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Faraday pilot-wave dynamics in a circular corral

  • Matthew Durey (a1) (a2), Paul A. Milewski (a1) and Zhan Wang (a3)

Abstract

A millimetric droplet of silicone oil may bounce and self-propel on the free surface of a vertically vibrating fluid bath due to the droplet’s interaction with its accompanying Faraday wave field. This hydrodynamic pilot-wave system exhibits many dynamics that were previously thought to be peculiar to the quantum realm. When the droplet is confined to a circular cavity, referred to as a ‘corral’, a range of dynamics may occur depending on the details of the geometry and the decay time of the subcritical Faraday waves. We herein present a theoretical investigation into the behaviour of subcritical Faraday waves in this geometry and explore the accompanying pilot-wave dynamics. By computing the Dirichlet-to-Neumann map for the velocity potential in the corral geometry, we can evolve the quasi-potential flow between successive droplet impacts, which, when coupled with a simplified model for the droplet’s vertical motion, allows us to derive and implement a highly efficient discrete-time iterative map for the pilot-wave system. We study the onset of the Faraday instability, the emergence and quantisation of circular orbits and simulate the exotic dynamics that arises in smaller corrals.

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Corresponding author

Email address for correspondence: mdurey@mit.edu

References

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Faraday pilot-wave dynamics in a circular corral

  • Matthew Durey (a1) (a2), Paul A. Milewski (a1) and Zhan Wang (a3)

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