Topological Defect — Nematic Annihilation

In a 2D nematic liquid crystal, the order parameter is a headless director field n(x,y). Topological defects carry winding numbers ±½ (disclinations). A +½ defect (comet-like) and −½ defect (trefoil-like) attract via a logarithmic Coulomb potential V ~ K·ln r, leading to annihilation — releasing energy into the bulk. The Frank free energy F = (K/2)∫|∇θ|² drives relaxation of the director angle θ(x,y) via ∂θ/∂t = K/η · Δθ (Ginzburg-Landau dynamics).