Tumbling of a polar order parameter
= Tumbling of a polar order parameter
{title2=$T=4\pi/(|g|\sqrt{1-\xi^2})$}
In <simple shear flow>, a persistent <polar order parameter> with $|\xi|<1$ has no fixed angle and rotates continuously. Integrating $\dot\theta=g(\xi\cos2\theta-1)/2$ through $2\pi$ gives the displayed period. An unoriented <nematic director> repeats after half that time. At $\xi=0$, the magnitude relaxes independently while the angular speed is $-g/2$.