Symmetry of uniaxial global Landau-de Gennes minimizers in the theory of nematic liquid crystals
We extend the recent radial symmetry results by Pisante [23] and Millot & Pisante [19] (who show that all entire solutions of the vector-valued Ginzburg-Landau equations in superconductivity theory, in the three-dimensional space, are comprised of the well-known class of equivariant solution...
| Main Authors: | , |
|---|---|
| Format: | Journal article |
| Published: |
2011
|
| _version_ | 1797102582536077312 |
|---|---|
| author | Henao, D Majumdar, A |
| author_facet | Henao, D Majumdar, A |
| author_sort | Henao, D |
| collection | OXFORD |
| description | We extend the recent radial symmetry results by Pisante [23] and Millot & Pisante [19] (who show that all entire solutions of the vector-valued Ginzburg-Landau equations in superconductivity theory, in the three-dimensional space, are comprised of the well-known class of equivariant solutions) to the Landau-de Gennes framework in the theory of nematic liquid crystals. In the low temperature limit, we obtain a characterization of global Landau-de Gennes minimizers, in the restricted class of uniaxial tensors, in terms of the well-known radial-hedgehog solution. We use this characterization to prove that global Landau-de Gennes minimizers cannot be purely uniaxial for sufficiently low temperatures. |
| first_indexed | 2024-03-07T06:07:58Z |
| format | Journal article |
| id | oxford-uuid:ee7e4337-22ff-4173-b5d7-25c919f54cbd |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:07:58Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:ee7e4337-22ff-4173-b5d7-25c919f54cbd2022-03-27T11:33:08ZSymmetry of uniaxial global Landau-de Gennes minimizers in the theory of nematic liquid crystalsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:ee7e4337-22ff-4173-b5d7-25c919f54cbdMathematical Institute - ePrints2011Henao, DMajumdar, AWe extend the recent radial symmetry results by Pisante [23] and Millot & Pisante [19] (who show that all entire solutions of the vector-valued Ginzburg-Landau equations in superconductivity theory, in the three-dimensional space, are comprised of the well-known class of equivariant solutions) to the Landau-de Gennes framework in the theory of nematic liquid crystals. In the low temperature limit, we obtain a characterization of global Landau-de Gennes minimizers, in the restricted class of uniaxial tensors, in terms of the well-known radial-hedgehog solution. We use this characterization to prove that global Landau-de Gennes minimizers cannot be purely uniaxial for sufficiently low temperatures. |
| spellingShingle | Henao, D Majumdar, A Symmetry of uniaxial global Landau-de Gennes minimizers in the theory of nematic liquid crystals |
| title | Symmetry of uniaxial global Landau-de Gennes minimizers in the
theory of nematic liquid crystals |
| title_full | Symmetry of uniaxial global Landau-de Gennes minimizers in the
theory of nematic liquid crystals |
| title_fullStr | Symmetry of uniaxial global Landau-de Gennes minimizers in the
theory of nematic liquid crystals |
| title_full_unstemmed | Symmetry of uniaxial global Landau-de Gennes minimizers in the
theory of nematic liquid crystals |
| title_short | Symmetry of uniaxial global Landau-de Gennes minimizers in the
theory of nematic liquid crystals |
| title_sort | symmetry of uniaxial global landau de gennes minimizers in the theory of nematic liquid crystals |
| work_keys_str_mv | AT henaod symmetryofuniaxialgloballandaudegennesminimizersinthetheoryofnematicliquidcrystals AT majumdara symmetryofuniaxialgloballandaudegennesminimizersinthetheoryofnematicliquidcrystals |