Orientability and Energy Minimization in Liquid Crystal Models
Orientability and Energy Minimization in Liquid Crystal Models
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DOI：
10.1007/s00205-011-0421-3
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发表时间：
2010-09
影响因子：
2.5
通讯作者：
J. Ball;A. Zarnescu
中科院分区：
文献类型：
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作者：
J. Ball;A. Zarnescu
在Oseen-Frank理论中，通过单位矢量场来模拟单轴双折射液晶。这个理论有一个明显的缺点，就是它不尊重n应该等于−n的首尾对称性。这种对称性在与张量一起工作的受限朗道-德热纳理论中得以保留。我们研究了这两种理论之间的差异和重叠。这些取决于所使用的规则性类以及底层域的拓扑结构。我们表明，对于简单连接域和自然能源类W1，2这两个理论相吻合，但在其他方面可以有两个理论之间的差异，我们确定。在平面域与孔和各种边界条件的情况下，对于最简单的形式的能量泛函，我们完全排除的情况下，约束Landau-de Gennes理论的预测不同于Oseen-Frank理论。
Uniaxial nematic liquid crystals are modelled in the Oseen–Frank theory through a unit vector fieldn. This theory has the apparent drawback that it does not respect the head-to-tail symmetry in whichnshould be equivalent to −n. This symmetry is preserved in the constrained Landau–de Gennes theory that works with the tensor. We study the differences and the overlaps between the two theories. These depend on the regularity class used as well as on the topology of the underlying domain. We show that for simply-connected domains and in the natural energy classW1,2the two theories coincide, but otherwise there can be differences between the two theories, which we identify. In the case of planar domains with holes and various boundary conditions, for the simplest form of the energy functional, we completely characterise the instances in which the predictions of the constrained Landau–de Gennes theory differ from those of the Oseen–Frank theory.