Gyrotactic orientation Fokker-Planck equation
= Gyrotactic orientation Fokker-Planck equation
For orientation <probability density> $f$ on the unit sphere, deterministic drift $\dot{\mathbf p}$ and isotropic rotational <diffusion> coefficient $D_R$ give $\partial_tf+\nabla_p\cdot(f\dot{\mathbf p}-D_R\nabla_pf)=0$. The derivatives are tangential to the sphere, and normalization is $\int f\,d\Omega=1$. The spherical divergence of $\mathbf k-p_3\mathbf p$ is $-2p_3$.