Instability of radial hedgehog configurations in nematic liquid crystals under Landau-de Gennes free-energy models

摘要

We consider radial hedgehog equilibrium configurations of the tensor order parameter in spherical droplets of nematic liquid crystals modeled by free energies of the Landau-de Gennes type. We show that such configurations must become unstable at sufficiently low temperatures in droplets of sufficiently large radii for all but a very limited range of elastic-constant ratios, which are very near the limit where the elastic-energy terms in the model cease to be positive definite. The analysis is complicated by the fact that no analytical solution is available for the hedgehog configuration. Nevertheless, using a combination of analytical bounds and numerical computation, we are able to construct a perturbation to which we can show that the spherically symmetric ground state becomes unstable. [S1063-651X(99)02901-3]. [References: 10]