تقرير
Spherical Particle in Nematic Liquid Crystal with a Magnetic Field and Planar Anchoring
| العنوان: | Spherical Particle in Nematic Liquid Crystal with a Magnetic Field and Planar Anchoring |
|---|---|
| المؤلفون: | Bronsard, Lia, Louizos, Dean, Stantejsky, Dominik |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, Mathematics - Classical Analysis and ODEs, 49J45, 35J50, 49S05, 76A15 |
| الوصف: | 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 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. Comment: 32 pages, 5 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2403.20274 |
| رقم الأكسشن: | edsarx.2403.20274 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |