Landau-de Gennes model of liquid crystals and critical wave number

Abstract

We study some variational problems of the Landau-de Gennes functional under Neumann or Dirichlet boundary conditions, which describes phase transitions of liquid crystals. We investigate the effect of the parameters, especially the chirality and the wave number, on the behavior of the minimizers. In order to describe bifurcation of a smectic phase from a nematic phase we introduce the critical wave number Qc3 and give various estimates. We examine the behavior of minimizers with small chirality and large elastic coefficients.