= Hookean dumbbell conformation equation
{c}
{title2=$\dot C-KC-CK^T=4k_BTI/\zeta-4HC/\zeta$}
Multiply the <Hookean dumbbell model> configuration equation by $R_iR_j$ and integrate twice by parts, with sufficient decay at large separation. The <linear velocity field> contributes $KC+CK^T$, the spring drift contributes $-4HC/\zeta$, and <diffusion> contributes $4k_BTI/\zeta$. Thus the dimensionless <conformation tensor> $A=HC/(k_BT)$ obeys $\dot A-KA-AK^T=-(A-I)/\lambda$, with <polymer relaxation time> $\lambda=\zeta/(4H)$. Its left side is an <upper-convected derivative> for this gradient convention.
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