Differential pom-pom model (source code)

= Differential pom-pom model
{title2=$\sigma=G\lambda^2A/\operatorname{tr}A-pI$}

This differential model separates normalized molecular orientation $B=A/\operatorname{tr}A$ from scalar stretch $\lambda$. With component-first <velocity gradient> $K$, it evolves by $D_tA=KA+AK^T-(A-I)/\tau_1$ and $D_t\lambda=\lambda B:K-(\lambda-1)/\tau_2$. Its relaxed state is $A=I$, $B=I/3$, $\lambda=1$. The displayed constant-relaxation stretch law is an idealization; variants can add saturation or nonlinear relaxation.