Scattering theory of walking droplets in the presence of obstacles
Scattering theory of walking droplets in the presence of obstacles
复制标题
存在障碍物时行走液滴的散射理论
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
John Martin
中科院分区：
文献类型：
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作者：
R. Dubertrand;M. Hubert;P. Schlagheck;N. Vandewalle;T. Bastin;John Martin
我们的目标是使用受量子力学启发的简单且高度通用的模型来描述振动浴上弹跳的液滴。接近法拉第不稳定性，每次弹跳时都会产生一个长寿命的表面波，作为液滴的导波。这导致了所谓的步行水滴或步行者。自从 Couder 等人（2006 Phys. Rev. Lett. 97 154101）的开创性实验以来，已经进行了许多尝试来准确地重现实验结果。我们建议使用格林函数方法来描述步行者的轨迹。格林函数与亥姆霍兹方程相关，该方程具有障碍物上的诺伊曼边界条件和无穷远处的传出边界条件。对于单缝几何结构，我们的模型是完全可解的，并且再现了实验观察到的一些一般特征。它代表了一个有前途的候选者，可以解释步行者动力学中任意边界的存在。
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.