The Second Ohio River Analysis Meeting

Title: Analysis of Equilibria with One-Half Degree Defects for the Landau-de Gennes Model of Nematic Liquid Crystals Abstract: We investigate the structure of nematic liquid crystal thin films described by the Landau–de Gennes tensor-valued order parameter model with Dirichlet boundary conditions on the sides of nonzero degree. We prove that as the elasticity constant goes to zero in the energy. a limiting liquid crystal uniaxial texture forms with a finite number of defects, all of degree one-half or all of degree minus one-half, corresponding to vertical disclination lines at those locations. We also describe a result on the limiting behavior of minimizers of the Chern-Simons-Higgs model without magnetic field that follows from a similar proof.