On Some Variational Problems Based on Disparate Elastic Constants

Peter Sternberg
Localisation: Université de l'Indiana, États-Unis
Type: Colloquium de Créteil
Site: UPEC
BM 006
Date de début:
03/03/2022 - 13:45
Date de fin:
03/03/2022 - 14:45

I will describe some "toy" variational models motivated by problems arising in the mathematical study of liquid crystals. In the classical Oseen-Frank theory, the state of a liquid crystal is describable through a unit length vector field called the director, and the energy is expressed in terms of deformations of this vector field, broken into a sum of splay, twist and bend. Here we will explore how to capture certain morphologies seen in experiments by analyzing a model that resembles such an energy under the assumption that the difference in cost of these three types of deformations is extreme. No background in the mathematics of liquid crystal modeling will be assumed and I will begin with a brief introduction to Oseen-Frank and the Landau-deGennes model. This talk will be a non-technical survey of some results obtained in collaboration with Dmitry Golovaty (Akron), Michael Novack (UT Austin) and Raghav Venkatraman (Courant).