On the analysis of data emerging in non-linear and complex systemscomparison of two X-Ray prony spectra
Autor(a) principal: | |
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Data de Publicação: | 2015 |
Outros Autores: | , , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.22/7440 |
Resumo: | New arguments proving that successive (repeated) measurements have a memory and actually remember each other are presented. The recognition of this peculiarity can change essentially the existing paradigm associated with conventional observation in behavior of different complex systems and lead towards the application of an intermediate model (IM). This IM can provide a very accurate fit of the measured data in terms of the Prony's decomposition. This decomposition, in turn, contains a small set of the fitting parameters relatively to the number of initial data points and allows comparing the measured data in cases where the “best fit” model based on some specific physical principles is absent. As an example, we consider two X-ray diffractometers (defined in paper as A- (“cheap”) and B- (“expensive”) that are used after their proper calibration for the measuring of the same substance (corundum a-Al2O3). The amplitude-frequency response (AFR) obtained in the frame of the Prony's decomposition can be used for comparison of the spectra recorded from (A) and (B) - X-ray diffractometers (XRDs) for calibration and other practical purposes. We prove also that the Fourier decomposition can be adapted to “ideal” experiment without memory while the Prony's decomposition corresponds to real measurement and can be fitted in the frame of the IM in this case. New statistical parameters describing the properties of experimental equipment (irrespective to their internal “filling”) are found. The suggested approach is rather general and can be used for calibration and comparison of different complex dynamical systems in practical purposes. |
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On the analysis of data emerging in non-linear and complex systemscomparison of two X-Ray prony spectraComplex systemsX-ray diffractometerCorundumFourier and Prony’s decompositionData treatment analysisIdeal experimentIntermediate modelNew arguments proving that successive (repeated) measurements have a memory and actually remember each other are presented. The recognition of this peculiarity can change essentially the existing paradigm associated with conventional observation in behavior of different complex systems and lead towards the application of an intermediate model (IM). This IM can provide a very accurate fit of the measured data in terms of the Prony's decomposition. This decomposition, in turn, contains a small set of the fitting parameters relatively to the number of initial data points and allows comparing the measured data in cases where the “best fit” model based on some specific physical principles is absent. As an example, we consider two X-ray diffractometers (defined in paper as A- (“cheap”) and B- (“expensive”) that are used after their proper calibration for the measuring of the same substance (corundum a-Al2O3). The amplitude-frequency response (AFR) obtained in the frame of the Prony's decomposition can be used for comparison of the spectra recorded from (A) and (B) - X-ray diffractometers (XRDs) for calibration and other practical purposes. We prove also that the Fourier decomposition can be adapted to “ideal” experiment without memory while the Prony's decomposition corresponds to real measurement and can be fitted in the frame of the IM in this case. New statistical parameters describing the properties of experimental equipment (irrespective to their internal “filling”) are found. The suggested approach is rather general and can be used for calibration and comparison of different complex dynamical systems in practical purposes.SC Biblioteca Chimiei SARepositório Científico do Instituto Politécnico do PortoNigmatullin, Raul R.Khramov, A.S.Kiyamov, A.G.Fatkhullin, B. F.Machado, J. A. TenreiroBaleanu, Dumitru2016-01-21T12:13:55Z20152015-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.22/7440enginfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-03-13T12:48:03Zoai:recipp.ipp.pt:10400.22/7440Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:27:56.362303Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
On the analysis of data emerging in non-linear and complex systemscomparison of two X-Ray prony spectra |
title |
On the analysis of data emerging in non-linear and complex systemscomparison of two X-Ray prony spectra |
spellingShingle |
On the analysis of data emerging in non-linear and complex systemscomparison of two X-Ray prony spectra Nigmatullin, Raul R. Complex systems X-ray diffractometer Corundum Fourier and Prony’s decomposition Data treatment analysis Ideal experiment Intermediate model |
title_short |
On the analysis of data emerging in non-linear and complex systemscomparison of two X-Ray prony spectra |
title_full |
On the analysis of data emerging in non-linear and complex systemscomparison of two X-Ray prony spectra |
title_fullStr |
On the analysis of data emerging in non-linear and complex systemscomparison of two X-Ray prony spectra |
title_full_unstemmed |
On the analysis of data emerging in non-linear and complex systemscomparison of two X-Ray prony spectra |
title_sort |
On the analysis of data emerging in non-linear and complex systemscomparison of two X-Ray prony spectra |
author |
Nigmatullin, Raul R. |
author_facet |
Nigmatullin, Raul R. Khramov, A.S. Kiyamov, A.G. Fatkhullin, B. F. Machado, J. A. Tenreiro Baleanu, Dumitru |
author_role |
author |
author2 |
Khramov, A.S. Kiyamov, A.G. Fatkhullin, B. F. Machado, J. A. Tenreiro Baleanu, Dumitru |
author2_role |
author author author author author |
dc.contributor.none.fl_str_mv |
Repositório Científico do Instituto Politécnico do Porto |
dc.contributor.author.fl_str_mv |
Nigmatullin, Raul R. Khramov, A.S. Kiyamov, A.G. Fatkhullin, B. F. Machado, J. A. Tenreiro Baleanu, Dumitru |
dc.subject.por.fl_str_mv |
Complex systems X-ray diffractometer Corundum Fourier and Prony’s decomposition Data treatment analysis Ideal experiment Intermediate model |
topic |
Complex systems X-ray diffractometer Corundum Fourier and Prony’s decomposition Data treatment analysis Ideal experiment Intermediate model |
description |
New arguments proving that successive (repeated) measurements have a memory and actually remember each other are presented. The recognition of this peculiarity can change essentially the existing paradigm associated with conventional observation in behavior of different complex systems and lead towards the application of an intermediate model (IM). This IM can provide a very accurate fit of the measured data in terms of the Prony's decomposition. This decomposition, in turn, contains a small set of the fitting parameters relatively to the number of initial data points and allows comparing the measured data in cases where the “best fit” model based on some specific physical principles is absent. As an example, we consider two X-ray diffractometers (defined in paper as A- (“cheap”) and B- (“expensive”) that are used after their proper calibration for the measuring of the same substance (corundum a-Al2O3). The amplitude-frequency response (AFR) obtained in the frame of the Prony's decomposition can be used for comparison of the spectra recorded from (A) and (B) - X-ray diffractometers (XRDs) for calibration and other practical purposes. We prove also that the Fourier decomposition can be adapted to “ideal” experiment without memory while the Prony's decomposition corresponds to real measurement and can be fitted in the frame of the IM in this case. New statistical parameters describing the properties of experimental equipment (irrespective to their internal “filling”) are found. The suggested approach is rather general and can be used for calibration and comparison of different complex dynamical systems in practical purposes. |
publishDate |
2015 |
dc.date.none.fl_str_mv |
2015 2015-01-01T00:00:00Z 2016-01-21T12:13:55Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.22/7440 |
url |
http://hdl.handle.net/10400.22/7440 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
SC Biblioteca Chimiei SA |
publisher.none.fl_str_mv |
SC Biblioteca Chimiei SA |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799131375418212352 |