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.
Original language | English |
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Pages (from-to) | 1851–1875 |
Number of pages | 25 |
Journal | SIAM Journal on Applied Mathematics |
Volume | 77 |
Issue number | 6 |
DOIs | |
Publication status | Published - 2017 |