KFU. Card publication. The justified data-curve fitting approach: Recognition of the new type of kinetic equations in fractional derivatives from analysis of raw dielectric data

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THE JUSTIFIED DATA-CURVE FITTING APPROACH: RECOGNITION OF THE NEW TYPE OF KINETIC EQUATIONS IN FRACTIONAL DERIVATIVES FROM ANALYSIS OF RAW DIELECTRIC DATA

Form of presentation

Articles in international journals and collections

Year of publication

2003

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Authors, employees of KFU

Nigmatullin Ravil Rashidovich, author

Osokin Sergey Igorevich, author

Other authors

Smith Geoff , author

Bibliographic description in the original language

Nigmatullin R.R, Osokin S.I, Smith G., The justified data-curve fitting approach: Recognition of the new type of kinetic equations in fractional derivatives from analysis of raw dielectric data//Journal of Physics D: Applied Physics. - 2003. - Vol.36, Is.18. - P.2281-2294.

Annotation

Usually, for the description of dielectric spectra one uses the empirical Cole–Davidson (CD) and Havriliak–Negami (HN) equations each of which contains one relaxation time. However, the parameters figuring in the CD and HN equations (or the linear combination of several CD or HN equations) do not have any clear physical meaning. For the description of such asymmetric dielectric spectra, we suggest complex permittivity functions containing two or more characteristic relaxation times. These complex susceptibility functions correspond, in the time-domain, to a new type of kinetic equation, which contains non-integer (fractional) integrals and derivatives. The physical meaning of these operators is discussed in [1]. We suppose that these kinetic equations describe a wide class of dielectric relaxation phenomena taking place in heterogeneous substances. To support and justify this statement, a special recognition procedure has been developed that helps to identify this new kinetic equation from real dielectric data. This recognition procedure can be considered as the justified data-curve fitting (JDCF) approach, in contrast to the conventional 'imposed' data-curve fitting (IDCF) treatment invariably used in modern dielectric spectroscopy. The JDCF approach incorporates the ratio presentation (RP) format and a separation procedure. It is shown how this separation procedure can be helpful in the detection of the many relaxation processes (each process is described by a characteristic relaxation time), which are taking place in the dielectric material under consideration.

Keywords

dielectric spectra, Cole-Davidson equation, Havriliak-Negami equation, asymmetric dielectric spectra, complex permittivity functions, non-integer (fractional) integrals and derivatives, justified data-curve fitting

The name of the journal

Journal of Physics D: Applied Physics

URL

https://iopscience.iop.org/article/10.1088/0022-3727/36/18/018

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=141103&p_lang=2

Resource files

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Full metadata record

Field DC	Value	Language
dc.contributor.author	Nigmatullin Ravil Rashidovich	ru_RU
dc.contributor.author	Osokin Sergey Igorevich	ru_RU
dc.contributor.author	Smith Geoff	ru_RU
dc.date.accessioned	2003-01-01T00:00:00Z	ru_RU
dc.date.available	2003-01-01T00:00:00Z	ru_RU
dc.date.issued	2003	ru_RU
dc.identifier.citation	Nigmatullin R.R, Osokin S.I, Smith G., The justified data-curve fitting approach: Recognition of the new type of kinetic equations in fractional derivatives from analysis of raw dielectric data//Journal of Physics D: Applied Physics. - 2003. - Vol.36, Is.18. - P.2281-2294.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=141103&p_lang=2	ru_RU
dc.description.abstract	Journal of Physics D: Applied Physics	ru_RU
dc.description.abstract	Usually, for the description of dielectric spectra one uses the empirical Cole–Davidson (CD) and Havriliak–Negami (HN) equations each of which contains one relaxation time. However, the parameters figuring in the CD and HN equations (or the linear combination of several CD or HN equations) do not have any clear physical meaning. For the description of such asymmetric dielectric spectra, we suggest complex permittivity functions containing two or more characteristic relaxation times. These complex susceptibility functions correspond, in the time-domain, to a new type of kinetic equation, which contains non-integer (fractional) integrals and derivatives. The physical meaning of these operators is discussed in [1]. We suppose that these kinetic equations describe a wide class of dielectric relaxation phenomena taking place in heterogeneous substances. To support and justify this statement, a special recognition procedure has been developed that helps to identify this new kinetic equation from real dielectric data. This recognition procedure can be considered as the justified data-curve fitting (JDCF) approach, in contrast to the conventional 'imposed' data-curve fitting (IDCF) treatment invariably used in modern dielectric spectroscopy. The JDCF approach incorporates the ratio presentation (RP) format and a separation procedure. It is shown how this separation procedure can be helpful in the detection of the many relaxation processes (each process is described by a characteristic relaxation time), which are taking place in the dielectric material under consideration.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	dielectric spectra	ru_RU
dc.subject	Cole-Davidson equation	ru_RU
dc.subject	Havriliak-Negami equation	ru_RU
dc.subject	asymmetric dielectric spectra	ru_RU
dc.subject	complex permittivity functions	ru_RU
dc.subject	non-integer (fractional) integrals and derivatives	ru_RU
dc.subject	justified data-curve fitting	ru_RU
dc.title	The justified data-curve fitting approach: Recognition of the new type of kinetic equations in fractional derivatives from analysis of raw dielectric data	ru_RU
dc.type	Articles in international journals and collections	ru_RU