Applied Mathematics Colloquium by Peter Sternberg: A Family of Toy Problems Modeling Liquid Crystals Exhibiting Large Disparity in the Elastic Coefficients

Speaker: Peter Sternberg, professor of mathematics, Indianan University

Title: A Family of Toy Problems Modeling Liquid Crystals Exhibiting Large Disparity in the Elastic Coefficients

Abstract: Certain classes of liquid crystals have been found to strongly favor particular types of deformations over others; for example, the cost of splay may greatly exceed the cost of bend or twist. In a series of studies with Dmitry Golovaty (Akron), Michael Novack (UT Austin) and Raghav Venkatraman (Courant), we explore the implications of assuming various asymptotic regimes for the elastic constants. Through a mixture of formal and rigorous analysis, along with computations, we identify the limiting behavior of minimizers to the associated energies. We find that a variety of singular structures emerge corresponding to jumps in the profile of these limiting minimizers that effectively save on the cost of splay, bend or twist—whichever is assumed to be most expensive.

 

Applied Mathematics Colloquia