Group 2 2014

Members: Bollenbacher, Chambers, Cunningham, Putzel

Introduction

First observed by Michael Faraday in 1831, Faraday waves are instabilities in the surface of a liquid arising at a fluid undergoing vertical oscillations above a critical amplitude and/or frequency. Faraday himself measured that the resulting surface wave frequency was equal to half the driving frequency. Above this critical amplitude/frequency the fluid surface can exhibit an incredible variety of patterns as well as spatial and temporal chaos and combinations of the two, attracting the attention of mathematicians and physicists alike. The precise patterns and critical values are highly dependent on boundary conditions (container geometries) and the properties of the fluid itself for example viscosity and surface tenstion. \\ \indent Beyond the mere satisfaction of mathematical curiousity, Faraday waves have several practical applications and have made contributions to other areas of physics. They play a role in the amplication of earthquakes through looser sediments and can allow one to deposit a film of material in a desired pattern through forming the wave, letting the material settle and the excess liquid of the suspension to evaporate; such a skill has interesting aplications in creating more precise optical instruments. In the field of quantum mechanics, Faraday waves have recently been observed in Bose-Einstein Condensates and there is a curious analogy one can make between a probability wave distribution in quantum mechanics and a 'walking' droplet guided by a precisely tuned Faraday wave. When confined to a circular container, an oil droplet can be made to bounce on a water suface supporting a Faraday wave within a small range of driving frequency and amplitude. Within an even narrower parameter range, the Faraday wave can guide the oil droplet in a random walk across the surface. This results in a probability distribution for the droplet reminiscent of the wave function of an atom confined in a circular geometry. The particle/wave guide pair also exhibits many effects similar to those predicted by quantum physics such as tunneling and bears a striking resemblence to wave/particle duality. These similarities have left many speculating that there may be a hidden variable theory for quantum mechanics that mimics the pilot wave in the walking droplet experiment.