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

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 0036-1399 (https://doi.org/10.1137/17M1124656)

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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.

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