Computing Nonlinear Waves in Bose-Einstein Condensates and Beyond: Adventures in Applied Mathematics

When

February 17, 2023 | 3:30 p.m. - 4:30 p.m.
Refreshments at 3:00 in Lobby

Where

University Hall 1005

Speaker

Stathis Charalampidis

Abstract

A Bose-Einstein Condensate (BEC) is a state of matter formed by a collection of bosons that are cooled to temperatures close to absolute zero. On the theoretical side, BECs can be described by a nonlinear PDE known as the NLS equation. In this talk, a mathematical and computational analysis of the NLS equation will be presented using Newton’s method for nonlinear systems together with penalty methods. We have developed the Deflated Continuation Method (DCM) to trace disconnected branches of solutions by factoring out previously computed ones. Finally, the study of nonlinear waves will be extended to various physical systems, including water waves and meta-materials which have a plethora of engineering and industrial applications.