Cell dynamics simulation for the phase ordering of nematic liquid crystals

A discrete model is presented to describe the dynamics of nematic liquid crystals for the case where topological defects dominate the spatial pattern. A numerical study is given of the annihilation kinetics of the defects in the two-dimensional nematic system with ${\mathit{P}}^2$ symmetry. The structure factor is found to obey a scaling law S(k,t)=〈k${\mathrm{〉}}_{\mathit{t}}^2$g(k/〈k${\mathrm{〉}}_{\mathit{t}}$) where the first moment 〈k${\mathrm{〉}}_{\mathit{t}}$ varies as 〈k${\mathrm{〉}}_{\mathit{t}}$∼${\mathit{t}}^{\mathrm{-}0.42}$. The asymptotic power-law tail g(x)∼${\mathit{x}}^{\mathrm{-}4.5}$ is found.