Fig. 4. Densities and MSDs of topological +1/2 and −1/2 defects.

(A) Snapshot of a pair of $\raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ (green) and $\raisebox{1ex}{$+1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ (magenta) defects. (B) Polar and nematic order near a $\raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ defect with C₁ symmetry. (C) Polar and nematic order near a $\raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ defect with C₃ symmetry. In (A) to (C), filament colors indicate the polar angle of filament orientation. In (B) and (C), the yellow lines indicate boundaries between polar domains. (D) MSD of the filament center-of-mass (red), $\raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ defect (green), and $\raisebox{1ex}{$+1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ defect (magenta). (E) Average distance between defects as a function of the active force. (F) Estimation of the domain size with three different approaches. Solid lines show the $1/\sqrt{{\tilde{F}}_{\text{act}}}$ dependence and symbols simulations with datasets from the table in Fig. 1 with $(\mathrm{\varphi },\tilde{L})=(0.66,20)$.