Journal
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
Volume 26, Issue 14, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202516500664
Keywords
Liquid crystals; Q-tensors; k-radially symmetric solutions; minimisers
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Funding
- Leverhulme [RPG-2014-226]
- EPSRC [EP/K02390X/1]
- Romanian National Authority for Scientific Research and Innovation, CNCS-UEFISCDI [PN-II-RU-TE-2014-4-0657]
- Basque Government through the BERC program
- Spanish Ministry of Economy and Competitiveness MINECO: BCAM Severo Ochoa accreditation [SEV-2013-0323]
- Mathematics Department at the University of Bristol, through Leverhulme [RPG-2014-226]
- Engineering and Physical Sciences Research Council [EP/I028714/1, EP/K02390X/1] Funding Source: researchfish
- EPSRC [EP/I028714/1, EP/K02390X/1] Funding Source: UKRI
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We consider the two-dimensional (2D) Landau-de Gennes energy with several elastic constants, subject to general k-radially symmetric boundary conditions. We show that for generic elastic constants the critical points consistent with the symmetry of the boundary conditions exist only in the case k = 2. In this case we identify three types of radial profiles: with two, three of full five components and numerically investigate their minimality and stability depending on suitable parametres. We also numerically study the stability properties of the critical points of the Landau-de Gennes energy and capture the intricate dependence of various qualitative features of these solutions on the elastic constants and the physical regimes of the liquid crystal system.
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