Nematic Disclination Dynamics — Active Liquid Crystal

Nematic liquid crystals have ±½ topological defects (disclinations) in the director field n̂. Active nematics (e.g., cytoskeletal filaments) spontaneously generate and annihilate ±½ defect pairs, driving chaotic flows. The topological charge is conserved: Σq = 0.

Parameters

Activity α: 1.0 Frank const K: 1.0 Rotation rate Γ: 0.5 Grid: 60×60

Defects: 0

Director: n̂(r) = (cos θ, sin θ)
∂θ/∂t = K∇²θ + α·noise
+½ defect: θ = φ/2 (comet)
-½ defect: θ = -φ/2 (trefoil)
Topological charge: q=±½
Active flow: v ~ α ∂_j Q_ij
Annihilation: +½ meets -½