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.
Original language | English |
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Pages (from-to) | 267–293 |
Number of pages | 27 |
Journal | SIAM Journal on Applied Mathematics |
Volume | 77 |
Issue number | 1 |
Early online date | 15 Feb 2017 |
DOIs | |
Publication status | Published - 28 Feb 2017 |
Keywords
- order reconstruction
- Landau-de Gennes
- gradient flow
- saddle solutions
- Allen-Cahn
- supercritical pitchfork bifurcation