Kinematics and dynamics of disclination lines in three-dimensional nematics

An exact kinematic law for the motion of disclination lines in nematic liquid crystals as a function tensor order parameter Q is derived. Unlike other fields that become singular at their respective defect cores, remains regular. Following earlier experimental and theoretical work, core defined to be line where uniaxial biaxial parameters are equal, or equivalently, two largest eigenvalues cross. This allows an expression relating velocity spatial temporal derivatives on line, specified by dynamical model evolution nematic. By introducing linear approximation , analytical results given several prototypical configurations, including interactions motion, loop annihilation, response external shear flows. Behaviour follows from topological constraints geometry highlighted. The analytic shown agreement with three-dimensional numerical calculations based Maier–Saupe free energy anisotropic elasticity.