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

Giacomo Canevari, Apala Majumdar, Amy Spicer

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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.

Original languageEnglish
Pages (from-to)267-293
Number of pages27
JournalSIAM Journal on Applied Mathematics
Issue number1
Early online date15 Feb 2017
Publication statusPublished - 31 Dec 2017


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


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