Active nematics — spontaneous alignment and topological defects
S = 0.000 | defects: 0
120
4
0.60
0.20
Self-propelled rods align nematically (head-tail symmetry): they align with neighbors but cannot distinguish "forward" from "backward." The nematic order parameter S = ⟨cos 2θ⟩ ranges from 0 (disordered) to 1 (perfectly aligned). Above a critical density/alignment, spontaneous global nematic order emerges (active analog of the Vicsek transition). Unlike equilibrium nematics, active nematics have topological defects (+½ and −½ disclinations) that self-propel (+½) or remain stationary (−½), driving spontaneous flows and turbulence.