外场作用下双折射液晶中的土星环效应：有效能和滞后
The saturn ring effect in nematic liquid crystals with external field: effective energy and hysteresis
摘要：
在这项工作中，我们考虑的Landau-de Gennes模型与外部电磁场的液晶模型的旋转等变性的假设下发生的土星环效应。在能量的重新标度之后，导出变分极限。我们的分析依赖于精确的估计周围的奇异性和研究的径向辅助问题的区域中，存在一个连续的导演场。通过对极限问题的研究，我们解释了偶极组态与土星环组态之间的跃迁和滞后现象的发生，从而对[H.斯塔克，欧洲B 10，311-321（1999）]。
英文摘要：
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)].
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