= Zero-flow steady gyrotactic orientation distribution
{title2=$f_0(\theta)=\Lambda e^{\Lambda\cos\theta}/(4\pi\sinh\Lambda)$}
For aligning rate $1/B$, positive rotational <diffusivity> $D_r$ and $\Lambda=(BD_r)^{-1}$, the zero-current steady <Fokker-Planck equation> gives $f_{0,\theta}=-\Lambda\sin\theta f_0$. Normalization over the unit sphere gives the displayed density per unit solid angle. Its mean direction is $\langle\mathbf p\rangle=(\coth\Lambda-1/\Lambda)\mathbf k$, the <Langevin function>. As $BD_r\to0$, it concentrates weakly into a point mass at the upward pole; the limit is not an ordinary bounded probability density.
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