The Effect of External Fields in the Theory of Liquid Crystals

We consider the response of external field to the theory of liquid crystals. We treat the Landau-de Gennes functional with the Dirichlet boundary condition for the director field which may be non-constant. We show that there exist two families of critical points such that one carries out the superheating fields of superconductors and the other one carries out strong stability. We also show that under some conditions, strong field does not bring the pure nematic state which is different response from superconductors.