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

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 0036-1399

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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.