On equilibrium configurations of nematic liquid crystals droplet with anisotropic elastic energy

摘要

We investigate the effect of anisotropic elastic energy on defect patterns of liquid crystals confined in a three-dimensional spherical domain within the framework of Landau–de Gennes model. Two typical strong anchoring boundary conditions, namely homeotropic and mirror-homeotropic anchoring conditions, are considered. For the homeotropic anchoring, we find three different configurations: uniaxial hedgehog, ring and split-core, in both cases with or without the anisotropic energy. For the mirror-homeotropic anchoring, there are also three analogue solutions: the uniaxial hyperbolic hedgehog, ring and split-core for the isotropic energy case. However, when the anisotropic energy is taken into account, the numerical results and rigorous analysis reveal that the uniaxial hyperbolic hedgehog is no longer a solution. Indeed, we find ring solution only for negative L2 (the elastic coefficient of the anisotropic energy), while both split-core and ring solutions can be stable minimizers for positive L2. More precisely, the uniaxial hyperbolic hedgehog for L2 = 0 bifurcates to a split-core solution when L2 increases and to a ring solution when L2 decreases. This example shows that the anisotropic energy may significantly affect the symmetry of point defects with degree −1 whenever it is introduced.

出版物
An D., Wang W., Zhang P. (2017). On equilibrium configurations of nematic liquid crystals droplet with anisotropic elastic energy. In Research in the Mathematical Sciences, 4.