Phototactic orientation Fokker-Planck equation (source code)

= Phototactic orientation Fokker-Planck equation
{title2=$\partial_tf=-\nabla_p\cdot(f\dot{\mathbf p})+D_r\nabla_p^2f$}

For isotropic <rotational diffusion>, orientation drift and <probability density> obey the displayed <Fokker-Planck equation>, normalized with respect to solid angle. Without flow, constant light $L\mathbf e_x$ gives the zero-current density $f_0=\lambda e^{\lambda p_x}/(4\pi\sinh\lambda)$, $\lambda=L/(\alpha D_r)$. Integration over the sphere gives unit mass; its mean projection is the <Langevin function>. The zero-light limit is the uniform density $1/(4\pi)$.