Thesis (M.S.)--West Virginia University, 2001. / Title from document title page. Document formatted into pages; contains vii, 47 p. : ill. Includes abstract. Includes bibliographical references (p. 45-47).

This thesis represents the first large-scale, systematic study to use the double trace moment (DTM) technique in order to characterize the universal multifractal nature of aircraft-based measurements of wind velocity and several passive scalar concentrations under a variety of ambient conditions. Power-law scaling behaviour was demonstrated for the examined fields, from the smallest accessible measurement scales up to at least 250 km, right through the "mesoscale gap" postulated by the standard model of atmospheric dynamics. DTM results indicate remarkable stability in the estimates of the multifractality index, $ alpha$, and the codimension of mean singularity, $C sb1$, for wind velocity measured under different conditions of surface type, time of year, and measurement height within the surface boundary layer. Estimates for $ rm CO sb2, H sb2O, and O sb3$ were largely dominated by the wind velocity statistics as expected, but slightly sensitive to measurement height and moderately sensitive to significant changes in the underlying surface. Results showed that all of the fields examined may be classified as "unconditionally hard" multifractals, which is consistent with previously-published results for ground-based wind velocity measurements. It was demonstrated using probability distribution and multifractal analyses that ensemble statistical moments above approximately second-order can be expected to diverge for all examined fields due to the extremely singular nature of the fields at sub-resolution scales, and that the currently-employed quasi-local aircraft based sampling strategy is capable of reliably characterizing the statistical behaviour of the examined fields up to this physically-imposed limit. (Abstract shortened by UMI.)

Submitted by Suelen Reis (suziy.ellen@gmail.com) on 2013-05-08T16:09:26Z No. of bitstreams: 1 Maria Caroline_dissertacao.pdf: 3000863 bytes, checksum: 39550ba0de49ddaa7a9d9df1eda48983 (MD5) / Rejected by Alda Lima da Silva(sivalda@ufba.br), reason: Documento de Física on 2013-05-08T18:28:33Z (GMT) / Submitted by Suelen Reis (suziy.ellen@gmail.com) on 2013-05-09T16:49:27Z No. of bitstreams: 1 Maria Caroline_dissertacao.pdf: 3000863 bytes, checksum: 39550ba0de49ddaa7a9d9df1eda48983 (MD5) / Approved for entry into archive by Rodrigo Meirelles(rodrigomei@ufba.br) on 2013-05-09T17:10:10Z (GMT) No. of bitstreams: 1 Maria Caroline_dissertacao.pdf: 3000863 bytes, checksum: 39550ba0de49ddaa7a9d9df1eda48983 (MD5) / Made available in DSpace on 2013-05-09T17:10:10Z (GMT). No. of bitstreams: 1 Maria Caroline_dissertacao.pdf: 3000863 bytes, checksum: 39550ba0de49ddaa7a9d9df1eda48983 (MD5) Previous issue date: 2009 / Nos últimos anos, buscando melhorar os diagnósticos em imagens biomédicas, foram desenvolvidos diversos métodos de filtragem das imagens de forma a facilitar a detecção de padrões estruturais associados aos tumores. Por outro lado, a geometria fractal pode ser aplicada para descrever a hierarquia das irregularidades dos fenômenos naturais. As propriedades de um fractal podem ser caracterizadas por um conjunto de expoentes que descrevem um padrão no comportamento das flutuações. Esse conjunto de expoentes representa uma descrição mais completa da medida fractal e é definida como multifractal. Os parâmetros obtidos através da caracterização multifractal contêm informações que podem relacionar as propriedades observadas em diferentesescalas com os diferentes padrões de ocupação das células no tecido. Tais parâmetros oferecem, portanto, um aprofundamento na compreensão da dinâmica de formação de tais padrões. O objetivo geral desta dissertação é avaliar o formalismo multifractal como uma ferramenta útil para a caracterização de padrões espaciais de tumores hepáticos e até onde nos sabemos trata-se de um trabalho original no tema. Nele discutimos um refinamento sobre os métodos de caracterização de tumores embasados na teoria fractal de forma a considerar o espectro de dimensões fractais mediante uma análise multifractal. As imagens de tumores utilizadas foram consideradas como superfícies multi-afins. Foi feito um estudo de casos a partir de três amostras de exames médicos tomográficos com o objetivo de se testar o método na obtenção do grau de heterogeneidade das imagens. O método de cálculo do espectro multifractal foi validado de maneira a avaliar o efeito das diferentes resoluções nas imagens e os diferentes valores dos expoentes de rugosidade para o caso de superfícies monofractais. As características multifractais foram analisadas por duas abordagens. Primeiro em relação às imagens lesadas pelo tumor e segundo, pela comparação desses resultados com as imagens não atingidas pela lesão. Com esta análise pôde-se verificar que nos casos analisados as imagens apresentam um comportamento multifractal, o que indica um padrão de heterogeneidade maior do que se supunham os métodos fractais. / Salvador

No description available.

Les multifractals universels (UM) sont un outil puissant et abondement utilisé d'analyse et de simulation de champs géophysiques, comme la pluie, extrêmement variables sur une large gamme d'échelle. Ils sont basés sur le concept de cascade multiplicative qui repose sur la notion physique d'invariance d'échelle pour explorer le phénomène fondamental qu'est l'intermittence. Dans ce cadre, toute la variabilité du champ est caractérisée à l'aide de simplement trois paramètres qui ont en plus une interprétation physique. Dans cette thèse on utilise ce cadre théorique pour quantifier l'impact de la variabilité à petite échelle de la pluie en hydrologie urbaine. La première étape consiste à analyser la variabilité spatio-temporelle de données radar de précipitation à l'aide d'un modèle multifractal anisotrope simple. Divers évènements pluvieux sont analysés. Un comportement scalant a été observé sur deux gammes d'échelles séparées par une rupture à 16 km qui est discutée. Ces données sont globalement en accord avec un modèle spatio-temporel simple reposant un exposant d'anisotropie entre l'espace et de temps. Les résultats suggèrent une possible universalité des paramètres UM pour les précipitations. Cette thèse aborde également un autre aspect de l'intermittence, particulièrement important pour les longues séries temporelles pluviométriques, que sont les nombreuses mesures nulles de la pluie (c'est-à-dire un pixel où aucune pluie n'est relevée), i.e. les longues périodes sèches. L'ancienne question de la source de cette intermittence, et notamment la nécessité d'un modèle dédié, est revisitée. D'abord les effets d'un seuil sur un champ multifractal sont analysés et ensuite un « toy model » qui introduit des zéros au sein du processus de cascade et conditionnellement aux valeurs du champ est développé. Cela permet d'expliquer la plupart des comportements observés, e.g. les différences entre les statistiques évènementielles et globales. L'impact de la variabilité de la pluie est analysé à travers l'étude de la sensibilité de modèles d'hydrologie/hydraulique urbaine à la donnée de pluie. Deux bassins versants essentiellement urbains (un de 3 400 ha en Seine-Saint-Denis à proximité de Paris, et un de 900 ha à Londres) modélisés avec des modèles opérationnels semi-distribués sont pris comme cas d'études. Par ailleurs le modèle distribué Multi-Hydro (en développement au LEESU) est testé sur une portion de 145 ha du cas d'étude parisien. L'impact de la variabilité à petites échelles non mesurée des précipitations (i.e. se produisant à des échelles plus petites que 1 km en espace et 5 min en temps qui sont disponibles avec les données radar à bande C) est d'abord évalué. Ceci est réalisé par la génération d'un ensemble de pluie réaliste désagrégée en continuant stochastiquement le processus sous-jacent de cascade au-delà de l'échelle d'observation, puis la simulation de l'ensemble correspondant d'hydrographes. Il apparaît que la variabilité à petites échelles de la pluie engendre une variabilité hydrologique qui ne doit pas être négligée. De plus le modèle Multi-Hydro génère une variabilité plus importante et pas seulement au niveau du pic de débit, i.e. même pour les pluies modérées. Ces résultats mettent en lumière la nécessité d'installer des radars en bande X (dont la résolution est hectométrique) en milieu urbain. Dans un deuxième temps les outils multifractals sont employés sur les pluies et les débits simulés qui présentent aussi un comportement scalant. Il apparaît que le réseau d'assainissement transmet simplement la variabilité des précipitations sans l'atténuer, au moins en termes de statistiques multifractals / The Universal Multifractals (UM) are a powerful tool which has been extensively used to analyze and simulate geophysical fields, such as rainfall, that are extremely variable over wide range of scales. It is based on the concept of cascade phenomenology that relies on the physical notion of scale invariance to explore the fundamental phenomenon of intermittency. In this framework the whole variability of a field is characterized with the help of only three parameters that are furthermore physically meaningful. In this PhD thesis we use this theoretical framework to quantify the impacts of small scale rainfall variability in urban hydrology. The first step consists in analysing radar rainfall space-time variability with the help of a simple anisotropic multifractal model. A variety of rainfall events are analyzed. It appears that a scaling behaviour was observed on two distinct ranges of scales separated by a break at roughly 16 km that is discussed. These data sets are in overall agreement with a simple space-time scaling model relying on single anisotropy exponent between space and time. The results hint at a possible universality of the UM parameters for rainfall. This thesis also explores another facet of intermittency, which is particularly important for long time series of precipitation, that of numerous zero rainfall measurements (a pixel or a time step with no recorded rainfall), i. e. long “dry” periods. We revisit the long lasting discussion on the source of this intermittency, e.g. whether it requires a specific modelling. First the effects of a threshold on a universal multifractal field are investigated and second a toy model that introduces some zeros within the cascade process conditioned by the field value is developed. This enables to explain most of the observed behaviour, e.g. the difference between event statistics and overall statistics. The impact of rainfall variability is investigated through the analysis of the sensitivity to the rainfall input of urban hydrologic-hydraulic models. Two predominantly urban catchments (a 3 400 ha one in Seine-Saint-Denis near Paris, and a 900 ha one in London) modelled with the help of operational semi-distributed models are used as case studies. The fully distributed model Multi-Hydro (under development at LEESU) is also tested on a 147 ha portion of the Paris case study. First the impact of unmeasured small scale rainfall variability (i.e. occurring at scales smaller than 1 km in space and 5 min in time which are available with C-band radar data) is evaluated. This is achieved by generating an ensemble of realistic downscaled rainfall fields by continuing the stochastic cascade process below the observation scale and then simulating the corresponding ensemble of hydrographs. It appears that the small scale rainfall variability generates significant hydrological variability that should not be neglected. Furthermore the Multi-Hydro model generates a larger variability not only during the peak flow, but during the whole event, i.e. for moderate rain rates. These findings highlight the need to implement X-band radars (whose resolution is hectometric) in urban areas. In a second part multifractal tools are used on both rainfall and simulated discharges that also exhibit a scaling behaviour. It appears that the rainfall drainage system basically transmits the rainfall variability without damping it, at least in terms of multifractal statistics

The term quantization refers to the process of estimating a given probability by a discrete probability supported on a finite set. The quantization dimension Dr of a probability is related to the asymptotic rate at which the expected distance (raised to the rth power) to the support of the quantized version of the probability goes to zero as the size of the support is allowed to go to infinity. This assumes that the quantized versions are in some sense ``optimal'' in that the expected distances have been minimized. In this dissertation we give a short history of quantization as well as some basic facts. We develop a generalized framework for the quantization dimension which extends the current theory to include a wider range of probability measures. This framework uses the theory of thermodynamic formalism and the multifractal spectrum. It is shown that at least in certain cases the quantization dimension function D(r)=Dr is a transform of the temperature function b(q), which is already known to be the Legendre transform of the multifractal spectrum f(a). Hence, these ideas are all closely related and it would be expected that progress in one area could lead to new results in another. It would also be expected that the results in this dissertation would extend to all probabilities for which a quantization dimension function exists. The cases considered here include probabilities generated by conformal iterated function systems (and include self-similar probabilities) and also probabilities generated by graph directed systems, which further generalize the idea of an iterated function system.

Dans une première partie, après avoir rappelé les principales caractéristiques statistiques des séries financières, en particulier l'existence de corrélations non linéaires à longue portée et d'une asymétrie fortement persistante, nous mettons en évidence la pertinence des processus multifractals pour la modélisation de ces faits stylisés. Les constructions récemment proposées dans la littérature demeurent cependant exclusivement symétriques et nous montrons comment introduire de l'asymétrie dans ces modèles sans sacrifier leurs propriétés d'échelle. Il est alors possible de rendre compte du phénomène de smile de volatilité. Dans une deuxième partie, nous proposons une méthode numérique pour la valorisation et la couverture d'options en marché incomplet. Notre algorithme peut en outre être généralisé sans difficulté pour tenir compte d'autres imperfections du marché comme les frais de transaction.

High frequency turbulent temperature measurements were performed above clipped grass in the lower atmospheric surface layer in conjunction with three-dimensional turbulent velocities. Measurements were also made of turbulent temperature inside a corn canopy and at the canopy top. The 500Hz temperature time series were collected over periods of varying intervals, to a maximum of 24 hours. / The multifractal analysis was performed on several datasets. First scaling properties of the temperature and the velocity fields were examined. Our results suggest that scaling is not observed throughout the entire range but on different regimes. The physically related regimes corresponding to the clipped grass experiment include the inertial subrange, the trend for diurnal peak, and a range between them, all together featuring the existence of the hourly gap. In the canopy experiment, except for the above feature, the effects of the presence of plant objects are also reflected by the presence of two regimes different from those for clipped grass field. / The double trace moment technique was performed on the inertial subrange of the temperature and velocity fields measured over clipped grass to obtain the parameters characterizing the multifractal fields. The variability of the parameters with the atmospheric stability was investigated and no apparent difference between stable and unstable conditions was found. The results reveal that those fields are universal multifractals with the characteristic parameters $ alpha$ near 1.7 and C$ sb1$ ranging from 0.04 to 0.12, implying that the fields can be modeled by a log-Levy process with unbounded singularities. We also found that the critical moment q$ rm sb{s}$ for the multifractal phase transition is close to 4.

Made available in DSpace on 2014-12-17T15:26:37Z (GMT). No. of bitstreams: 1 KalineAFCA.pdf: 1172688 bytes, checksum: f41b32900941fd7aa7f11ba28ed0cf1b (MD5) Previous issue date: 2009-08-28 / In this work we present the principal fractals, their caracteristics, properties abd their classification, comparing them to Euclidean Geometry Elements. We show the importance of the Fractal Geometry in the analysis of several elements of our society. We emphasize the importance of an appropriate definition of dimension to these objects, because the definition we presently know doesn t see a satisfactory one. As an instrument to obtain these dimentions we present the Method to count boxes, of Hausdorff- Besicovich and the Scale Method. We also study the Percolation Process in the square lattice, comparing it to percolation in the multifractal subject Qmf, where we observe som differences between these two process. We analize the histogram grafic of the percolating lattices versus the site occupation probability p, and other numerical simulations. And finaly, we show that we can estimate the fractal dimension of the percolation cluster and that the percolatin in a multifractal suport is in the same universality class as standard percolation. We observe that the area of the blocks of Qmf is variable, pc is a function of p which is related to the anisotropy of Qmf / Neste trabalho, apresentamos uma colet?nea dos principais fractais, observamos suas propriedades, m?todo de constru??o, e a classifica??o entre fractais auto-similares, autoafins e fractais aleat?rios, comparando-os a elementos da Geometria Euclidiana. Evidenciamos a import?ncia da Geometria Fractal na an?lise de v?rios elementos da nossa realidade. Enfatizamos a import?ncia de uma defini??o adequada de dimens?o para estes objetos pois, a tradicional defini??o de dimens?o que conhecemos, n?o reflete satisfatoriamente as propriedades dos fractais. Como instrumentos para a obten??o dessas dimens?es, s?o apresentados os M?todos de Contagem de Caixas, de Hausdorff-Besicovitch e de Escala. Estudamos o Processo de Percola??o na rede quadrada, comparando-o ? percola??o no objeto Multifractal Qmf. Desta compara??o, verifica-se algumas diferen?as entre esses dois porcessos: na rede quadrada o n?mero de coordena??o c ? fixo, em Qmf ? vari?vel; cada c?lula no multifractal Qmf pode afetar de maneira diferente o aglomerado percolante e, o limiar de percola??o pc em Qmf, ? menor do que na rede quadrada. Analisamos o gr?fico do histograma das redes percolantes versus a probabilidade de ocupa??o p e, dependendo do par?metro p e do tamanho da rede L , o histograma pode apresentar estat?stica bimodal. Motramos que se pode estimar a dimens?o fractal do aglomerado percolante. Percebemos que o processo de percola??o num suporte multifractal est? muito pr?ximo ? percola??o na rede quadrada, al?m disso, a ?rea dos blocos de Qmf varia e pc ? uma fun??o de p, o qual est? intimamente ligado a anisotropia do multifractal em estudo

Orientador: Lee Luan Ling / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-10T06:59:04Z (GMT). No. of bitstreams: 1 Perlingeiro_FirmianoRamos_D.pdf: 3410071 bytes, checksum: c0484605d794231363118e1130a5e764 (MD5) Previous issue date: 2006 / Resumo: O provisionamento de QoS garantida é de extrema importância no desenvolvimento das futuras redes. Os recentes avanços tecnológicos em comutação e em transmissão permitem a implementação de redes com velocidades extremamente altas que podem transportar grandes quantidades de tráfego geradas por aplicações mais sensíveis aos requisitos de qualidade de serviço. A próxima geração de redes deverá suportar novas aplicações multimídia em um ambiente global e disponibilizar novos serviços em plataformas flexíveis sem necessidade de alteração da infra-estrutura. Isto requer uma nova arquitetura de redes capaz de oferecer serviços de transporte e de processamento para aplicações de comunicação com fortes requisitos de QoS. No amplo escopo da engenharia de tráfego de redes e do provimento de serviços com qualidade assegurada, esta tese se dedica a propor algumas soluções para os problemas de alocação de recursos de rede, em especial soluções para a estimação da banda efetiva. Para tanto, se utiliza de forma intensiva a caracterização de tráfego, métodos analíticos, heurísticos e de simulação. Os métodos propostos de alocação de banda neste estudo estão fundamentados na Teoria dos Grandes Desvios, aproximação Gaussiana e de caracterização de tráfego. Em termos de caracterização de tráfego, além de vários parâmetros já adotados na literatura é abordada a teoria fractal, incluindo mono e multifractais em seus diferentes aspectos, e ainda, é introduzido um novo parâmetro de tráfego que inclui as características mono e multifractal. Adicionalmente são consideradas as restrições de atraso e jitter, através de adoção de critérios para validação da estimação da banda efetiva, para tráfego em tempo real. A validação da metodologia proposta neste trabalho foi efetivada através de exaustivos testes de simulação com arquivos de tráfego real / Abstract: The assured QoS provisioning has great importance in the development of future networks. Recently, the technological advances in transmission and switching has allowed the implementation of very high speed networks which can transport a huge amount of traffic generated by QoS sensitive applications. The next generation networks must support new multimedia applications in a global environment and deliver new services over flexible platforms without the need of change in the infrastructure. That means that the new network architecture has to be able to transport and process information with strong QoS requirements. Under the wide scope of teletraffic engineering and assured quality of service provisioning, this thesis proposes solutions for some open problems of network resource allocation, especially bandwidth allocation. In order to get reliable solutions, we use intensive traffic characterization, analytical and heuristical methods and simulations. The proposed bandwidth allocation methods in this study are based on the Large Deviation Theory, Gaussian Approximation and traffic characterization. In terms of traffic characterization, in addition to the well known traffic parameters, the fractal theory, including mono and multifractals, are considered. Besides, we introduce a new traffic parameter that takes the mono and multifractal characteristics into account. The proposed bandwidth estimation approaches were tested with real real time traffic under both delay and jitter criteria. All proposed methodologies in this work have been validated by exhaustive simulation tests with real traffic traces / Doutorado / Telecomunicações e Telemática / Doutor em Engenharia Elétrica