Tempered relaxation with clustering patterns

This work is motivated by the relaxation data for materials which exhibit a change of the relationship between the fractional power-law exponents when different relaxation peaks in their dielectric susceptibility are observed. Within the proposed framework we derive a frequency-domain relaxation fun...

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Bibliographic Details
Published in:Physics letters. A 2011-11, Vol.375 (48), p.4244-4248
Main Authors: Stanislavsky, Aleksander, Weron, Karina
Format: Article
Language:English
Subjects:
Clustering
Compound subordination
Dielectric relaxation
Exponents
Fittings
Fractional two-power relaxation
High frequencies
Plugs
Solid state physics
Tempered α-stable process
Temporal logic
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Summary:This work is motivated by the relaxation data for materials which exhibit a change of the relationship between the fractional power-law exponents when different relaxation peaks in their dielectric susceptibility are observed. Within the proposed framework we derive a frequency-domain relaxation function fitting the whole range of the two-power-law dielectric spectroscopy data with independent low- and high-frequency fractional exponents γ and −α, respectively. We show that this effect results from a contribution of different processes. For high frequencies it is determined by random stops and movement of relaxing components, and the low-frequency slope is caused by clustering in their temporal changes. ► Further development in the theory of tempered relaxation. ► Based on the subordination of random processes with finite moments. ► Derived the relaxation function fitting the whole range of two-power-law data. ► Independence of low- and high-frequency fractional exponents in susceptibility.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2011.10.021