КФУ. Карточка публикации. Signal processing and recognition of true kinetic equations containing non-integer derivatives from raw dielectric data

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ФЕДЕРАЛЬНЫЙ УНИВЕРСИТЕТ

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

Форма представления

Статьи в зарубежных журналах и сборниках

Год публикации

2003

Язык

английский

Авторы, сотрудники КФУ

Нигматуллин Равиль Рашидович, автор

Осокин Сергей Игоревич, автор

Библиографическое описание на языке оригинала

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.

Аннотация

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.

Ключевые слова

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

Название журнала

Signal Processing

URL

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

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https://repository.kpfu.ru/?p_id=141102

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Полная запись метаданных

Поле DC	Значение	Язык
dc.contributor.author	Нигматуллин Равиль Рашидович	ru_RU
dc.contributor.author	Осокин Сергей Игоревич	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/?p_id=141102	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	Статьи в зарубежных журналах и сборниках	ru_RU