Title: Branched Flow and Applications
Speaker: Eric J. Heller
Duration: 58 min.
Abstract: In classical and quantum phase space flow, there exists a regime of great physical relevance that is belatedly but rapidly generating a new field. In evolution under smooth, random, weakly deflecting but persistent perturbations, a remarkable regime develops, called branched flow. Lying between the first cusp catastrophes at the outset, leading to fully chaotic statistical flow much later, lies the visually beautiful regime of branched flow.
It applies to tsunami wave propagation, freak wave formation, light propagation, cosmic microwaves arriving from pulsars, electron flow in metals and devices, sound propagation in the atmosphere and oceans, the large scale structure of the universe, and much more. The mathematical structure of this flow is only partially understood, involving exponential instability coexisting with "accidental" stability. The flow is qualitatively universal, but this has not been quantified. Many questions arise, including the scale(s) of the random medium, and the time evolution of manifolds and "fuzzy" manifolds in phase space. The classical-quantum (ray-wave) correspondence in this flow is only partially understood. This talk will be an introduction to the phenomenon, both visual and mathematical, emphasizing unanswered questions