KFU. Card publication. Signal processing and recognition of true kinetic equations containing non-integer derivatives from raw dielectric data

KAZAN
FEDERAL UNIVERSITY

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SIGNAL PROCESSING AND RECOGNITION OF TRUE KINETIC EQUATIONS CONTAINING NON-INTEGER DERIVATIVES FROM 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

Bibliographic description in the original language

Nigmatullin R.R, Osokin S.I., Signal processing and recognition of true kinetic equations containing non-integer derivatives from raw dielectric data//Signal Processing. - 2003. - Vol.83, Is.11. - P.2433-2453.

Annotation

Signal processing in dielectric spectroscopy implies that it is necessary to find a 'true' fitting function (having a certain physical meaning), which describes well the complex permittivity and impedance data. In dielectric spectroscopy for description of complex permittivity/impedance data researches usually use the empirical Cole–Davidson (CD) and Havriliak–Negami (HN) equations that contains one relaxation time. But the parameters figuring in CD and HN equations do not have clear physical meaning as well as fitting parameters entering into linear combination of several CD or HN equations. For description of dielectric (especially asymmetric) spectra we suggest the complex permittivity functions containing two or more characteristic relaxation times. These complex susceptibility functions correspond in time domain to new type of kinetic equation containing non-integer (fractional) integrals and derivatives. 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 the special recognition procedure has been developed that helps to identify this new kinetic equation from raw dielectric data. It incorporates the ratio presentation (or RP) format and separation procedure. Separation procedure was turned out to be helpful in detection of number of relaxation processes (each process is described by a characteristic relaxation time) taking place in the dielectric material under consideration. We suppose that this procedure can be applicable also for identification of fractal noises.

Keywords

dielectric spectroscopy, ratio presentation, kinetic equations, fractional integrals, fractional derivatives

The name of the journal

Signal Processing

URL

https://doi.org/10.1016/S0165-1684(03)00195-6

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

https://repository.kpfu.ru/eng/?p_id=141102&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.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., Signal processing and recognition of true kinetic equations containing non-integer derivatives from raw dielectric data//Signal Processing. - 2003. - Vol.83, Is.11. - P.2433-2453.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=141102&p_lang=2	ru_RU
dc.description.abstract	Signal Processing	ru_RU
dc.description.abstract	Signal processing in dielectric spectroscopy implies that it is necessary to find a 'true' fitting function (having a certain physical meaning), which describes well the complex permittivity and impedance data. In dielectric spectroscopy for description of complex permittivity/impedance data researches usually use the empirical Cole–Davidson (CD) and Havriliak–Negami (HN) equations that contains one relaxation time. But the parameters figuring in CD and HN equations do not have clear physical meaning as well as fitting parameters entering into linear combination of several CD or HN equations. For description of dielectric (especially asymmetric) spectra we suggest the complex permittivity functions containing two or more characteristic relaxation times. These complex susceptibility functions correspond in time domain to new type of kinetic equation containing non-integer (fractional) integrals and derivatives. 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 the special recognition procedure has been developed that helps to identify this new kinetic equation from raw dielectric data. It incorporates the ratio presentation (or RP) format and separation procedure. Separation procedure was turned out to be helpful in detection of number of relaxation processes (each process is described by a characteristic relaxation time) taking place in the dielectric material under consideration. We suppose that this procedure can be applicable also for identification of fractal noises.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	dielectric spectroscopy	ru_RU
dc.subject	ratio presentation	ru_RU
dc.subject	kinetic equations	ru_RU
dc.subject	fractional integrals	ru_RU
dc.subject	fractional derivatives	ru_RU
dc.title	Signal processing and recognition of true kinetic equations containing non-integer derivatives from raw dielectric data	ru_RU
dc.type	Articles in international journals and collections	ru_RU