Active nematics (e.g., bacterial layers, cytoskeletal filaments) self-organize through activity-driven instabilities. ±½ topological defects spontaneously form, move, and annihilate. The +½ defect is self-propelled (comet-like); the −½ defect is stationary. Activity drives continuous defect pair creation/annihilation.
Q = S(nn − ½I) — nematic tensor
∂ₜQ = K∇²Q + αQ/|Q| (active)
Defect charge: q = ±½
+½ defect: self-propelled (v ∝ α)
−½ defect: stationary (3-fold symmetry)
Activity threshold αc ∼ K/L²