Prony series coefficients

Prony Series Coefficients for Catsiff and Tobolsky Data... 

Fig. 7.19 Prony series coefficients used to obtain tensile modulus for Polyisobutylene. Fit to data shown in Fig. 7.18.

Once the relaxation times are selected, the problem reduces to finding the coefficients Ej such that the Prony series function optimally matches the provided time domain data. An obvious procedure to use is a generalized least squares approach, which was done in the multidata method (Cost and Becker, 1970). In this approach, coefficients are found that minimize the error between the modulus data (given as P data pairs (Ep,tp)) and the calculated function, E(t),... 

Another model (Roy et al. 2000) is based upon the assumption that the time dependence resides in the diffusion coefficient ), with the generalization that, due to the time-temperature analogy, depends also on the temperature T. Thus, in analogy with the common viscoelastic formulation D is expressed by a Prony series, namely... 

Figure 5. Time dependent strain optical coefficient as determined from Figure h. The points and interpolated dashed line show that the data can be described very well by a Prony series (from Arenz, Ferguson and Williams, Ref. 5)...

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