Order reconstruction for nematics on squares and hexagons

Giacomo Canevari, Apala Majumdar, Amy Spicer

OAI: oai:purehost.bath.ac.uk:openaire_cris_publications/78a25627-e8b3-4998-85b7-b212132f74b6 • DOI: https://doi.org/10.1137/16M1087990

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.

Allen-Cahn Gradient ow Landau-de Gennes Order reconstruction Saddle solutions Supercritical pitchfork bifurcation