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@MastersThesis{Zeferino:2017:GeSÚTe,
               author = "Zeferino, Paulo Giovani de Faria",
                title = "3DBMO: um gerador de s{\'e}ries temporais can{\^o}nicas para 
                         estudar a depend{\^e}ncia dimensional do espectro de 
                         pot{\^e}ncias em sistemas f{\'{\i}}sicos complexos",
               school = "Instituto Nacional de Pesquisas Espaciais (INPE)",
                 year = "2017",
              address = "S{\~a}o Jos{\'e} dos Campos",
                month = "2017-02-21",
             keywords = "an{\'a}lise de s{\'e}ries temporais, an{\'a}lise espectral, 
                         modelagem tridimensional, sistema de osciladores acoplados, time 
                         series analysis, spectral analysis, three-dimensional modelling, 
                         coupled oscillator system.",
             abstract = "O estudo espectral das oscila{\c{c}}{\~o}es de plasma 3D em 
                         sistemas reais, tais como processos n{\~a}o-lineares no plasma 
                         solar, magnetosfera e ionosfera, {\'e} geralmente realizado a 
                         partir da an{\'a}lise PSD (Power Spectral Density) de dados 
                         unidimensionais na forma de s{\'e}ries temporais. Os altos 
                         desvios no valor do PSD encontradas por exemplo no estudo das 
                         bolhas de plasmas, comprometem a caracteriza{\c{c}}{\~a}o 
                         precisa de processos f{\'{\i}}sicos subjacentes (ex. 
                         turbul{\^e}ncia). Tais desvios podem ser causados pela 
                         restri{\c{c}}{\~a}o dimensional imposta pela an{\'a}lise 
                         unidimensional de processos que ocorrem, na verdade, em 
                         dimens{\~o}es mais altas (2D e/ou 3D). Nesta 
                         disserta{\c{c}}{\~a}o propomos, portanto, testar a hip{\'o}tese 
                         da exist{\^e}ncia de uma depend{\^e}ncia dimensional dos valores 
                         obtidos atrav{\'e}s da an{\'a}lise espectral calculadas a partir 
                         de series temporais 1D. Aqui chamamos de hip{\'o}tese 
                         depend{\^e}ncia dimens{\~a}o-espectro, um tema ainda n{\~a}o 
                         abordado, de forma expl{\'{\i}}cita, na literatura. Para isso, 
                         estudamos e desenvolvemos um simulador composto por m{\'u}ltiplos 
                         osciladores massa-mola que permite variar as 
                         configura{\c{c}}{\~o}es geom{\'e}tricas e dimensionais para 
                         an{\'a}lise espectral das s{\'e}ries temporais da 
                         posi{\c{c}}{\~a}o e velocidade de um {\'u}nico elemento do 
                         sistema. O simulador, denominado de 3DBMO (3D Big Mechanical 
                         Oscillator) foi implementado em Python dentro das 
                         especifica{\c{c}}{\~o}es que permitem o estudo da hip{\'o}tese 
                         depend{\^e}ncia dimens{\~a}o-espectro. As an{\'a}lises 
                         espectrais foram realizadas a partir de tr{\^e}s t{\'e}cnicas 
                         distintas: PSD, DFA (Detrended Fluctuation Analysis) e GWS (Global 
                         Wavelet Spectrum). A s{\'{\i}}ntese dos resultados encontrados, 
                         a partir da aplica{\c{c}}{\~a}o das tr{\^e}s t{\'e}cnicas, 
                         admitem a confirma{\c{c}}{\~a}o da hip{\'o}tese da 
                         depend{\^e}ncia dimens{\~a}o-espectro. ABSTRACT: The spectral 
                         investigation of 3D plasma oscillations in real systems, such as 
                         nonlinear processes in solar plasma, magnetosphere and ionosphere, 
                         is usually performed from the PSD (Power Spectral Density) 
                         analysis of one-dimensional data in the form of time series. The 
                         high deviations in the value of PSD found for example in the study 
                         of plasma bubbles compromise the precise characterization of 
                         underlying physical processes (e.g. turbulence). Such deviations 
                         can be caused by the dimensional constraint imposed by the 
                         one-dimensional analysis of processes that actually occur in 
                         higher dimensions (2D and/or 3D). In this thesis we propose, 
                         therefore, to test the hypothesis of the existence of a 
                         dimensional dependence of the parameters obtained by applying the 
                         spectral analysis on 1D time series. Here we call 
                         dimension-spectrum dependency hypothesis, a subject not yet 
                         explicitly addressed in the literature. For this, we studied and 
                         developed a simulator composed of multiple mass-spring oscillators 
                         that allows to vary the geometric and dimensional configurations 
                         for spectral analysis of the oscillatory time series (position and 
                         velocity of a single element of the system). The simulator, called 
                         3D Big Mechanical Oscillator (3DBMO) was implemented in Python 
                         within the specifications that allow the study of the 
                         dimension-spectrum dependency hypothesis. The spectral analyses 
                         were carried out from three different techniques: PSD, DFA 
                         (Detrended Fluctuation Analysis) and GWS (Global Wavelet 
                         Spectrum). The synthesis of the results found, from the 
                         application of the three techniques, allows the confirmation of 
                         the hypothesis of the dimension-spectrum dependency.",
            committee = "Vijaykumar, Nandamudi Lankalapalli (presidente) and Rosa, Reinaldo 
                         Roberto (orientador) and Dantas, Murilo da Silva (orientador) and 
                         Domingues, Margarete Oliveira and Luz, Eduardo F{\'a}vero Pacheco 
                         da",
         englishtitle = "3DBMO: a time series canonical generator to study the PSD 
                         dimensional dependence in complex physical systems",
             language = "pt",
                pages = "143",
                  ibi = "8JMKD3MGP3W34P/3NB54DL",
                  url = "http://urlib.net/rep/8JMKD3MGP3W34P/3NB54DL",
           targetfile = "publicacao.pdf",
        urlaccessdate = "28 nov. 2020"
}


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