Cell dynamics simulation for the phase ordering of nematic liquid crystals

Abstract

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${\mathrm{〉}}_{\mathit{t}}$\ensuremath{\sim}${\mathit{t}}^{\mathrm{\ensuremath{-}}0.42}$. The asymptotic power-law tail g(x)\ensuremath{\sim}${\mathit{x}}^{\mathrm{\ensuremath{-}}4.5}$ is found.