Spontaneous flow and ±½ topological defect dynamics
Defects: +½: — | −½: — | Activity: —
Active nematics are orientational fluids driven by internal activity (motor proteins, bacteria). The director field Q_{ij} = S(n_i n_j − δ_{ij}/2) evolves via relaxation and active stress ζQ. Above a threshold activity, the uniform state is unstable to spontaneous flow. Topological defects form: +½ defects (comet-shaped) self-propel; −½ (trefoil) are advected passively, creating "active turbulence" at low Reynolds number.