论文标题
具有外场的列液晶的土星环效应：有效的能量和磁滞
The saturn ring effect in nematic liquid crystals with external field: effective energy and hysteresis
论文作者
论文摘要
在这项工作中，我们考虑了具有外部电磁场的液晶的Landau-de Gennes模型，以模拟在旋转率的假设下的土星环效应的发生。重新恢复能量后，得出了变异极限。我们的分析依赖于围绕奇异性和研究径向辅助问题的精确估计值，而该区域中存在一个连续的董事场。在研究极限问题时，我们解释了偶极子和土星环构型与发生磁滞现象的发生之间的过渡，从而对先前由[H.斯塔克，欧洲。物理。 J. B 10，311-321（1999）]。
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)].
