Effect of elastic anisotropy on dynamics of pair-annihilating disclination lines in nematic liquid crystals

Current experiments in both lyotropic chromonics and mixtures of actin filaments involve highly anisotropic elasticity, with elastic constants differing by orders of magnitude. To understand the motion of disclinations in these elastically anisotropic media we use a Ball and Majumdar singular potential Q-tensor theory to numerically simulate the pair-annihilation of disclination lines. We provide an approximate scaling law for the coalescence time of the annihilation. To verify these numerical results we use a perturbative expansion in the anisotropy parameter to find the director field around a disclination in the presence of another disclination. Using the singularity tracking method proposed by Schimming we find approximate analytic solutions of disclination separation as a function of time during pair-annihilation.