2.15 Rheology

Figure 16:

Comparison of relaxation time distribution functions obtained by Winter’s discrete parsimonius algorithm and by direct Stieltjes inversion, [38].

The mathematical problems encountered in advanced questions of rheology often involve integral transformations and their inversions. Although these are usually 1d in nature, i.e. relating the time to the frequency domain, not 3d as in scattering theory, the knowledge and experience accumulated in the latter can nevertheless often be favorably applied to the former. Examples for this are a fairly simple straightforward analytical inversion of an experimental dynamic modulus curve leading to a relaxation time distribution quite similar to that obtained by an elaborate numerical iterative procedure, figure 16, or an excellent approximation in fully analytical closed form for the complex modulus corresponding to a relaxation time distribution given as a log-normal distribution. Details are discussed in [38].