论文标题
具有不同弹性常数的胆固醇液晶的一维变分问题
A One-Dimensional Variational Problem for Cholesteric Liquid Crystals with Disparate Elastic Constants
论文作者
论文摘要
我们考虑与胆固醇液晶模型有关的一维变分问题。我们研究的主要特征是假设列表导演的扭曲变形比其他变形模式更高。然后，弹性常数的适当比率给出了一个小参数$ \ varepsilon $，输入了通过扭曲项增强的allen-cahn型能量功能。我们将能源的行为视为$ \ varepsilon $趋于零。我们证明了通过其整体扭曲分类的局部能量最小化的存在，找到了轻松的能量的$γ$限制，并表明它由扭曲和跳跃术语组成。此外，我们将结果扩展到包括胆固醇螺距消失以及$ \ varepsilon $的情况。
We consider a one-dimensional variational problem arising in connection with a model for cholesteric liquid crystals. The principal feature of our study is the assumption that the twist deformation of the nematic director incurs much higher energy penalty than other modes of deformation. The appropriate ratio of the elastic constants then gives a small parameter $\varepsilon$ entering an Allen-Cahn-type energy functional augmented by a twist term. We consider the behavior of the energy as $\varepsilon$ tends to zero. We demonstrate existence of the local energy minimizers classified by their overall twist, find the $Γ$-limit of the relaxed energies and show that it consists of the twist and jump terms. Further, we extend our results to include the situation when the cholesteric pitch vanishes along with $\varepsilon$.
