Sums of Exponentials Approximations for the Kohlrausch Function

Abstract: The mathematical foundation of many real-world problems can be quite deep. Such a situation arises in the study of the flow and deformation (rheology) of viscoelastic materials such as naturally occurring and synthetic polymers. In order to advance polymer science and the efficient manufacture of synthetic polymers, it is necessary to recover information about the molecular structure within such materials. For the recovery of such information about a specific polymer, it is necessary to determine its relaxation modulus G(t) and its creep modulus J(t). They correspond to the kernels of the Boltzmann causal integral equation models of stress relaxation and strain accumulation experiments performed on viscoelastic solids and fluids. In order to guarantee that the structure of such models is consistent with the conservation of energy, both the relaxation modulus and the derivative of the creep modulus must be completely monotone (CM) functions.