Models of dielectric relaxation based on completely monotone functions

By Roberto Garrappa, Francesco Mainardi, Maione Guido. 2016

165 citations recorded by the source corpus.

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.

Subfields: Mechanics of Materials, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/5a718ad12aa03d52917adf3963d521f5e642a5df

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In Mechanics of Materials

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

A practical guide to Prabhakar fractional calculus (2020, background): “This is, however, not the case for several other empirical laws for anomalous dielectrics such as the Davidson–Cole [24] and Havriliak–Negami [63] models, described by [37]”