Velocity-dispersion tensor of collisionless matter (source code)

= Velocity-dispersion tensor of collisionless matter
{title2=$\sigma^{ij}$}

The velocity-dispersion tensor is the second central moment of a phase-space distribution,
$$
\sigma^{ij}=\langle u^iu^j\rangle-v^iv^j.
$$
It contributes the stress-divergence term $\rho^{-1}\partial_j(\rho\sigma^{ij})$ to the Euler equation and vanishes in the ideal single-stream limit.