 Nematic defect-antidefect annihilation

A neutral pair of opposite nematic disclinations can annihilate under dissipative relaxation, because the total topological charge of a two-dimensional nematic disclination is zero. Its far-field elastic energy increases as $2\pi K{\lambda }_0^2{q}^2\log (R/r_0)$ with separation $R$, so the pair has an attractive elastic force proportional to $-1/R$. As opposite cores meet, the nematic order parameter may vanish locally and the two windings disappear. Integer defects may first undergo energetic fission of an integer nematic disclination, leading to encounters of elementary half-charge defects. The actual paths and annihilation time require a dynamical law; the free energy alone does not specify core mobility. Pinning, imposed boundary winding or thermal defect production can obstruct a defect-free final state.