@MastersThesis{Zeferino:2017:GeSéTe,
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/ibi/8JMKD3MGP3W34P/3NB54DL",
targetfile = "publicacao.pdf",
urlaccessdate = "05 maio 2024"
}