Multistability for a reduced nematic liquid crystal model in the exterior of 2D polygons

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Han, Yucen and Majumdar, Apala (2023) Multistability for a reduced nematic liquid crystal model in the exterior of 2D polygons. Journal of Nonlinear Science, 33 (2). 24. ISSN 1432-1467 (https://doi.org/10.1007/s00332-022-09884-9)

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Abstract

We study nematic equilibria in an unbounded domain, with a two-dimensional regular polygonal hole with K edges, in a reduced Landau-de Gennes framework. This complements our previous work on the 'interior problem' for nematic equilibria confined inside regular polygons (SIAM Journal on Applied Mathematics, 80(4):1678-1703, 2020). The two essential dimensionless model parameters are λ-the ratio of the edge length of polygon hole to the nematic correlation length, and an additional degree of freedom, ϒ*-the nematic director at infinity. In the λ → 0 limit, the limiting profile has two interior point defects outside a generic polygon hole, except for a triangle and a square. For a square hole, the limiting profile has either no interior defects or two line defects depending on ϒ*, and for a triangular hole, there is a unique interior point defect outside the hole. In the λ → ∞ limit, there are at least (K 2) stable states and the multistability is enhanced by ϒ*, compared to the interior problem. Our work offers new insights into how to tune the existence, location, and dimensionality of defects.

ORCID iDs

Han, Yucen and Majumdar, Apala ORCID logoORCID: https://orcid.org/0000-0003-4802-6720;
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