Mathematical Sciences Department, Colloquium - André Nachbin (IMPA, Brazil) "Water Waves in Highly Irregular Domains" UH 500
Mathematical Sciences Department
Speaker: André Nachbin
Monday, February 13, 2023
3:00 pm - 4:00 pm
Unity Hall 500
Title: Water Waves in Highly Irregular Domains
Abstract: This is a research topic on Partial Differential Equations (PDEs) and applications. Reduced modeling, asymptotic theory and scientific computing are the main ingredients, always having in mind a concrete physical problem. I will very briefly describe some of my main results in the past 20 years, concerning surface waves propagating over a highly disordered bottom topography. Together with collaborators this led to results on water waves in random media. Of particular interest is the apparent diffusion and the time-reversed refocusing of surface waves. The main goal of this talk is to present my current research topics. One topic considers water waves on branching channels and its reduction to nonlinear dispersive PDEs on graphs. The other topic considers a wave-particle system not imagined to exist in Classical Mechanics. A bouncing droplet on a vibrating bath is self-propelled through the underlying surface waves it generates. This gives rise to a new dynamical system with many quantum-like properties. Trapped in separate cavities, two nearby oscillating droplets can spontaneously synchronize as in the celebrated Kuramoto system. At a distance these two oscillators cease to synchronize but remain statistically correlated in a non-separable fashion. Most results will be presented in a pictorial (non-technical) fashion.