Landau-de Gennes Corrections to the Oseen-Frank Theory of Nematic Liquid Crystals

被引：8
|
作者：
Di Fratta, Giovanni [1 ]
Robbins, Jonathan M. [2 ]
Slastikov, Valeriy [2 ]
Zarnescu, Arghir [3 ,4 ,5 ]
机构：
[1] TU Wien, Inst Anal & Sci Comp, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria
[2] Univ Bristol, Sch Math, Univ Walk, Bristol BS8 1TW, Avon, England
[3] Basque Fdn Sci, Ikerbasque, Maria Diaz de Haro 3, Bilbao 48013, Bizkaia, Spain
[4] BCAM, Mazarredo 14, Bilbao 48009, Bizkaia, Spain
[5] Romanian Acad, Simion Stoilow Inst, 21 Calea Grivitei, Bucharest 010702, Romania
来源：
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2020年 / 236卷 / 02期
基金：
英国工程与自然科学研究理事会; 奥地利科学基金会;
关键词：
HARMONIC MAPS; POINT-DEFECTS; MINIMIZATION; MINIMIZERS; REGULARITY; SYMMETRY;
D O I：
10.1007/s00205-019-01488-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the asymptotic behavior of the minimisers of the Landau-de Gennes model for nematic liquid crystals in a two-dimensional domain in the regime of small elastic constant. At leading order in the elasticity constant, the minimum-energy configurations can be described by the simpler Oseen-Frank theory. Using a refined notion of Gamma-development we recover Landau-de Gennes corrections to the Oseen-Frank energy. We provide an explicit characterisation of minimizing Q-tensors at this order in terms of optimal Oseen-Frank directors and observe the emerging biaxiality. We apply our results to distinguish between optimal configurations in the class of conformal director fields of fixed topological degree saturating the lower bound for the Oseen-Frank energy.
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页码：1089 / 1125
页数：37
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