The radial-hedgehog solution in Landau-de Gennes' theory
The radial-hedgehog solution in Landau-de Gennes' theory
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发表时间：
2010-09
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通讯作者：
A. Majumdar
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作者：
A. Majumdar
在向列型液晶的Landau-de Gennes理论下，我们研究了三维单位球上具有同向同性边界条件的径向刺激解。径向Hedgehog解是该模型框架中全局稳定组态的候选者，也是研究凝聚态物理中孤立点缺陷的原型组态。我们利用Ginzburg-Landau技巧、摄动方法和稳定性分析相结合的方法研究了径向-刺激解的定性性质，它的缺陷核的结构，以及它在双轴扰动下的稳定性和不稳定性。我们的结果补充了前人在这一领域的工作，本质上是严格的，给出了几何、弹性常数和温度对径向-刺激解的性质以及相关的双轴不稳定性的作用的信息。
We study the radial-hedgehog solution on a unit ball in three dimensions, with homeotropic boundary conditions, within the Landau-de Gennes theory for nematic liquid crystals. The radial-hedgehog solution is a candidate for a globally stable configuration in this model framework and is also a prototype configuration for studying isolated point defects in condensed matter physics. We use a combination of Ginzburg-Landau techniques, perturbation methods and stability analyses to study the qualitative properties of the radial-hedgehog solution, the structure of its defect core, its stability and instability with respect to biaxial perturbations. Our results complement previous work in the field, are rigorous in nature, give information about the role of geometry, elastic constants and temperature on the properties of the radial-hedgehog solution and the associated biaxial instabilities.