Journal
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE
Volume 37, Issue 4, Pages 817-853Publisher
ELSEVIER
DOI: 10.1016/j.anihpc.2020.02.002
Keywords
Calculus of variations; Partial differential equations; Liquid crystals; Defects
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We study a two-dimensional variational problem which arises as a thin-film limit of the Landau-de Gennes energy of nematic liquid crystals. We impose an oblique angle condition for the nematic director on the boundary, via boundary penalization (weak anchoring.) We show that for strong anchoring strength (relative to the usual Ginzburg-Landau length scale parameter), defects will occur in the interior, as in the case of strong (Dirichlet) anchoring, but for weaker anchoring strength all defects will occur on the boundary. These defects will each carry a fractional winding number; such boundary defects are known as boojums. The boojums will occur in ordered pairs along the boundary; for angle alpha is an element of (0, pi/2) they serve to reduce the winding of the phase by steps of 2 alpha and (2 pi - 2 alpha) in order to avoid the formation of interior defects. We determine the number and location of the defects via a Renormalized Energy and numerical simulations. (C) 2020 Elsevier Masson SAS. All rights reserved.
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