachbin2, Peter J Baddoo3
1Department of Applied Mathematics and Electrical and Computer Engineering, University of Washington, Seattle, Washington 98195, USA.
Physical Review. E
|October 18, 2023
Summary
This study uses dynamic mode decomposition (DMD) to analyze bouncing droplets, revealing how wave fields evolve and link to quantum mechanics. The findings offer a new perspective on fluid dynamics and wave phenomena.
Area of Science:
- Fluid Dynamics
- Nonlinear Dynamics
- Wave Phenomena
Background:
- Bouncing droplets on vibrating baths exhibit complex behaviors.
- Understanding the underlying wave dynamics is crucial for characterizing droplet motion.
- Existing models may not fully capture the emergent complexity.
Purpose of the Study:
- To develop a data-driven characterization of the pilot-wave hydrodynamic system.
- To analyze the evolution of the wave field using dynamic mode decomposition (DMD).
- To establish links between pilot-wave physics and quantum mechanics.
Main Methods:
- Applying dynamic mode decomposition (DMD) to spatiotemporal data of the wave field.
- Reducing complex nonlinear interactions to a low-dimensional linear superposition of DMD modes.
- Analyzing the bifurcation structure of the pilot-wave system.
Main Results:
- DMD successfully characterized the wave field evolution with increasing vibrational acceleration.
- The study identified Hopf bifurcations leading to a chaotic wave field.
- A connection was established between pilot-wave field evolution and emergent droplet statistics.
Conclusions:
- DMD provides a novel, low-dimensional framework for understanding bouncing droplet systems.
- The pilot-wave system exhibits a bifurcation structure analogous to quantum mechanics.
- This approach offers a wave theory capable of predicting particle statistics.
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