= 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 $2\pi K\lambda_0^2q^2\log(R/r_0)$ 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.
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