Abstract
In order to describe relaxation processes not obeying an exponential law a model of a self-similar relaxation process is proposed which is described by an equation containing fractional differentiation operators. It turns out that the complex susceptibility corresponding to such a model system has a form which agrees with the known empirical Cowle—Cowle expression.
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References
P. P. Kobeko, Amorphous Materials [in Russian], Akad. Nauk SSSR, Moscow-Leningrad (1952).
A. K. Jonsher, Dielectric Relaxation in Solids, Chelsea Dielectric Press, London (1983).
A. N. Gubkin, Izv. Vyssh. Uchebn. Zaved., Fizika, No. 1, 56 (1979).
G. A. NiKlasson, J. Appl. Phys.,66, No. 9, 4350 (1989).
K. L. Ngai and C. T. White, Phys. Rev. B,20, No. 6, 2475 (1979).
H. Fröhlich, Theory of Dielectrics, Clarendon Press, Oxford (1958).
D. N. Zubarev, Nonequlibrium Statistical Thermodynamics [in Russian], Nauka, Moscow (1971).
E. Feder, Fractals [Russian translation], Mir, Moscow (1991).
V. V. Zososimov and L. M. Lyamshev, Usp. Fiz. Nauk,165, No. 4, 361 (1995).
N. N. Bogolyubov, Selected Works in Three Volumes [in Russian], Naukova Dumka, Kiev (1971).
P. P. Nagmatullin, TMF,90, No. 3, 345 (1992).
K. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley, New York (1993).
S. G. Samko, A. A. Kilbas, and O. I. Marichev, Integrals and Derivatives of Fractional Order and Certain of Their Applications [in Russian], Nauka i Tekhnika, Minsk (1987).
M. A. Lavren'tev and B. V. Shabat, Methods of the Theory of Funtions of a Complex Variable [in Russian], Nauka, Moscow (1965).
Additional information
Kazan State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 6–11, April, 1997.
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Nigmatullin, R.R., Ryabov, Y.E. Dielectric relaxation of the cowle-cowle type and self-similar relaxation processes. Russ Phys J 40, 314–318 (1997). https://doi.org/10.1007/BF02508850
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DOI: https://doi.org/10.1007/BF02508850