Defect Configuration
Director angle at defect charge s:
θ(φ) = s·φ + θ₀
Winding number = ∮ dθ/2π
Nematic: n̂ ≡ -n̂ → half-integer allowed
Active Defects
Topological charge conserved:
Creation/annihilation in ±s pairs
Frank free energy: F = ½K∫|∇θ|²dr
Energy ~ πKs²ln(R/a)
Legend
Rod orientation = director n̂
Color = orientation angle
Interaction
Same-sign defects repel
Opposite-sign attract
In active matter: +½ self-propels
−½ remains passive (symmetric)