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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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 |
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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: | 31 Jul 2021 20:33 |
URI: | http://nrl.northumbria.ac.uk/id/eprint/41539 |
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