dc.contributor.author |
Khamzin A. |
|
dc.contributor.author |
Nigmatullin R. |
|
dc.contributor.author |
Popov I. |
|
dc.date.accessioned |
2018-09-18T20:09:18Z |
|
dc.date.available |
2018-09-18T20:09:18Z |
|
dc.date.issued |
2013 |
|
dc.identifier.issn |
0378-4371 |
|
dc.identifier.uri |
https://dspace.kpfu.ru/xmlui/handle/net/137057 |
|
dc.description.abstract |
A model of the self-similar process of relaxation is given, and a method of derivation of the kinetic equations for the total polarization based on the ideas of fractional kinetics is suggested. The derived kinetic equations contain integro-differential operators having non-integer order. They lead to the Cole-Cole expression for the complex dielectric permittivity. It is shown rigorously that the power-law exponent α in the Cole-Cole expression coincides with the dimension of the mixed space-temporal fractal ensemble. If the discrete scale invariance for the temporal-space structure of the dielectric medium considered becomes important, then the expression for the complex dielectric permittivity contains log-periodic corrections (oscillations) and, hence, it generalizes the conventional Cole-Cole expression. The corrections obtained in this model suggest another way of interpretation and analysis of dielectric spectra for different complex materials. © 2012 Elsevier B.V. All rights reserved. |
|
dc.relation.ispartofseries |
Physica A: Statistical Mechanics and its Applications |
|
dc.subject |
Cole-Cole expression |
|
dc.subject |
Dielectric permittivity |
|
dc.subject |
Fractals |
|
dc.subject |
Fractional derivation |
|
dc.subject |
Log-periodic oscillations |
|
dc.title |
Log-periodic corrections to the Cole-Cole expression in dielectric relaxation |
|
dc.type |
Article |
|
dc.relation.ispartofseries-issue |
1 |
|
dc.relation.ispartofseries-volume |
392 |
|
dc.collection |
Публикации сотрудников КФУ |
|
dc.relation.startpage |
136 |
|
dc.source.id |
SCOPUS03784371-2013-392-1-SID84867328841 |
|