Nematic equilibria on a two-dimensional annulus: defects and energies
Abstract
We study planar nematic equilibria on a two-dimensional annulus with strong and weak tangent anchoring, within the Oseen-Frank and Landau-de Gennes theories for nematic liquid crystals. We analyse the defect-free state in the Oseen-Frank framework and obtain analytic stability criteria in terms of the elastic anisotropy, annular aspect ratio and anchoring strength. We consider radial and azimuthal perturbations of the defect-free state separately, which yields a complete stability diagram for the defect-free state. We construct nematic equilibria with an arbitrary number of defects on a two-dimensional annulus with strong tangent anchoring and compute their energies; these equilibria are generalizations of the diagonal and rotated states observed in a square. This gives novel insights into the correlation between preferred numbers of defects, their locations and the geometry. In the Landau-de Gennes framework, we adapt Mironescu's powerful stability result in the Ginzburg-Landau framework (P. Mironescu, On the stability of radial solutions of the Ginzburg-Landau equation, 1995) to compute quantitative criteria for the local stability of the defect-free state in terms of the temperature and geometry.
Keywords
Cite
@article{arxiv.1504.05501,
title = {Nematic equilibria on a two-dimensional annulus: defects and energies},
author = {Alexander H. Lewis and Peter D. Howell and Dirk G. A. L. Aarts and Apala Majumdar},
journal= {arXiv preprint arXiv:1504.05501},
year = {2015}
}