Landau-De Gennes theory of nematic liquid crystals: the Oseen-Frank limit and beyond
We study global minimizers of a continuum Landau-De Gennes energy functional for nematic liquid crystals, in three-dimensional domains, subject to uniaxial boundary conditions. We analyze the physically relevant limit of small elastic constant and show that global minimizers converge strongly, i...
| मुख्य लेखकों: | , |
|---|---|
| स्वरूप: | Journal article |
| प्रकाशित: |
2009
|
| _version_ | 1826300868544167936 |
|---|---|
| author | Majumdar, A Zarnescu, A |
| author_facet | Majumdar, A Zarnescu, A |
| author_sort | Majumdar, A |
| collection | OXFORD |
| description | We study global minimizers of a continuum Landau-De Gennes energy functional for nematic liquid crystals, in three-dimensional domains, subject to uniaxial boundary conditions. We analyze the physically relevant limit of small elastic constant and show that global minimizers converge strongly, in W 1,2 , to a global minimizer predicted by the Oseen-Frank theory for uniaxial nematic liquid crystals with constant order parameter. Moreover, the convergence is uniform in the interior of the domain, away from the singularities of the limiting Oseen-Frank global minimizer. We obtain results on the rate of convergence of the eigenvalues and the regularity of the eigenvectors of the Landau-De Gennes global minimizer. We also study the interplay between biaxiality and uniaxiality in Landau-De Gennes global energy minimizers and obtain estimates for various related quantities such as the biaxiality parameter and the size of admissible strongly biaxial regions. |
| first_indexed | 2024-03-07T05:23:41Z |
| format | Journal article |
| id | oxford-uuid:dfceb1fc-1e80-4b31-954f-ab9cc8ff6306 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T05:23:41Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:dfceb1fc-1e80-4b31-954f-ab9cc8ff63062022-03-27T09:42:03ZLandau-De Gennes theory of nematic liquid crystals: the Oseen-Frank limit and beyond Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:dfceb1fc-1e80-4b31-954f-ab9cc8ff6306Mathematical Institute - ePrints2009Majumdar, AZarnescu, A We study global minimizers of a continuum Landau-De Gennes energy functional for nematic liquid crystals, in three-dimensional domains, subject to uniaxial boundary conditions. We analyze the physically relevant limit of small elastic constant and show that global minimizers converge strongly, in W 1,2 , to a global minimizer predicted by the Oseen-Frank theory for uniaxial nematic liquid crystals with constant order parameter. Moreover, the convergence is uniform in the interior of the domain, away from the singularities of the limiting Oseen-Frank global minimizer. We obtain results on the rate of convergence of the eigenvalues and the regularity of the eigenvectors of the Landau-De Gennes global minimizer. We also study the interplay between biaxiality and uniaxiality in Landau-De Gennes global energy minimizers and obtain estimates for various related quantities such as the biaxiality parameter and the size of admissible strongly biaxial regions. |
| spellingShingle | Majumdar, A Zarnescu, A Landau-De Gennes theory of nematic liquid crystals: the Oseen-Frank limit and beyond |
| title | Landau-De Gennes theory of nematic liquid
crystals: the Oseen-Frank limit and beyond
|
| title_full | Landau-De Gennes theory of nematic liquid
crystals: the Oseen-Frank limit and beyond
|
| title_fullStr | Landau-De Gennes theory of nematic liquid
crystals: the Oseen-Frank limit and beyond
|
| title_full_unstemmed | Landau-De Gennes theory of nematic liquid
crystals: the Oseen-Frank limit and beyond
|
| title_short | Landau-De Gennes theory of nematic liquid
crystals: the Oseen-Frank limit and beyond
|
| title_sort | landau de gennes theory of nematic liquid crystals the oseen frank limit and beyond |
| work_keys_str_mv | AT majumdara landaudegennestheoryofnematicliquidcrystalstheoseenfranklimitandbeyond AT zarnescua landaudegennestheoryofnematicliquidcrystalstheoseenfranklimitandbeyond |