Equilibrium order parameters of nematic liquid crystals in the Landau-De Gennes theory
We study equilibrium liquid crystal configurations in three-dimensional domains, within the continuum Landau-De Gennes theory. We obtain explicit bounds for the equilibrium scalar order parameters in terms of the temperature and material-dependent constants. We explicitly quantify the temperatur...
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| Format: | Journal article |
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2009
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| _version_ | 1797076252501213184 |
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| author | Majumdar, A |
| author_facet | Majumdar, A |
| author_sort | Majumdar, A |
| collection | OXFORD |
| description | We study equilibrium liquid crystal configurations in three-dimensional domains, within the continuum Landau-De Gennes theory. We obtain explicit bounds for the equilibrium scalar order parameters in terms of the temperature and material-dependent constants. We explicitly quantify the temperature regimes where the Landau-De Gennes predictions match and the temperature regimes where the Landau-De Gennes predictions don’t match the probabilistic second-moment definition of the Q-tensor order parameter. The regime of agreement may be interpreted as the regime of validity of the Landau-De Gennes theory since the Landau-De Gennes theory predicts large values of the equilibrium scalar order parameters - larger than unity, in the low-temperature regime. We discuss a modified Landau-De Gennes energy functional which yields physically realistic values of the equilibrium scalar order parameters in all temperature regimes. |
| first_indexed | 2024-03-07T00:01:29Z |
| format | Journal article |
| id | oxford-uuid:76198787-2691-43de-b6b6-7d67e5e451f3 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:01:29Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:76198787-2691-43de-b6b6-7d67e5e451f32022-03-26T20:13:31ZEquilibrium order parameters of nematic liquid crystals in the Landau-De Gennes theory Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:76198787-2691-43de-b6b6-7d67e5e451f3Mathematical Institute - ePrints2009Majumdar, A We study equilibrium liquid crystal configurations in three-dimensional domains, within the continuum Landau-De Gennes theory. We obtain explicit bounds for the equilibrium scalar order parameters in terms of the temperature and material-dependent constants. We explicitly quantify the temperature regimes where the Landau-De Gennes predictions match and the temperature regimes where the Landau-De Gennes predictions don’t match the probabilistic second-moment definition of the Q-tensor order parameter. The regime of agreement may be interpreted as the regime of validity of the Landau-De Gennes theory since the Landau-De Gennes theory predicts large values of the equilibrium scalar order parameters - larger than unity, in the low-temperature regime. We discuss a modified Landau-De Gennes energy functional which yields physically realistic values of the equilibrium scalar order parameters in all temperature regimes. |
| spellingShingle | Majumdar, A Equilibrium order parameters of nematic liquid crystals in the Landau-De Gennes theory |
| title | Equilibrium order parameters of nematic liquid
crystals in the Landau-De Gennes theory
|
| title_full | Equilibrium order parameters of nematic liquid
crystals in the Landau-De Gennes theory
|
| title_fullStr | Equilibrium order parameters of nematic liquid
crystals in the Landau-De Gennes theory
|
| title_full_unstemmed | Equilibrium order parameters of nematic liquid
crystals in the Landau-De Gennes theory
|
| title_short | Equilibrium order parameters of nematic liquid
crystals in the Landau-De Gennes theory
|
| title_sort | equilibrium order parameters of nematic liquid crystals in the landau de gennes theory |
| work_keys_str_mv | AT majumdara equilibriumorderparametersofnematicliquidcrystalsinthelandaudegennestheory |