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Bifurcations and chaos in a Lorenz-like pilot-wave system
1Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Chaos (Woodbury, N.Y.)
|November 3, 2020
Summary
Millimetric droplets can bounce and self-propel on vibrating fluid surfaces, mimicking quantum behaviors. This study simplifies their complex dynamics into a model similar to the Lorenz system, revealing chaotic phenomena.
Area of Science:
- Fluid Dynamics
- Nonlinear Dynamics
- Wave Phenomena
Background:
- Millimetric droplets exhibit self-propulsion on vibrating fluid baths, guided by self-generated waves.
- This hydrodynamic pilot-wave system displays complex dynamics, including behaviors previously associated with quantum mechanics.
Purpose of the Study:
- To theoretically investigate an idealized pilot-wave model.
- To simplify the system's evolution into a reduced three-dimensional dynamical system.
- To elucidate pilot-wave phenomena, including chaos, by drawing parallels with the Lorenz system.
Main Methods:
- Development of a theoretical model for a particle guided by a one-dimensional wave.
- Projection of the pilot-wave system onto a three-dimensional dynamical system.
- Analysis of the dynamical system's similarity to the Lorenz system.
Main Results:
- The pilot-wave system's evolution can be described by a three-dimensional dynamical system.
- This reduced system shares characteristics with the Lorenz system.
- The study identifies and characterizes phenomena such as the onset of chaos in pilot-wave systems.
Conclusions:
- The simplified pilot-wave model provides insights into complex fluid dynamics.
- The connection to the Lorenz system aids in understanding chaotic behaviors in wave-guided systems.
- Hydrodynamic pilot-wave systems offer a macroscopic analog for quantum-like phenomena.
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