Journal
EUROPEAN JOURNAL OF APPLIED MATHEMATICS
Volume 23, Issue -, Pages 61-97Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S0956792511000295
Keywords
Defects; Landau de Gennes; Ginzburg-Landau
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Funding
- King Abdullah University of Science and Technology (KAUST) [KUK-C1-013-04]
- Engineering and Physical Sciences Research Council [EP/J001686/1] Funding Source: researchfish
- EPSRC [EP/J001686/1] Funding Source: UKRI
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We study the radial-hedgehog solution in a three-dimensional spherical droplet, with homeotropic boundary conditions, within the Landau-de Gennes theory for nematic liquid crystals. The radial-hedgehog solution is a candidate for a global Landau-de Gennes minimiser in this model framework and is also a prototype configuration for studying isolated point defects in condensed matter physics. The static properties of the radial-hedgehog solution are governed by a non-linear singular ordinary differential equation. We study the analogies between Ginzburg-Landau vortices and the radial-hedgehog solution and demonstrate a Ginzburg- Landau limit for the Landau-de Gennes theory. We prove that the radial-hedgehog solution is not the global Landau-de Gennes minimiser for droplets of finite radius and sufficiently low temperatures and prove the stability of the radial-hedgehog solution in other parameter regimes. These results contain quantitative information about the effect of geometry and temperature on the properties of the radial-hedgehog solution and the associated biaxial instabilities.
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