Revisiting the two-dimensional defect-free azimuthal nematic equilibrium on an annulus

Tools

Lewis, A. H. and Aarts, D. G. A. L. and Howell, P. D. and Majumdar, A. (2017) Revisiting the two-dimensional defect-free azimuthal nematic equilibrium on an annulus. SIAM Journal on Applied Mathematics, 77 (6). 1851–1875. ISSN 1095-712X (https://doi.org/10.1137/17M1124656)

[thumbnail of Lewis-etal-JAM-2017-Revisiting-the-two-dimensional-defect-free-azimuthal-nematic-equilibrium]
Preview
 Text. Filename: Lewis_etal_JAM_2017_Revisiting_the_two_dimensional_defect_free_azimuthal_nematic_equilibrium.pdf
Accepted Author Manuscript
Download (8MB)| Preview

Abstract

We study the azimuthal defect-free nematic state on a two-dimensional annulus within a simplified and reduced two-dimensional Landau--de Gennes model for nematic liquid crystals. We perform a detailed asymptotic analysis of the instabilities of the defect-free state in terms of a dimensionless material and temperature-dependent variable and the annular aspect ratio. The asymptotic analysis is accompanied by a rigorous local stability result, again in terms of a dimensionless material and temperature-dependent parameter and annular aspect ratio. In contrast to Oseen--Frank predictions, the defect-free state can be unstable in this model, with elastic isotropy and strong anchoring, for a range of macroscopically relevant annular aspect ratios.

ORCID iDs

Lewis, A. H., Aarts, D. G. A. L., Howell, P. D. and Majumdar, A. ORCID logoORCID: https://orcid.org/0000-0003-4802-6720;
CORE (COnnecting REpositories)