在单一弹性常数近似下,利用映射方法和拓扑流理论研究了液晶中向错线对自由能密度的影响.指出自由能密度可以分为两部分,一部分是通常的液晶指向矢场在向错线周围的畸变能密度;另一部分是向错线自身的自由能密度,当指向矢场的Jacobian行列式在指向矢场的奇点处不等于零时,它是集中在向错线上并以(1)/(2)kπ为单位拓扑量子化的,拓扑量子数由指向矢场在向错线处的Hopf指数和Brouwer度(即向错强度)决定.当Jacobian行列式等于零时,利用拓扑流分歧理论详细研究了在指向矢场的极限点和分岔点处向错线自身的自由能密度的产生、湮灭和分歧过程,最后得出,具有高的拓扑量子数的向错线是不稳定的,它将通过分歧过程演化到拓扑量子数比较低的状态.
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