Thin film liquid crystals with oblique anchoring and boojums

Alama, Stan; Bronsard, Lia; Golovaty, Dmitry

doi:10.1016/j.anihpc.2020.02.002

Alama, Stan ¹ ; Bronsard, Lia ¹ ; Golovaty, Dmitry ²

¹ Department of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S 4K1, Canada
² Department of Mathematics, University of Akron, Akron, OH 44325, United States of America

Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 4, pp. 817-853

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Résumé

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 $α \in (0, \frac{π}{2})$ , they serve to reduce the winding of the phase by steps of 2α and $(2 π - 2 α)$ 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.

MR Zbl

DOI : 10.1016/j.anihpc.2020.02.002

Keywords: Calculus of variations, Partial differential equations, Liquid crystals, Defects

Affiliations des auteurs :

Alama, Stan ¹ ; Bronsard, Lia ¹ ; Golovaty, Dmitry ²

¹ Department of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S 4K1, Canada
² Department of Mathematics, University of Akron, Akron, OH 44325, United States of America

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     author = {Alama, Stan and Bronsard, Lia and Golovaty, Dmitry},
     title = {Thin film liquid crystals with oblique anchoring and boojums},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {817--853},
     publisher = {Elsevier},
     volume = {37},
     number = {4},
     year = {2020},
     doi = {10.1016/j.anihpc.2020.02.002},
     mrnumber = {4104827},
     zbl = {1446.76066},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2020.02.002/}
}

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Alama, Stan; Bronsard, Lia; Golovaty, Dmitry. Thin film liquid crystals with oblique anchoring and boojums. Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 4, pp. 817-853. doi: 10.1016/j.anihpc.2020.02.002

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