Start-up and stationary flows

We first consider a shear flow. By carrying out the Gaussian integral, we find that the chain survival function of this model network is explicitly given by 

Similarly, for the initial terms we carry out the coordinate Gaussian integrals, and find 

In the case of an elongational flow with a constant flow rate e, a similar procedure leads to the same form for the time evolution of the number of active chains v (f) that have been active from the initial stage, but the function must now be replaced by 

Quite analogously, the elongational stress supported by the initially active chains can be found by 

The t = 0 component of this function gives the stress propagator for the elongational flow a (f) = B7 (t,0). 

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