Justification of the empirical laws of the anomalous dielectric relaxation in the framework of the memory function formalism

Using the memory conception developed in the framework of the Mori-Zwanzig formalism, the kinetic equations for relaxation functions that correspond to the previously suggested empirical functions (Cole-Davidson and Havriliak-Negami) are derived. The obtained kinetic equations contain differential o...

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Bibliographic Details
Published in:Fractional calculus & applied analysis 2014-03, Vol.17 (1), p.247-258
Main Authors: Khamzin, Airat A., Nigmatullin, Raoul R., Popov, Ivan I.
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Analysis
Functional Analysis
Integral Transforms
Mathematics
Mathematics and Statistics
Operational Calculus
Research Paper
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Summary:Using the memory conception developed in the framework of the Mori-Zwanzig formalism, the kinetic equations for relaxation functions that correspond to the previously suggested empirical functions (Cole-Davidson and Havriliak-Negami) are derived. The obtained kinetic equations contain differential operators of non-integer order and have clear physical meaning and interpretation. The derivation of the memory function corresponding to the Havriliak-Negami relaxation law in the frame of Mori-Zwanzig formalism is given. A physical interpretation of the power-law exponents involved in the Havriliak-Negami empirical expression is provided too.
ISSN:1311-0454
1314-2224
DOI:10.2478/s13540-014-0165-5