تقرير
The saturn ring effect in nematic liquid crystals with external field: effective energy and hysteresis
| العنوان: | The saturn ring effect in nematic liquid crystals with external field: effective energy and hysteresis |
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| المؤلفون: | Alouges, François, Chambolle, Antonin, Stantejsky, Dominik |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, 35B40, 35J50, 49J45, 49S05, 76A15 |
| الوصف: | In this work we consider the Landau-de Gennes model for liquid crystals with an external electromagnetic field to model the occurrence of the saturn ring effect under the assumption of rotational equivariance. After a rescaling of the energy, a variational limit is derived. Our analysis relies on precise estimates around the singularities and the study of a radial auxiliary problem in regions, where a continuous director field exists. Studying the limit problem, we explain the transition between the dipole and saturn ring configuration and the occurrence of a hysteresis phenomenon, giving a rigorous explanation of what was conjectured previously by [H. Stark, Eur. Phys. J. B 10, 311-321 (1999)]. Comment: 42 pages, 6 figures |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s00205-021-01674-z |
| URL الوصول: | http://arxiv.org/abs/2005.06238 |
| رقم الأكسشن: | edsarx.2005.06238 |
| قاعدة البيانات: | arXiv |
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