We construct an order reconstruction (OR-)type Landau de Gennes critical point on a square domain of edge length 2 lambda, 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 lambda 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.

Order Reconstruction for Nematics on Squares and Hexagons: A Landau--de Gennes Study

Canevari, Giacomo;
2017-01-01

Abstract

We construct an order reconstruction (OR-)type Landau de Gennes critical point on a square domain of edge length 2 lambda, 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 lambda 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.
order reconstruction; Landau de Gennes; gradient flow; saddle solutions; Allen-Cahn; supercritical pitchfork bifurcation
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/1010157
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