Nematic Defect Annihilation

Nematic liquid crystals host topological defects with winding numbers ±1/2. Opposite-charge pairs attract and annihilate, releasing Frank elastic energy. Watch the director field evolve and defects collide.

Controls

Frank constant K1.0

Mobility μ1.0

Noise (T)0.05

Pink = +½ defect
Cyan = −½ defect
Opposite pairs annihilate

Theory

Frank free energy:
F = K/2 ∫|∇n|² dA

Defect charge:
q = 1/2π ∮ dθ

Force on defect:
f = πK(q₁q₂)/r

Annihilation when r→0:
+½ + (−½) → 0