Order Reconstruction for Nematics on Squares and Regular Polygons: A Landau-de Gennes Study
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...
| Главные авторы: | , , |
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| Формат: | Journal article |
| Опубликовано: |
2016
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| _version_ | 1826256786571657216 |
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| author | Canevari, G Majumdar, A Spicer, A |
| author_facet | Canevari, G Majumdar, A Spicer, A |
| author_sort | Canevari, G |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T18:07:47Z |
| format | Journal article |
| id | oxford-uuid:0200ff02-e240-422f-a8c3-d32c5f15d34c |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:07:47Z |
| publishDate | 2016 |
| record_format | dspace |
| spelling | oxford-uuid:0200ff02-e240-422f-a8c3-d32c5f15d34c2022-03-26T08:38:11ZOrder Reconstruction for Nematics on Squares and Regular Polygons: A Landau-de Gennes StudyJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:0200ff02-e240-422f-a8c3-d32c5f15d34cSymplectic Elements at Oxford2016Canevari, GMajumdar, ASpicer, AWe 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. |
| spellingShingle | Canevari, G Majumdar, A Spicer, A Order Reconstruction for Nematics on Squares and Regular Polygons: A Landau-de Gennes Study |
| title | Order Reconstruction for Nematics on Squares and Regular Polygons: A
Landau-de Gennes Study |
| title_full | Order Reconstruction for Nematics on Squares and Regular Polygons: A
Landau-de Gennes Study |
| title_fullStr | Order Reconstruction for Nematics on Squares and Regular Polygons: A
Landau-de Gennes Study |
| title_full_unstemmed | Order Reconstruction for Nematics on Squares and Regular Polygons: A
Landau-de Gennes Study |
| title_short | Order Reconstruction for Nematics on Squares and Regular Polygons: A
Landau-de Gennes Study |
| title_sort | order reconstruction for nematics on squares and regular polygons a landau de gennes study |
| work_keys_str_mv | AT canevarig orderreconstructionfornematicsonsquaresandregularpolygonsalandaudegennesstudy AT majumdara orderreconstructionfornematicsonsquaresandregularpolygonsalandaudegennesstudy AT spicera orderreconstructionfornematicsonsquaresandregularpolygonsalandaudegennesstudy |