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Abstract
We study the radial-hedgehog solution on a three-dimensional (3D) spherical shell with radial boundary conditions, within the Landau-de Gennes theory for nematic liquid crystals. We prove that the radial-hedgehog solution is the unique minimizer of the Landau-de Gennes energy in two separate regimes: (i) for thin shells when the temperature is below the critical nematic supercooling temperature and (ii) for a fixed shell width at sufficiently low temperatures. In case (i), we provide explicit geometry-dependent criteria for the global minimality of the radial-hedgehog solution.
Original language | English |
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Pages (from-to) | 18-34 |
Number of pages | 17 |
Journal | Physica D: Nonlinear Phenomena |
Volume | 314 |
DOIs | |
Publication status | Published - 1 Jan 2016 |
Keywords
- Landau-de Gennes theory
- Minimizing configurations
- Nematic liquid crystals
- Radial-hedgehog
- Stable configurations
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Dive into the research topics of 'Radial symmetry on three-dimensional shells in the Landau-de Gennes theory'. Together they form a unique fingerprint.Projects
- 1 Finished
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Fellowship - The Mathematics of Liquid Crystals: Analysis, Computation and Applications
Majumdar, A. (PI)
Engineering and Physical Sciences Research Council
1/08/12 → 30/09/16
Project: Research council