Spherical Particle in Nematic Liquid Crystal with a Magnetic Field and Planar Anchoring
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917823642599424 |
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| author | Bronsard, Lia Louizos, Dean Stantejsky, Dominik |
| author_facet | Bronsard, Lia Louizos, Dean Stantejsky, Dominik |
| contents | We study minimizers of the Landau-de Gennes energy in $\mathbb{R}^3\setminus B_1(0)$ with external magnetic field in the large particle limit. We impose strong tangential anchoring and uniaxiality of the $Q-$tensor on the boundary. We derive a lower bound for the energy in terms of the boundary condition and show in the extreme cases of strong and weak magnetic field strength that the longitudinal director field is energy minimizing, indicating the presence of two half-point defects, so called boojums, at two opposite points of the sphere. Using a recovery sequence, we show that the energy bound is optimal in these extreme cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_20274 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spherical Particle in Nematic Liquid Crystal with a Magnetic Field and Planar Anchoring Bronsard, Lia Louizos, Dean Stantejsky, Dominik Analysis of PDEs Classical Analysis and ODEs 49J45, 35J50, 49S05, 76A15 We study minimizers of the Landau-de Gennes energy in $\mathbb{R}^3\setminus B_1(0)$ with external magnetic field in the large particle limit. We impose strong tangential anchoring and uniaxiality of the $Q-$tensor on the boundary. We derive a lower bound for the energy in terms of the boundary condition and show in the extreme cases of strong and weak magnetic field strength that the longitudinal director field is energy minimizing, indicating the presence of two half-point defects, so called boojums, at two opposite points of the sphere. Using a recovery sequence, we show that the energy bound is optimal in these extreme cases. |
| title | Spherical Particle in Nematic Liquid Crystal with a Magnetic Field and Planar Anchoring |
| topic | Analysis of PDEs Classical Analysis and ODEs 49J45, 35J50, 49S05, 76A15 |
| url | https://arxiv.org/abs/2403.20274 |