From stretched exponential to inverse power-law: fractional dynamics, Cole-Cole relaxation processes, and beyond

By Ralf Metzler, Joseph Klafter. 2002

137 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/bcafe97c49db039ce91a13c542c81af81e4e1b36

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In Modeling and Simulation

In Statistical and Nonlinear Physics

Citations in the corpus

Power-law rheology in the bulk and at the interface: quasi-properties and fractional constitutive equations (2013, background): “This broad spectral response is indicative of the wide range of distinct relaxation processes available to the microstructural elements that compose the material, and there is no single characteristic relaxation time [7].”
Hysteresis in Piezoelectric and Ferroelectric Materials (2006, methodology): “It has been suggested by Metzler and Klafter [84] that the power-law dependence 1/ is simply a medium-to-low frequency approximation of the Davidson--Cole extension of the Debye-type relaxation (Section 4.3.3).”
Some New Fractional-Calculus Connections between Mittag–Leffler Functions (2019, methodology): “The one-parameter Mittag–Leffler function has already discovered many applications via the AB model, and also previously in relaxation models which involve interpolation between exponential and power-law behaviours [39].”
Time-fractional derivatives in relaxation processes: a tutorial survey (2008, background): “our CISM Lecture Notes [55, 57, 80], the review papers [85, 86, 116], and the books [88, 70, 66, 69, 77, 94, 108, 118, 119] with references therein.”
The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics (2004, background): “Dielectric susceptibilities in glassy systems are of strong non-Debye form (compare Déjardin 2003, Metzler and Klafter 2002) and can in some systems be studied over some 15 decades in frequency10 (Hilfer 2002a, 2002b, Schneider et al 1999, Lunkenheimer and Loidl 8 Poly-3,4-ethylenedioxythiophene.”