Warner or "FENE" spring:(2.2)

This spring has a maximum length of . It can describe

many nonlinear rheological properties, but is difficult to

handle analytically. (FENE = finitely extensible nonlinear

elastic)

"FENE-P" spring:(2.3)

Here the ratio in the denominator is averaged at the local

conditions. "P" stands for Anton Peterlin who used a similar

approximation.

Fraenkel spring:(2.4)

When the spring constant is allowed to go to infinity, the

Fraenkel spring becomes a rigid rod of length L.

Whatever model is chosen, the beads are presumed to be acted on by a Stokes law type of drag force, with a drag coefficient .

2a. The Liouville equation for general bead-spring models

(i.e., models with any connectivity and complexity)