Scattering theory of walking droplets in the presence of obstacles. (22nd November 2016)

• Record Type: Journal Article
• Authors: Dubertrand, Rémy; Hubert, Maxime; Schlagheck, Peter; Vandewalle, Nicolas; Bastin, Thierry; Martin, John
• Is Part Of: New journal of physics. Volume 18:Number 11(2016:Nov.)
• Publication Date: 2016-11-22
• Subjects: drops -- nonlinear dynamics -- walking droplets -- quantum mechanics; 47.55.D- -- 03.65.-w; Physics -- Periodicals; Physics; Periodicals; 530.05
• DOI: 10.1088/1367-2630/18/11/113037
• Languages: English
• ISSNs: 1367-2630

Abstract

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.