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http://hdl.handle.net/11375/29833
Title: | Planar Anchoring for a Colloid in Nematic Liquid Crystal with a Magnetic Field |
Authors: | Louizos, Dean |
Advisor: | Bronsard, Lia |
Department: | Mathematics |
Keywords: | Liquid crystals, calculus of variations, applied math |
Publication Date: | 2024 |
Abstract: | We study minimizers of the Landau-de Gennes energy in the exterior region around a smooth 2-manifold in R3 with a constant external magnetic field present. Uniaxial boundary data and a strong tangential anchoring are imposed on the surface of the manifold and we consider the large particle limit in a regime where the magnetic field is relatively weak. Before studying the general manifold, we analyze a more simple case in which the manifold is spherical. After deriving a lower bound for the energy in this limiting regime, we prove that a director field on the boundary which maximizes its vertical component yields a minimal lower bound. We then construct a recovery sequence to show that this lower bound is in fact the optimal energy bound. These steps are later repeated in more generality for a larger class of smooth manifolds. |
URI: | http://hdl.handle.net/11375/29833 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
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Louizos_Dean_D_2024May_MSc.pdf | 443.91 kB | Adobe PDF | View/Open |
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