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arXiv · 1605.02370

Scattering theory of walking droplets in the presence of obstacles

Rémy Dubertrand·Maxime Hubert·Peter Schlagheck·Nicolas Vandewalle·Thierry Bastin·John Martin
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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 {\it Couder et al} [Phys. Rev. Lett. {\bf 97}, 154101 (2006)] 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.

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Rémy Dubertrand, Maxime Hubert, Peter Schlagheck, Nicolas Vandewalle, Thierry Bastin, John Martin. 2016-11-23. Scattering theory of walking droplets in the presence of obstacles. https://doi.org/10.1088/1367-2630%2F18%2F11%2F113037

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