Abstract

Defects are local breakings of symmetry in an ordered medium, which can be found in various fields of physics such as solids, liquid crystals, astrophysics and high energy physics. Defects in liquid crystals are of great practical importance in material science and theoretical interest in physics and mathematics. In this talk, I will review the representation, modeling and computation of defects in liquid crystals. Within the Landau-de Gennes tensor model, we found a rich variety of defect patterns in topologically confined nematic liquid crystals, and the profiles of point defect and disclination line are obtained. The connection and difference between defect patterns under the tensor model and the vector model will be discussed. Finally, some conjectures and challenges are proposed to summarize the common characteristics of defects, in the hope of providing a deeper understanding of the defect pattern in nematic liquid crystals.