Scattering theory of walking droplets in the presence of obstacles

Dubertrand, Remy, Hubert, Maxime, Schlagheck, Peter, Vandewalle, Nicolas, Bastin, Thierry and Martin, John (2016) Scattering theory of walking droplets in the presence of obstacles. New Journal of Physics, 18 (11). p. 113037. ISSN 1367-2630

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Official URL: https://doi.org/10.1088/1367-2630/18/11/113037

Abstract

We aim to describe a droplet bouncing on a vibrating bath using a simple and highly versatile model inspired from quantum mechanics. Close to the Faraday instability, a long-lived surface wave is created at each bounce, which serves as a pilot wave for the droplet. This leads to so called walking droplets or walkers. Since the seminal experiment by Couder et al (2006 Phys. Rev. Lett. 97 154101) there have been many attempts to accurately reproduce the experimental results.We propose to describe the trajectories of a walker using a Green function approach. The Green function is related to the Helmholtz equation with Neumann boundary conditions on the obstacle(s) and outgoing boundary conditions at infinity. For a single-slit geometry our model is exactly solvable and reproduces some general features observed experimentally. It stands for a promising candidate to account for the presence of arbitrary boundaries in the walker's dynamics.

Item Type: Article
Uncontrolled Keywords: drops, nonlinear dynamics, walking droplets, quantum mechanics
Subjects: F300 Physics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Elena Carlaw
Date Deposited: 20 Nov 2019 10:55
Last Modified: 20 Nov 2019 11:00
URI: http://nrl.northumbria.ac.uk/id/eprint/41539

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