Fractal traffic models capture uniquely statistical scaling characteristics and the burstiness of the real network traffic. The impact of such traffic models on existing networks has been studied extensively in the related literature and the relevance of such analysis to dimension the necessary resources and evaluate correctly the performance of these systems using computational simulation is well-known. On the other hand, the project of network algorithms already taking into account these models possesses several open issues due to the constant evolving network technologies. The design of high-speed networks considering fractal traffic models is the objective of this work and in order to illustrate the extension of the universe of possible applications, several different network scenarios were chosen: traffic monitoring applied to an intrusion detection system, traffic regulation to maintain the necessary quality of service in a domain according to some service level agreement, arriving traffic conformation at the entrance of an optical network domain and the planning of the necessary bandwidth for a satellite-based network carrying Internet traffic. In this work, important contributions were obtained for the previous enumerated scenarios: statistical process controls to monitor fractal sequences were developed; the leaky bucket, a traditional traffic regulator, was extended to be able to deal with fractal traffic; approaches to plan burst assembly algorithms, a class of traffic shaping mechanisms of optical burst switching networks, were introduced for the case when the incoming traffic is fractal and an estimative of the necessary bandwidth of a satellite-based demand-assignment multiple access system receiving fractal traffic at its entrance was obtained. All the presented results were theoretically and numerically studied. The results show the superior performance of the proposed solutions compared with existent techniques when the local traffic is fractal.

Horizontal scanning instruments, such as, atomic force microscopes and scanning laser microscopes, acquire three-dimensional topographic maps of surfaces, at scales ranging from tenths of nanometers to hundreds of millimeters, by measuring elevations along a series of traces scanning a region of the surface. Random and systematic errors may influence parameters calculated from these topographic maps. This work investigates anisotropic artifacts in atomic force microscope and a scanning laser microscope measurements by looking at difference between parameters calculated in the tracing and scanning directions. It is found that horizontal scanning profiling instruments systematically introduce anisotropic measurement artifacts when measuring both isotropic and anisotropic surfaces.

Made available in DSpace on 2011-03-23T21:19:37Z (GMT). No. of bitstreams: 0 / Item created via OAI harvest from source: http://www.bdtd.ufpa.br/tde_oai/oai2.php on 2011-03-23T21:19:37Z (GMT). Item's OAI Record identifier: oai:bdtd.ufpa.br:267 / A Geometria Fractal é um ramo novo da Matemática que vem sendo estudado desde sua descoberta nos anos sessenta por Benoit Mandelbrot. Por se tratar de uma geometria essencialmente intuitiva, muito se tem comentado a respeito da possibilidade de sua introdução ainda no Ensino Fundamental e Médio de nossas escolas. Assim, um grande número de atividades envolvendo Geometria Fractal foram e ainda estão sendo desenvolvidas com o intuito de tornar o conteúdo da Matemática curricular mais significativo ao aluno. Entretanto, muitas carecem de um estudo mais aprofundado no que tange ao seu verdadeiro grau de eficácia. Para tentar vislumbrar até que ponto estas atividades podem se caracterizar como um recurso didático válido, elaboramos e ministramos um curso sobre Geometria Fractal para onze alunos do 3 ano do Ensino Médio de uma escola pública estadual na cidade de Santarém-Pa. O curso consistia de uma parte teórica sobre o assunto e algumas atividades selecionadas de tal forma que estas pudessem abranger alguns tópicos da Matemática curricular já visto por eles em suas trajetórias escolares. Aplicamos antes do curso um pré-teste e no final um pós-teste para avaliar a compreensão dos assuntos abordados. Os resultados obtidos mostram uma evolução tanto quantitativa, quanto qualitativa na (re)apropriação dos conceitos matemáticos trabalhados durante o curso. O estudo ainda sugere que a Geometria Fractal pôde proporcionar aos alunos uma relação mais forte entre os saberes do cotidiano e o escolar, além de ter proporcionado uma visão dinâmica da Matemática como uma ciência que avança, e não como um corpo de conhecimentos prontos e acabados.

Orientador: André Ricardo Oliveira da Fonseca / Dissertação (mestrado) - Universidade Federal do ABC. Programa de Mestrado Profissional em Matemática em Rede Nacional - PROFMAT, 2013

L’évolution des structures poreuses du graphite et de la vermiculite expansés a été étudiée insitu sous pression uniaxiale. Les propriétés d'un matériau résultant des propriétés intrinsèques à lamatrice et de celles dues à la porosité, les études faites dans ce travail ont porté sur deux échellesdifférentes. Les évolutions structurales de la structure cristalline du graphite et de la vermiculite ontd'abord été étudiées à haute pression en cellule à enclumes de diamant. Cette partie du travail a permisd'établir les équations d'état de la vermiculite et de contribuer, de manière significative, à lacaractérisation de la phase haute pression du graphite: une nouvelle phase, le Carbone Z, a étéproposée après l’analyse des données de la spectroscopie Raman couplée aux simulations. Desdéveloppements techniques ont été particulièrement réalisés pour permettre d’étudier in situl'évolution de la porosité sous pression par diffusion aux petits angles sous pression. L’application dumodèle fractale à l’analyse des données a permis de suivre l’évolution de la dimension fractale et de lasurface spécifique apparente. Les échantillons étudiés sont des formes comprimées de graphite et devermiculite expansés dans lesquelles les plans basaux des cristallites ont une orientation préférentielle.Sous pression uniaxiale, la structure poreuse du graphite expansé comprimé évolue à travers uneffondrement irréversible des pores ou un cisaillement de la matrice suivant l'orientation de la pressionappliquée par rapport à l'orientation préférentielle des plans basaux des cristallites. Des expériencescomplémentaires de mesures électriques et de mesures de la porosité par intrusion de mercure ontpermis de confirmer ces modèles proposés. Dans la vermiculite expansée comprimée, les fissuresapparaissent, de manière générale, sous l’effet de la pression uniaxiale. / The porous structure of expanded graphite and expanded vermiculite has been studied insitu under uniaxial stress. The properties of a porous material being related to the matrix and to theporosity, the in situ evolution under of the crystalline structure (of the matrix) under high pressurehave been first investigated using diamond anvil cell. The equation of state of expanded vermiculitehas been established. This first part of this work allowed giving a particular insight to the study of theunsolved high pressure phase of graphite. Combining Raman scattering data and calculations, a newstructure, called Z-Carbon, has been proposed. Thanks to the specific technical developments of thiswork, the porosities of expanded graphite and expanded vermiculite based systems have been studiedin situ under uniaxial stress. The used of fractal model in data analysis allowed following the evolutionof the fractal dimension and of the apparent specific surface The studied samples were made ofcompressed forms of expanded graphite and expanded vermiculite in which the basal plane of thecrystallites have a preferential orientation. The uniaxial stress was taken perpendicular and parallel tothis preferential direction. The porous structure of the expanded graphite sample was found to undergoan irreversible collapse of the pores or a cracks and creation and propagation. Additional electrical andporosity measurements supported the proposed models. In the expanded vermiculite based systems,the crack apparition was observed under uniaxial stress.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / In the last years, the fractal geometry has become widely studied. Its application in several areas increased substantially, particularly in materials engineering and science, aiming the analysis of failures and the study of the mechanical properties of materials. Some studies have shown the relationship between the fracture surfaces and their mechanical properties using the fractal geometry and its properties of fractal dimension and selfsimilarity. In this research, the fracture surface of duplex stainless steel, which was obtained by the Charpy impact test, was studied applying the fractal geometry. Considering the 475ÂC embrittlement, the steel was submitted to thermal aging to obtain the fracture surfaces, whose images were captured by the scanning electron microscope (SEM). In the fractal analysis, a study was made applying the island method and profile analysis through the digitalization of the images and the application of image analyzing software. Emphasis was given on the calculation of the fractal dimension (FD) of the surface, on the energy absorbed during the impact test, on the involved fracture mechanisms and as well on the relationship between FD and thermal aging. In order to better understanding the subject, it was done the review about fracture mechanics, of duplex stainless steel and of fractal geometry. Finishing the research, the obtained fracture surface, the absorbed energy and the obtained values of FD were analyzed. The obtained results demonstrated a relationship between the fractal dimension, the size of the dimples in fracture surfaces and the impact energy to obtain them. / A geometria dos fractais nos Ãltimos anos tem se tornado bastante difundida no meio cientÃfico. O seu emprego em diversas Ãreas aumentou substancialmente, em particular na engenharia e ciÃncia dos materiais, com o objetivo de analisar falhas e estudar as propriedades mecÃnicas dos materiais. Alguns estudos tÃm mostrado a relaÃÃo entre as propriedades mecÃnicas de superfÃcies de fratura com a geometria dos fractais e suas propriedades de dimensÃo fractal e auto-similaridade. Nesta pesquisa, foi estudada, com base na geometria dos fractais, a superfÃcie de fratura do aÃo inoxidÃvel duplex obtida atravÃs do ensaio de impacto Charpy. Considerando a fragilizaÃÃo a 475C, o aÃo foi submetido ao tratamento tÃrmico de envelhecimento para a obtenÃÃo das superfÃcies de fraturas cujas imagens foram captadas no microscÃpio eletrÃnico de varredura (MEV). Na anÃlise fractal foi feito um estudo aplicando os mÃtodos das ilhas e anÃlise de perfil atravÃs da digitalizaÃÃo das imagens e aplicaÃÃo de softwares de anÃlise de imagem. Foi dada Ãnfase na anÃlise do cÃlculo da dimensÃo fractal (Df) da superfÃcie, na energia absorvida no ensaio de impacto, nos mecanismos de fratura envolvidos, bem como na relaÃÃo entre Df e o tratamento tÃrmico de envelhecimento. Para o melhor entendimento do trabalho foi feita uma revisÃo bibliogrÃfica sobre a mecÃnica da fratura, o aÃo inoxidÃvel duplex e a geometria dos fractais. Para finalizar a pesquisa, foi feita a anÃlise da superfÃcie da fratura obtida, da energia absorvia e de valores de Df alcanÃados. Os resultados obtidos demonstraram uma relaÃÃo entre a dimensÃo fractal, o tamanho dos dimples em superfÃcies de fratura e a energia de impacto para a obtenÃÃo das mesmas.

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A city consists of many elements such as humans, buildings, and roads. The complexity of cities is difficult to measure using Euclidean geometry. In this study, we use fractal geometry (scaling analysis) to measure the complexity of urban areas. We observe urban development from different perspectives using the bottom-up approach. In a bottom-up approach, we observe an urban region from a basic to higher level from our daily life perspective to an overall view. Furthermore, an urban environment is not constant, but it is complex; cities with greater complexity are more prosperous. There are many disciplines that analyze changes in the Earth’s surface, such as urban planning, detection of melting ice, and deforestation management. Moreover, these disciplines can take advantage of remote sensing for research. This study not only uses satellite imaging to analyze urban areas but also uses check-in and points of interest (POI) data. It uses straightforward means to observe an urban environment using the bottom-up approach and measure its complexity using fractal geometry.   Web 2.0, which has many volunteers who share their information on different platforms, was one of the most important tools in this study. We can easily obtain rough data from various platforms such as the Stanford Large Network Dataset Collection (SLNDC), the Earth Observation Group (EOG), and CloudMade. The check-in data in this thesis were downloaded from SLNDC, the POI data were obtained from CloudMade, and the nighttime lights imaging data were collected from EOG. In this study, we used these three types of data to derive natural cities representing city regions using a bottom-up approach. Natural cities were derived from open geographic data without human manipulation. After refining data, we used rough data to derive natural cities. This study used a triangulated irregular network to derive natural cities from check-in and POI data.   In this study, we focus on the four largest US natural cities regions: Chicago, New York, San Francisco, and Los Angeles. The result is that the New York City region is the most complex area in the United States. Box-counting fractal dimension, lacunarity, and ht-index (head/tail breaks index) can be used to explain this. Box-counting fractal dimension is used to represent the New York City region as the most prosperous of the four city regions. Lacunarity indicates the New York City region as the most compact area in the United States. Ht-index shows the New York City region having the highest hierarchy of the four city regions. This conforms to central place theory: higher-level cities have better service than lower-level cities. In addition, ht-index cannot represent hierarchy clearly when data distribution does not fit a long-tail distribution exactly. However, the ht-index is the only method that can analyze the complexity of natural cities without using images.

La plupart des séries d'observations hydrologiques possèdent des caractéristiques peu communes (grande variabilité sur une large gamme d'échelles spatiales et temporelles, périodicité, corrélation temporelle à faible décroissance), difficiles à mesurer (séries tronquées et intégrées sur des pas de temps qui ne respectent pas la nature du phénomène) et compliquées à intégrer dans un modèle stochastique classique (ARMA, Markov). Le modélisateur doit aussi faire face aux problèmes liés à l'échelle : en hydrologie (et en météorologie) où les données sont issues de pas de temps très divers, il est particulièrement intéressant de disposer de modèles à la fois capable d'intégrer des données à pas de temps différents et de fournir des résultats à un pas de temps différent de celui des entrées (désagrégation ou agrégation de séries temporelles).Ce travail de thèse explore les possibilités d'application d'un nouveau type de modèle, les modèles multifractals, qui traduisent le plus simplement possible des propriétés d'invariance de certains paramètres (invariance spatiale, temporelle ou spatio-temporelle). En particulier, dans les modèles de cascades multifractales de générateur algébrique, c'est le coefficient de décroissance algébrique qui est un invariant d'échelle. Des résultats issus de la théorie probabiliste des valeurs extrêmes sont dès lors très utiles pour estimer ce paramètre. L'élaboration d'un outil statistique capable de détecter un comportement algébrique et d'estimer le paramètre de décroissance algébrique constitue une étape préalable au développement de cette thèse. Il est aussi montré dans ce travail, que la forme de dépendance (longue ou courte) des modèles en cascade multifractale diffère selon le générateur de la cascade.<br />L'étude exploite une base de données de 232 séries annuelles de divers sites, de nombreuses séries de pluie à divers pas de temps (mois, jour, heure, minute) ainsi que quelques séries de débits. Elle conduit aux résultats suivants :<br />- Les lois de type algébrique sont adaptées à la modélisation des grandes périodes de retour des séries de pluie étudiées.<br />- Sur ces mêmes séries, le coefficient de décroissance algébrique est un paramètre invariant d'échelle (sur des gammes d'échelles supérieures à l'heure).<br />- L'estimation de ce coefficient en divers sites à travers le monde est très peu variable.<br />- La propriété de longue dépendance est décelable au sein de certaines séries de débits, notamment des séries de rivières sur craie.<br />Ces résultats incitent donc à l'emploi de cascades multifractales pour la modélisation des séries de pluie, bien qu'un travail concernant la détection et l'estimation de longue dépendance reste à accomplir pour que le choix du générateur respecte la forme de dépendance de la série.

Nous étudions des champs aléatoires pouvant modéliser certains milieux poreux. Nous nous intéressons à leurs statistiques au second ordre et en particulier à leur autosimilarité. Sous des hypothèses de stationnarité, une mesure spectrale caractérise le champ. L'homogénéité asymptotique directionnelle de la mesure détermine l'autosimilarité asymptotique du champ; le plus petit coefficient d'homogénéité dans une échelle logarithmique en donne l'ordre. Pour déterminer l'anisotropie on peut considérer une transformée de Radon du champ dont l'ordre d'autosimilarité dépend de la direction. Ces résultats au second ordre sont adaptés à des modèles gaussiens, l'ordre d'autosimilarité s'estimant par les variations quadratiques. Nous considérons le problème de l'injectivité des transformées de Radon. Enfin, nous étudions un modèle poissonien obtenu par agrégation de petites boules. Les propriétés d'autosimilarité sont analogues au second ordre mais atypiques pour la convergence en loi.