We analyze single-core and split-core defect structures in nematic liquid crystals within the Landau-de Gennes framework by studying minimizers of the associated energy functional. A bifurcation occurs at a critical temperature threshold, below which both split-core and single-core configurations are solutions to the Euler-Lagrange equation, with the split-core defect possessing lower energy. Above the threshold, the split-core configuration vanishes, leaving the single-core defect as the only stable solution. We analyze the dependence of such temperature threshold on the domain size and characterize the nature of the transition between the two defect types. We carry out a quantitative study of defect core sizes as functions of temperature and domain size for both single and split core defects.

翻译：我们在朗道-德热纳理论框架下，通过研究相关能量泛函的极小化问题，分析了向列相液晶中的单核与分裂核缺陷结构。在临界温度阈值处发生分岔现象：低于该阈值时，分裂核与单核构型均为欧拉-拉格朗日方程的解，且分裂核缺陷具有更低的能量；高于该阈值时，分裂核构型消失，仅剩单核缺陷作为唯一稳定解。我们研究了该温度阈值对区域尺寸的依赖关系，并表征了两类缺陷间转变的本质特性。针对单核与分裂核缺陷，我们定量研究了缺陷核尺寸随温度及区域尺寸的变化规律。