Calculus of Variations and Geometric Measure Theory
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G. Canevari - A. Majumdar - A. Spicer

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

created by canevari on 29 Jan 2021

[BibTeX]

preprint

Inserted: 29 jan 2021

Year: 2016

ArXiv: 1606.06575 PDF

Abstract:

We construct an order reconstruction (OR)-type Landau-de Gennes critical point on a square domain of edge length $\lambda$, motivated by the well order reconstruction solution numerically reported by Kralj and Majumdar. The OR critical point is distinguished by an 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.

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