Back to Departmental Colloquium: Spring 2023
Departmental Colloquium
Date: Wednesday, Jan 25, 2023
Time: 4:00PM - 5:00PM
Location: JWB 335
Note special day
Raghav Venkatraman
New York University
Title |
Variational principles in materials science with small parameters: a case study of liquid crystals |
Abstract |
Variational principles are ubiquitous and are at the heart of a broad range of applications. Common challenges in the analysis of such principles is the interplay between the effects of nonconvexity, nonlocality, spatial heterogeneity, and even randomness. What results is a diverse array of phenomena that display concentration, oscillations or both, and the presence of small parameters helps us coarse-grain and quantify these effects. Tools from analysis, PDEs, and the calculus of variations have had a long, rich, and fruitful symbiosis with materials science. After a broad survey of a few examples from diverse applications, I’ll focus on some questions relating to nematic liquid crystals (LCs) and liquid crystal suspensions. LCs arise in a number of distinct applications, the most common being wafer-thin displays. The mathematics underlying their behavior, even in the absence of external fields, presents rich challenges at the confluence of analysis, PDEs, and geometry. We’ll first present some work that seeks to explain the formation of interfacial singularities such as cusps, along the phase boundaries of liquid crystals. Then we’ll present the first rigorous explanation of the widely used “electrostatics analogy” in the study of LC colloids. We’ll conclude with some open problems. This talk represents joint work with Peter Sternberg (Indiana), Dmitry Golovaty (Akron), Michael Novack (UT Austin), Stan Alama and Lia Bronsard (McMaster) and Xavier Lamy (Toulouse). |
Applied Mathematics
Materials Science