Lia Bronsard

McMaster University

Ring defect in Liquid Crystal

The mathematical analysis of liquid crystal models poses many challenging questions, as can be seen by their close relationship to the study of singularities for harmonic maps. In this talk, I will discuss the structure of defects in the context of different models of nematic liquid crystals, and their connection to classical results on harmonic maps into the sphere. To illustrate, I will present the physically fundamental problem of defects created by a colloid particle immersed in a nematic, and present recent results using the Landau-de Gennes energy. We find that the Landau–de Gennes model allows for a greater variety of types of singularity than the (harmonic map-based) Oseen–Frank energy, including line singularities such as the “Saturn Ring” defect. This work is joint with S. Alama, D. Golovaty and X. Lamy.