= Hookean dumbbell conformation equation with anisotropic mobility
{title2=$C^{\nabla}=-(2H/\zeta)(MC+CM)+(4k_BT/\zeta)M$}
Let $C=\langle\mathbf R\mathbf R^T\rangle$ be the unnormalized <conformation tensor>, $G_{ij}=\partial_j u_i$ the <velocity gradient>, and $M/\zeta$ a symmetric positive <hydrodynamic mobility matrix> independent of the individual connector. The connector <Fokker-Planck equation> has drift $G\mathbf R-(2H/\zeta)M\mathbf R$ and <diffusion> matrix $(2k_BT/\zeta)M$. Integrating its second moment twice by parts gives the displayed <upper-convected derivative>, $C^{\nabla}=D_tC-GC-CG^T$. If $M$ is a polynomial in $C$, the two matrices commute and the relaxation term simplifies to $-(4H/\zeta)M(C-k_BT I/H)$. No <Gaussian distribution> assumption is required for this <moment closure>.
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