MLC

Abstract

We describe mathematical results and techniques of analysis on the structure of defects in thin nematic liquid crystals described by minimizers of the Landau-de Gennes energy involving a tensor-valued order parameter with Dirichlet boundary conditions of nonzero degree. We prove that as the coefficient of the elasticity term tends to zero, a limiting uniaxial texture forms with a finite number of defects, all of degree 1/2 or -1/2. We also describe the location of defects and the limiting energy.