Order reconstruction for nematics on squares and hexagons : a Landau-de Gennes study

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Canevari, Giacomo and Majumdar, Apala and Spicer, Amy (2017) Order reconstruction for nematics on squares and hexagons : a Landau-de Gennes study. SIAM Journal on Applied Mathematics, 77 (1). 267–293. ISSN 1095-712X (https://doi.org/10.1137/16M1087990)

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Abstract

We construct an order reconstruction (OR-)type Landau-de Gennes critical point on a square domain of edge length 2λ, motivated by the well order reconstruction solution numerically reported in [S. Kralj and A. Majumdar, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 470 (2014), 20140276]. The OR critical point is distinguished by a uniaxial cross with negative scalar order parameter along the square diagonals. The OR critical point is defined in terms of a saddle-type critical point of an associated scalar variational problem. The OR-type critical point is globally stable for small λ and undergoes a supercritical pitchfork bifurcation in the associated scalar variational setting. We consider generalizations of the OR-type critical point to a regular hexagon, accompanied by numerical estimates of stability criteria of such critical points on both a square and a hexagon in terms of material-dependent constants.

ORCID iDs

Canevari, Giacomo, Majumdar, Apala ORCID logoORCID: https://orcid.org/0000-0003-4802-6720 and Spicer, Amy;
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