Generalized Distribution Function of Relaxation Times with the Davidson-Cole Model as a Kernel
Chemical Physics
2024-01-15 v1 Disordered Systems and Neural Networks
Mathematical Physics
math.MP
Applied Physics
Abstract
In this paper we propose a generalized distribution function of relaxation times (DFRT) considering the Davidson-Cole model as an elementary process instead of the standard Debye model. The distribution function is retrieved from the inverse of the generalized Stieltjes transform expressed in terms of iterated Laplace transforms. We derive computable analytical expressions of the generalized DFRT for some of the most known normalized impedance (or admittance) models including the constant phase element, the Davidson-Cole, Havriliak-Negami and the Kohlrausch-Williams-Watts models.
Cite
@article{arxiv.2401.06490,
title = {Generalized Distribution Function of Relaxation Times with the Davidson-Cole Model as a Kernel},
author = {Anis Allagui and Ahmed Elwakil},
journal= {arXiv preprint arXiv:2401.06490},
year = {2024}
}