论文标题
三维nematics中的披露线的运动学和动力学
Kinematics and dynamics of disclination lines in three-dimensional nematics
论文作者
论文摘要
列出液晶中披露线运动的精确运动定律是张量顺序参数$ \ mathbf {q} $的函数。与其他在其各自的缺陷芯上变得奇异的阶参数字段不同，张量顺序参数仍然是规则的。在较早的实验和理论工作之后，披露核心被定义为单轴和双轴阶参数相等或等效的线，其中两个最大的特征值为$ \ mathbf {q} $ cross。这允许将线路的速度与线上的$ \ mathbf {q} $的空间和时间导数相关的精确表达式，该表达式由动力学模型指定，用于列明的演变。通过引入$ \ mathbf {q} $的线性核心近似，为多种典型配置提供了分析结果，包括线相互作用和运动，环歼灭，以及对外部场和剪切流的响应。突出显示了拓扑约束或缺陷几何形状遵循的行为。分析结果显示出基于单个Maier-Saupe自由能的三维数值计算一致，该计算允许各向异性弹性。
An exact kinematic law for the motion of disclination lines in nematic liquid crystals as a function of the tensor order parameter $\mathbf{Q}$ is derived. Unlike other order parameter fields that become singular at their respective defect cores, the tensor order parameter remains regular. Following earlier experimental and theoretical work, the disclination core is defined to be the line where the uniaxial and biaxial order parameters are equal, or equivalently, where the two largest eigenvalues of $\mathbf{Q}$ cross. This allows an exact expression relating the velocity of the line to spatial and temporal derivatives of $\mathbf{Q}$ on the line, to be specified by a dynamical model for the evolution of the nematic. By introducing a linear core approximation for $\mathbf{Q}$, analytical results are given for several prototypical configurations, including line interactions and motion, loop annihilation, and the response to external fields and shear flows. Behaviour that follows from topological constraints or defect geometry is highlighted. The analytic results are shown to be in agreement with three dimensional numerical calculations based on a singular Maier-Saupe free energy that allows for anisotropic elasticity.
