Models of dielectric relaxation based on completely monotone functions
Abstract
The relaxation properties of dielectric materials are described, in the frequency domain, according to one of the several models proposed over the years: Kohlrausch-Williams-Watts, Cole-Cole, Cole-Davidson, Havriliak-Negami (with its modified version) and Excess wing model are among the most famous. Their description in the time domain involves some mathematical functions whose knowledge is of fundamental importance for a full understanding of the models. In this work, we survey the main dielectric models and we illustrate the corresponding time-domain functions. In particular, we stress the attention on the completely monotone character of the relaxation and response functions. We also provide a characterization of the models in terms of differential operators of fractional order.
Keywords
Cite
@article{arxiv.1611.04028,
title = {Models of dielectric relaxation based on completely monotone functions},
author = {Roberto Garrappa and Francesco Mainardi and Guido Maione},
journal= {arXiv preprint arXiv:1611.04028},
year = {2017}
}
Comments
44 pages, 26 figures