Friday, October 20th, 2023
12:00pm - 13:00pm, in Wheatley 03-154-28

Ricardo Carretero

San Diego State University

Dynamical Reduction for Coherent Structures: A Quasi-Particle Approach for Vortices, Vortex Rings, and Solitonic Filaments

Abstract: In this talk we describe techniques for the dynamical reduction of localized structures (such as solitons, kinks, filaments, vortices, and vortex rings) in nonlinear spatio-temporal systems. The central idea is to use mathematical reductions to accurately describe these complex spatio-temporal structures with lower-dimensional models that are more easily tackled, both mathematically and computationally. In turn, the reduced models allow for an unprecedented description of the statics, stability, dynamics, and interactions of these structures. After showcasing the success of this reduction methodology in a wide range of situations, we will focus on the interesting case of vortices in complex fields bearing applications to condensed matter physics, nonlinear optics, and superfluids. In particular, motivated by recent experiments studying vortex dynamics in Bose-Einstein condensates (the coldest form of matter in the Universe), we show that considering these vortices as quasi-particles allows for a full understanding of their dynamics, stability, and bifurcations. We will also explore some extensions of the quasi-particle approach for 3D vortex rings which are formed when a vortex filament (a "twister") is looped back onto itself creating a close ring that carries vorticity.