液晶表面近晶态的存在性
Existence of Surface Smectic States of Liquid Crystals
摘要：
液晶的Landau-de Gennes模型是作用于波函数（序参数）和向量场（指向矢场）的泛函。在一个特定的渐近极限的物理参数，我们构造临界点，使波函数（序参数）是本地化的边界附近的域，我们确定了一个尖锐的本地化的边界区域的波函数集中。此外，我们还计算了这些临界点的能量以及边界能量的渐近性，这些边界能量可以用于定位指向矢场。在物理上，我们的结果证明了表面近晶态的存在。
英文摘要：
The Landau-de Gennes model of liquid crystals is a functional acting on wave functions (order parameters) and vector fields (director fields). In a specific asymptotic limit of the physical parameters, we construct critical points such that the wave function (order parameter) is localized near the boundary of the domain, and we determine a sharp localization of the boundary region where the wave function concentrates. Furthermore, we compute the asymptotics of the energy of such critical points along with a boundary energy that may serve in localizing the director field. In physical terms, our results prove the existence of a surface smectic state.
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