An analysis of dielectric relaxation using the fractional master equation of the stochastic Ising model

In this paper, we begin introducing some basic definitions and mathematical preliminaries of the fractional calculus theory. By using the fractional calculus technique (that is, calculus of derivatives and integrals of any arbitrary real or complex order) a solution of the fractional master equation...

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Bibliographic Details
Published in:Journal of non-crystalline solids 2011, Vol.357 (1), p.202-205
Main Author: CAVUS, M. Serdar
Format: Article
Language:English
Subjects:
Calculus
Condensed matter: electronic structure, electrical, magnetic, and optical properties
Decay
Derivatives
Dielectric loss and relaxation
Dielectric properties of solids and liquids
Dielectric relaxation
Dielectrics, piezoelectrics, and ferroelectrics and their properties
Dispersions
Exact sciences and technology
Fractional calculus
Ising model
Master equation
Mathematical analysis
Mathematical models
Physics
Stochasticity
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Summary:In this paper, we begin introducing some basic definitions and mathematical preliminaries of the fractional calculus theory. By using the fractional calculus technique (that is, calculus of derivatives and integrals of any arbitrary real or complex order) a solution of the fractional master equation derived from the stochastic Ising model of Glauber has been obtained and the result is applied to an analysis of the dielectric relaxation processes. From the solution of the equation, the Cole–Cole dispersion relation, KWW (Kohlrausch–William–Watts) equation and algebraic decay relaxation functions are obtained easily. Then these functions are compared with Bozdemir's earlier analysis of the stochastic Ising model.
ISSN:0022-3093
1873-4812
DOI:10.1016/j.jnoncrysol.2010.09.029