Curvature and topology in smectic-A liquid crystals
Curvature and topology in smectic-A liquid crystals
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近晶A液晶的曲率和拓扑
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
R. Kamien
中科院分区：
文献类型：
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作者：
C. Santangelo;R. Kamien
考虑一维调制系统（例如近晶-A）中的旋转不变性，需要自由能的非线性。这些非线性的存在对于确定缺陷周围的层配置至关重要。我们将我们最近的构造推广到寻找近似非线性自由能的精确最小值到完整的、旋转不变的近晶自由能。我们的构造展示了平均曲率、高斯曲率和层间距之间的详细联系。对于没有高斯曲率的层，我们将欧拉-拉格朗日方程简化为控制表面演化的方程。例如，我们确定边缘位错的层轮廓和自由能。
Considerations of rotational invariance in one-dimensionally modulated systems such as smectics-A, necessitate nonlinearities in the free energy. The presence of these nonlinearities is critical for determining the layer configurations around defects. We generalize our recent construction for finding exact minima of an approximate nonlinear free energy to the full, rotationally invariant smectic free energy. Our construction exhibits the detailed connection between mean curvature, Gaussian curvature and layer spacing. For layers without Gaussian curvature, we reduce the Euler–Lagrange equation to an equation governing the evolution of a surface. As an example, we determine the layer profile and free energy of an edge dislocation.