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
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