Affiliation:
1. Faculty of Fundamental Problems of Technology Wrocław University of Technology Wybrzeże Wyspiańskiego 27 Wrocław – 50-370, Poland
Abstract
Abstract
We present a probabilistic model of the microscopic scenario of dielectric relaxation relating to the atypical case of two-power-law responses.The surveyed approach extends the cluster model concept used for the description of the typical, Havriliak-Negami (HN) law. Within the proposed framework, all empirical two-power-law relaxation patterns may be derived. Their relaxation functions are expressed in terms of the three-parameter Mittag-Leffler function, and the kinetic equation takes the pseudodifferential form generalizing the Riemann-Louiville fractional calculus. This provides a clue to explain the universality observed in relaxation phenomena.
Subject
Applied Mathematics,Analysis
Reference34 articles.
1. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables.Ch. 13, Dover, New York1965).
2. E. Capelas de Oliveira, F. Mainardi, J. Vaz Jr, Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics. The European Physical Journal, Special Topics193 (2011), 161–171
3. W. Chen, Y. Liang, S. Hu, H. Sun, Fractional derivative anomalous diffusion equation modeling prime number distribution. Fract. Calc. Appl. Anal. 18 (2015), 789–798; DOI: 10.1515/fca-2015-0047;http://www.degruyter.com/view/j/fca.2015.18.issue-3/issue files/fca.2015.18.issue-3.xml.
4. W. Chen, X. Zhang, X. Cai, A study on modified Szabo’s wave equation modeling of frequency-dependent dissipation in ultrasonic medical imaging. Phys. ScrT. 136 (2009), #014014.
5. R.L. Dobrushin, Lemma on the limit of a composite random function. Uspekhi Mat. Nauk 10 (1955), 157–159 (in Russian)
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