= Effective orientation angle from nematic order
{title2=$\theta_{\rm eff}=\arccos\sqrt{(2S+1)/3}$}
For scalar <nematic order parameter> $S=\langle(3\cos^2\theta-1)/2\rangle$, the displayed angle has $\cos^2\theta_{\rm eff}=\langle\cos^2\theta\rangle$. It summarizes a second moment, not the literal mean angle. For example an isotropic orientation distribution has $S=0$, giving $\theta_{\rm eff}=\arccos(1/\sqrt3)$; the average acute angle to its unoriented axis is instead one radian, obtained by integrating $\theta\sin\theta$ over $[0,\pi/2]$.
Back to article page
