The radial-hedgehog solution in Landau–de Gennes' theory for nematic liquid crystals


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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. © Copyright Cambridge University Press 2011.
Original languageEnglish (US)
Pages (from-to)61-97
Number of pages37
JournalEuropean Journal of Applied Mathematics
Issue number1
StatePublished - Sep 6 2011
Externally publishedYes


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