11 February 2016
Roughly a decade ago, Yves Couder and coworkers demonstrated that droplets walking on a vibrating fluid bath exhibit several features previously thought to be peculiar to the microscopic quantum realm, including single-particle diffraction, tunneling, quantized orbits, and wave-like statistics in a corral. We here develop an integro-differential trajectory equation for these walking droplets with a view to gaining insight into their subtle dynamics. We then rationalize the emergence of orbital quantization in a rotating frame by assessing the stability of the orbital solutions. In the limit of large vibrational forcing, the chaotic walker dynamics gives rise to a coherent statistical behavior with wave-like features.
I will then describe recent efforts to model the dynamics of interacting flapping swimmers. Our study is motivated by recent experiments using a one-dimensional array of wings in a water tank, in which the system adopts “schooling modes” characterized by specific spatial phase relationships between swimmers. We develop a discrete dynamical system that models the swimmers as airfoils shedding point vortices, and study the existence and stability of steady solutions. We expect that our model may be used to understand how schooling behavior is influenced by hydrodynamics in more general contexts.
- Industrial and Applied Mathematics Seminar