Submitted by Angela Maria de Oliveira (amolivei@uepg.br) on 2018-11-22T18:11:23Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Tiago Jacumasso.pdf: 9316680 bytes, checksum: 9e1e6195d90b660e6d32c4f13481bf5b (MD5) / Made available in DSpace on 2018-11-22T18:11:23Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Tiago Jacumasso.pdf: 9316680 bytes, checksum: 9e1e6195d90b660e6d32c4f13481bf5b (MD5) Previous issue date: 2018-08-31 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / A mecânica da fratura foi desenvolvida, utilizando-se uma descrição geométrica euclidiana que pressupõem uma trinca lisa sem irregularidades. Por esta razão, a modelagem matemática de uma trinca rugosa, usando a geometria fractal, tem sido a preocupação de vários autores nas últimas décadas. O intuito destes pesquisadores é descrever o fenômeno da fratura de forma mais autentica e precisa. Uma das formas de se avaliar as propriedades mecânicas de um material fraturado é usando o conceito de integral-J. Este conceito aplicado ao fenômeno da fratura define uma curva de resistência ao crescimento de trinca chamado de curva J-R. Sendo assim, vários modelos fractais de curva J-R têm sido propostos. Um dos modelos que vem ganhando destaque na literatura científica foi proposto por ALVES (2010, 2011). Por esta razão investigou-se, neste trabalho, a aplicação desse modelo no estudo da fratura do ferro fundido nodular e ferro fundido nodular austemperado (ADI). O objetivo foi avaliar os efeitos dos tratamentos térmicos de austêmpera na microestrutura e nas propriedades mecânicas de uma liga de ferro fundido nodular. Para tanto foi empregado duas rotas de tratamentos térmicos: austêmpera convencional, consistindo de austenitização a 900ºC por 60min, seguida de austêmpera até 250ºC e à 300ºC, com permanência por 60min e 120min para cada temperatura, totalizando quatro condições, com resfriamento ao ar. As amostras tratadas termicamente foram caracterizadas com auxílio de microscopia óptica, microscopia eletrônica de varredura (FEG) e difração de raios X (DRX), com objetivo de determinar suas fases e microconstituintes. O efeito das condições de tratamento nas propriedades mecânicas foi verificado por ensaios de dureza Vickers e de impacto instrumentado Charpy. Por meio de ensaios de impacto instrumentado e solicitação mecânica de tração e com o auxílio de microscopia eletrônica por emissão de campo (FEG) foi possível estudar o crescimento de trincas rugosas na fratura do ferro fundido nodular austemperado, comparando os resultados entre as quatro condições de tratamento térmico de austêmpera. Deste modo, foi possível fornecer dados experimentais para comprovar a validade da equação da curva J-R na presença de uma trinca rugosa proposta por ALVES (2010, 2011) com base na geometria fractal e na mecânica da fratura. Os resultados obtidos permitiram comparar e discutir o efeito das rotas de tratamento térmico, no sentido de desenvolver as propriedades mecânicas do ferro fundido nodular para aplicações diversas. As curvas D J ajustadas pelo modelo fractal mostraram-se em boa concordância com aquelas obtidas pelo método descrito na ASTM E1820-17a (2017). O ADI tratado a 300ºC por 60 minutos foi o material que apresentou as melhores condições de resistência mecânica a tração e ao impacto, superando o material bruto de fundição na tenacidade a fratura, calculada pelos parâmetros fractais da curva. Este ferro fundido nodular austemperado é comparado ao da classe de alta resistência de ADI. / The mechanics of the fracture were developed using a geometric Euclidean description that assumes a smooth crack without irregularities. For this reason, the mathematical modeling of a rough crack, using fractal geometry, has been the concern of several authors in the last decades. The aim of these researchers is to describe the fracture phenomenon more authentically and accurately. One of the ways to evaluate the mechanical properties of a fractured material is by using the concept of integral-J. This concept applied to the fracture phenomenon defines a crack growth resistance curve called the J-R curve. Thus, several fractal J-R curve models have been proposed. One of the models that have gained prominence in the scientific literature was proposed by ALVES (2010, 2011). For this reason we investigated the application of this model in the study of nodular cast iron and austempered nodular cast iron (ADI). The objective was to evaluate the effects of thermal treatments of austempering in the microstructure and mechanical properties of a ductile cast iron alloy. Two routes of thermal treatments were used: conventional austenitic, consisting of austenitization at 900ºC for 60min, followed by tempering up to 250ºC and at 300ºC, with permanence for 60min and 120min for each temperature, totaling four conditions, with air cooling. The thermally treated samples were characterized by optical microscopy, scanning electron microscopy (FEG) and X - ray diffraction (XRD), in order to determine their phases and microconstituents. The effect of the treatment conditions on the mechanical properties was verified by tests of Vickers hardness and instrumented impact Charpy. By means of instrumented impact and mechanical tensile stress tests and with the aid of field emission electron microscopy (FEG), it was possible to study the growth of rough cracks in austempered nodular cast iron fracture, comparing the results between the four conditions of heat treatment. Thus, it was possible to provide experimental data to prove the validity of the J-R curve equation in the presence of a rough crack proposed by ALVES (2010, 2011) based on fractal geometry and fracture mechanics. The results obtained allowed to compare and discuss the effect of heat treatment routes in order to develop the mechanical properties of nodular cast iron for different applications. The D J curves fitting by the fractal model show in agreement with the curves obtained by the method described in the ASTM E1820-17a (2017). The ADI treated at 300ºC for 60 minutes was the material that presented the best conditions of tensile and impact mechanical strength, surpassing the crude casting material in the fracture toughness, calculated by the fractal parameters of the curve. This austempered nodular cast iron is compared to that of the ADI high strength class.

O processo de conformação de chapas planas, estampagem, consiste na obtenção de peças conforme o projeto do processo e do produto. Faz-se necessária uma margem de segurança para que as variações de processo e do material possam ser absorvidas e o sucesso seja alcançado no processo de produção do componente. O presente trabalho mostra aspectos de estampabilidade de uma chapa de aço de baixo teor de carbono, o material mais utilizado no processo de estampagem. Estes aspectos são descritos e demonstrados como influenciam no processo de estampagem. No caso prático apresentado, evidencia-se que com a aplicação dos conhecimentos científicos de comportamento mecânico do material obtém-se uma melhoria no desempenho do processo e, conseqüentemente, na redução de custos e no aumento de competitividade. Como objetivo principal, tem o presente trabalho estudar a influência da redução a frio de acabamento do processo de relaminação no coeficiente de encruamento e mostrar como este estudo teve participação na solução e aplicação de uma peça-exemplo. Conseqüentemente há como objetivos secundários o estudo da influencia do tamanho de grão no coeficiente de encruamento, o desenvolvimento da textura cristalográfica antes e após a conformação da peça-exemplo e demonstrar a importância da utilização do método de elementos finitos no processo de conformação por estampagem para determinação dos tipos de conformação predominante no processo. Para realização do trabalho foram utilizados dois aços de baixo teor de carbono com composição química semelhantes porem com processos de fabricação diferenciados. Atenção especial foi dada a redução aplicada na laminação de acabamento de ambos os aços, através do uso de medidores de espessura e redução através de raios-X. Os aços foram caracterizados antes da conformação da peça-exemplo quanto a orientação cristalográfica através de difração de raios-X e EBSD, quanto as propriedades mecânicas através de ensaios mecânicos de tração e quanto a microestrutura e tamanho de grão através de metalografia. Foi realizada uma simulação de estampagem da peça-exemplo através de elementos finitos afim de determinar o tipo de conformação predominante na região mais solicitada da peça-exemplo. A peça exemplo foi conformada na pratica e caracterizada a distribuição das deformações através da medições da rede circulo previamente impressa na superfície da chapa na região mais solicitada conforme previamente determinado através da simulação. A orientação cristalográfica da região mais solicitada também foi caracterizada. Os resultados mostram a influencia de uma pequena variação na redução, 0,73% e 0,34%, aplicada na laminação de acabamento no coeficiente de encruamento. Para confirmação de que a redução aplicada foi a principal influenciadora no resultado o coeficiente de encruamento foi calculado através de equações disponíveis na literatura que correlacionam composição e tamanho de grão com o coeficiente de encruamento. A textura preferencial dos dois aços também foi avaliada através de figuras de função de orientação da distribuição e o comportamento dos dois aços foi relativamente semelhante, onde o aço com melhor desempenho demonstrou um aumento na componente {223} também conhecida como γ'. O estudo através de elementos finitos mostra que região mais solicitada da peça tem conformação predominada por estiramento. Por fim é mostrada a melhor distribuição das deformações na peça-exemplo produzida com aço de maior coeficiente de encruamento. Concluindo o trabalho permitiu a avaliação da influencia da redução aplicada na laminação de acabamento de aços de baixo teor de carbono nas propriedades mecânicas do aço e também o resultado deste comportamento mecânico na peça-exemplo adotada.Também permitiu avaliar a evolução da textura cristalográfica dos dois aços escolhidos antes e após a conformação da peça-exemplo. / The forming process of plain sheets, stamping, consists on the obtainment of parts according to the project of the process and the product. A safety margin becomes necessary so that the process variations and of the material can be absorbed and the success is reached in the process of production of the component. The present paper shows aspects of formability of a steel sheet of low carbon content, the most used material in the stamping process. These aspects are described and demonstrated how they influence the stamping process. In the presented case, it is proven that with the application of the scientific knowledge of mechanical behavior of the material an improvement in the performance of the process is reached and, consequently, the reduction of costs and the increase of competitiveness. As main objective, the present work study the influence of the cold reduction applied on skin pass of the cold rolling process on the strain hardening coefficient and to show how this study had participated on the solution and application of an part. Consequently it has as secondary objective the study of influences of the size of grain in the coefficient of strain hardening, the development of texture before and after forming of the part and to demonstrate the importance of the use of the method of finite elements in the forming process for determination of the predominant types of forming in the stamping process. For accomplishment of this paper two steel of low carbon content had been used with similar chemical composition but with differentiated rolling processes of manufacture. Special attention was given to the reduction applied in the skin pass of both steel, through the use of measurers of thickness and reduction through x-ray. The steel had been characterized before the stamping of the part above crystallographic texture through x-ray diffraction and EBSD, above mechanical properties through mechanical tensile tests and above microstructure and size of grain through metallography. A simulation of stamping process of the part through finite elements was carried out with the objective of determine the type of predominant forming in the most requested region of the part. The part was formed in mechanical presses and characterized the distribution of the deformations through the measurements circle grids, previously printed in the surface of the sheet, in the region most requested as previously determined through the simulation. The crystallographic orientation of the most requested region was also characterized. The results show influence of a small variation in the rolling reduction, 0.73% and 0.34%, applied in the skin pass on the strain hardening coefficient. For confirmation that the pplied skin pass was the main influence in the strain hardening coefficient result, was calculated hrough available equations in literature that correlate composition and grain size with the strain hardening coefficient. The preferential texture of two steel was also evaluated through figures of orientation function distribution and the behavior of two steel was relatively similar, where the steel with better performance demonstrated an increase in the {223} component also known as γ'. The study through finite elements shows that the more requested region of the part has forming predominated for stretching. Finally the best distribution of the deformations in the part produced with steel of higher coefficient of train hardening is shown. Concluding the work allowed the evaluation of influences of the skin pass on the rolling of steel of low carbon content in the mechanical properties of the steel and the result of this mechanical behavior in the adopted part. Also it allowed to evaluate the evolution of the crystallographic texture of two steel chosen before and after.

The subject of this thesis is the development of localization algorithms for target localization in wireless sensor networks using received signal strength (RSS) measurements or Quantized RSS (QRSS) measurements. In chapter 3 of the thesis, target localization using RSS measurements is investigated. Many existing works on RSS localization assumes that the shadowing components are uncorrelated. However, here, shadowing is assumed to be spatially correlated. It can be shown that localization accuracy can be improved with the consideration of correlation between pairs of RSS measurements. By linearizing the corresponding Maximum Likelihood (ML) objective function, a weighted least squares (WLS) algorithm is formulated to obtain the target location. An iterative technique based on Newtons method is utilized to give a solution. Numerical simulations show that the proposed algorithms achieves better performance than existing algorithms with reasonable complexity. In chapter 4, target localization with an unknown path loss model parameter is investigated. Most published work estimates location and these parameters jointly using iterative methods with a good initialization of path loss exponent (PLE). To avoid finding an initialization, a global optimization algorithm, particle swarm optimization (PSO) is employed to optimize the ML objective function. By combining PSO with a consensus algorithm, the centralized estimation problem is extended to a distributed version so that can be implemented in distributed WSN. Although suboptimal, the distributed approach is very suitable for implementation in real sensor networks, as it is scalable, robust against changing of network topology and requires only local communication. Numerical simulations show that the accuracy of centralized PSO can attain the Cramer Rao Lower Bound (CRLB). Also, as expected, there is some degradation in performance of the distributed PSO with respect to the centralized PSO. In chapter 5, a distributed gradient algorithm for RSS based target localization using only quantized data is proposed. The ML of the Quantized RSS is derived and PSO is used to provide an initial estimate for the gradient algorithm. A practical quantization threshold designer is presented for RSS data. To derive a distributed algorithm using only the quantized signal, the local estimate at each node is also quantized. The RSS measurements and the local estimate at each sensor node are quantized in different ways. By using a quantization elimination scheme, a quantized distributed gradient method is proposed. In the distributed algorithm, the quantization noise in the local estimate is gradually eliminated with each iteration. Simulations show that the performance of the centralized algorithm can reach the CRLB. The proposed distributed algorithm using a small number of bits can achieve the performance of the distributed gradient algorithm using unquantized data.

A numerical study of fundamental aspects of turbulent mixing has been performed,with emphasis on the behavior of passive scalars of low molecular diffusivity (high Schmidt number Sc). Direct Numerical Simulation is used to simulate incompressible, stationary and isotropic turbulence carried out at high grid resolution. Data analyses are carried out by separate parallel codes using up to 1024^3 grid points for Taylor-scale Reynolds number (R_lambda) up to 390 and Sc up to 1024.Schmidt number of order 1000 is simulated using a double-precision parallel code in a turbulent flow at a low Reynolds number of R_lambda 8 to reduce computational cost to achievable level. The results on the scalar spectrum at high Schmidt numbers appear to have a k^{-1} scaling range. In the presence of a uniform mean scalar gradient, statistics of scalar gradients are observed to deviate substantially from Kolmogorov's hypothesis of local isotropy, with a skewness factor remaining at order unity as the Reynolds number increases. However, this skewness decreases with Schmidt number suggesting that local isotropy for scalars at high Schmidt number is a better approximation. Intermittency exponents manifested by three types of two-point statistics of energy and scalar dissipation, i.e., the two-point correlator (chi(x)chi(x+r)), the second-order moment of local scalar dissipation (chi_r^2) and the variance of the logarithmic local scalar dissipation sigma^2_{lnchi_r} are discussed. Several basic issues in differential diffusion between two scalars of different molecular diffusivities transported by the same turbule nt flow, the physical process of scalar spectral transfer and subgrid-scale transfer are also briefly addressed.

<p>The theory of Gibbs measures belongs to the borderlandbetween statistical mechanics and probability theory. In thiscontext, the physical phenomenon of phase transitioncorresponds to the mathematical concept of non-uniqueness for acertain type of probability measures.</p><p>The most studied model in statistical mechanics is thecelebrated Ising model. The Potts model is a natural extensionof the Ising model, and the beach model, which appears in adifferent mathematical context, is in certain respectsanalogous to the Ising model. The two main parts of this thesisdeal with the Potts model and the beach model,respectively.</p><p>For the<i>q</i>-state Potts model on an infinite lattice, there are<i>q</i>+1 basic Gibbs measures: one wired-boundary measure foreach state and one free-boundary measure. For infinite trees,we construct "new" invariant Gibbs measures that are not convexcombinations of the basic measures above. To do this, we use anextended version of the random-cluster model together withcoupling techniques. Furthermore, we investigate the rootmagnetization as a function of the inverse temperature.Critical exponents to this function for different parametercombinations are computed.</p><p>The beach model, which was introduced by Burton and Steif,has many features in common with the Ising model. We generalizesome results for the Ising model to the beach model, such asthe connection between phase transition and a certain agreementpercolation event. We go on to study a<i>q</i>-state variant of the beach model. Using randomclustermodel methods again we obtain some results on where in theparameter space this model exhibits phase transition. Finallywe study the beach model on regular infinite trees as well.Critical values are estimated with iterative numerical methods.In different parameter regions we see indications of both firstand second order phase transition.</p><p><b>Keywords and phrases:</b>Potts model, beach model,percolation, randomcluster model, Gibbs measure, coupling,Markov chains on infinite trees, critical exponent.</p>

Matematikundervisningen i svensk skola verkar i stor utsträckning kretsa kring läroboken, och att granska användandet av läroböcker är inget nytt fenomen. Ämnesplanen i matematik för gymnasieskolan framhåller att matematikundervisningen ska ge eleverna förutsättningar att utveckla förmågan att sätta in matematiken i bland annat ett historiskt sammanhang. För detta ska kunna vara möjligt antas kunskaper om matematikens historiska utveckling vara fördelaktiga, kunskaper som kan tillägnas genom historiska inslag i läroböckerna. Detta examensarbete syftar till att genom en jämförande studie med innehållsanalys som analysverktyg ge en bild av vilka historiska aspekter av det matematiska innehållet som förekommer i kurs 1, 3 och 5 för tre olika läromedel i matematik för gymnasieskolan. I undersökningen fokuseras dels inom vilka matematiska områden det förekommer historiska inslag, och dels hur dessa framställs. Studien visar att det i kurs 1 är mest vanligt förekommande med historiska inslag i kapitlen om geometri. Motsvarande i kurs 3 rör kapitel om derivata, och i kurs 5 förekommer det historiska inslag i samtliga kapitel oberoende av läromedelsserie. Med avseende på hur de historiska inslagen framställs visar resultatet på att i stort sett de allra flesta historiska inslagen kan sägas beskriva ursprunget av matematiskt begrepp eller metoder. / Mathematics education in Swedish schools seems to focus or circulate around textbooks, and audits on the use of a textbook is not a new phenomenon. The mathematics curriculum for the Swedish upper secondary school stresses that mathematics education should provide students the opportunity to develop their ability putting mathematics in a historical context. For this to be possible, knowledge of the history of mathematics is considered to be beneficial and this knowledge can be acquired by historical elements in textbooks. This study aims at providing a picture of the historical content that appears in courses 1, 3 and 5 for three different mathematical textbook series in the Swedish upper secondary school through a comparative study using content analysis as ananalysis tool. The study focuses on the following questions: In which chapters can historical elements be found, and how are they presented? The study shows that in course 1, historical elements are most common in the geometry chapters. Correspondingly in course 3, they are most common in the chapters on derivates, and in course 5 there are historical elements in all chapters independent of textbooks series. Furthermore, regarding how the historical elements are presented, the study shows that essentially a vast majority of the historical elements describe the origin of mathematical concepts or methods.

Made available in DSpace on 2015-05-15T11:46:23Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 590579 bytes, checksum: 4c4cd48135a64532856a71b6336c52f4 (MD5) Previous issue date: 2014-07-31 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we studied existence of positive solutions for an elliptic problem with critical Sobolev exponent (-u = up + f(x; u) em u = 0 sobre @ that vanishes on the boundary of a bounded domain of Rn. The nonlinearity f(x; u) has subcritical growth. This is done by showing that the minimax level is below a constant that depends only on the dimension of the domain and the best Sobolev constant. / Nesta dissertação procuramos abordar a existência de soluções positivas para um problema elíptico com expoente crítico de Sobolev (-u = up + f(x; u) em u = 0 sobre @ onde é um domínio limitado do Rn. A não-linearidade de f(x; u) possui crescimento subcrítico. Para isso mostraremos que o nível minimax fica abaixo de uma constante que depende apenas da dimensão do domínio e da melhor constante de Sobolev.

Submitted by (ana.araujo@ufrpe.br) on 2016-05-25T15:27:20Z No. of bitstreams: 1 Carlos Andre Batista.pdf: 1088768 bytes, checksum: 7819bd86b2d74fe0f2599519c5bdf4cb (MD5) / Made available in DSpace on 2016-05-25T15:27:20Z (GMT). No. of bitstreams: 1 Carlos Andre Batista.pdf: 1088768 bytes, checksum: 7819bd86b2d74fe0f2599519c5bdf4cb (MD5) Previous issue date: 2006-02-16 / The main objective of the present work was to apply recently developed in methods in physics-statistics to the time series, especifically in this work, to intervals of heart beats obtained from blood pressure signs (BP) of the sloth (Bradypus variegatus), with the purpose of identifying differences in fractality terms in the system of autonomous control related to the different situations lived by the animal along 48 hours (light-dark cycles). One tried to investigate if environmental changings may produce tendencies or have influence on the autonomous control system, using analysis multifractal methods, like Multifractal Detrended Fluctuations Analysis (MF-DFA). Due to the conditions in which the sloth BP data were obtained, that is, obtained to intervals of 15 minutes, it was necessary the adaptation of data for application of the technique MF-DFA. For validation of the adaptations, tests with humans' electrocardiograms gave us support to work with the interbeats data of sloth. The obtained results showed asignificant increasement of multifractalidade in the intervals of heartbeats of the sloth in the light cycle in relation to the dark cycle. / O principal objetivo do presente trabalho foi aplicar métodos recentemente desenvolvidos em física-estatística às séries temporais, em especial neste trabalho, a intervalos de batimentos cardíacos obtidos a partir de sinais de pressão arterial (PA) do bicho preguiça (Bradypus variegatus), com a finalidade de identificar diferenças em termos de fractalidade no sistema de controle autonômico relacionadas às diferentes situações vividas pelo animal ao longo de 48 horas (períodos claro e escuro). Procurou-se investigar se alterações ambientais produzem tendências ou têm influências sobre o sistema de controle autonômico, utilizando métodos de análise multifractal, como Multifractal Detrended Fluctuations Analysis (MF-DFA). Devido às condições nas quais os dados de PA de preguiça foram obtidos, isto é, obtidos a intervalos de 15 minutos, fez-se necessário a adaptação dos dados para aplicação da técnica MF-DFA. Para validação das adaptações, testes com eletrocardiogramas de humanos nos deram suporte para trabalhar com os dados de intervalos de batimentos cardíacos do bicho-preguiça. Os resultados obtidos mostraram que existe um aumento significativo demultifractalidade nos intervalos de batimentos cardíacos do bicho preguiça no período claro em relação ao escuro.

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2016-07-22T13:22:56Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Tese-Ricardo-Castillo.pdf: 814247 bytes, checksum: 0f3a9a10694a3324cae6464d5e29a2f6 (MD5) / Made available in DSpace on 2016-07-22T13:22:56Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Tese-Ricardo-Castillo.pdf: 814247 bytes, checksum: 0f3a9a10694a3324cae6464d5e29a2f6 (MD5) Previous issue date: 2016-02-17 / Estudamos condições de existência e não existência de soluções globais para um sistema acoplado de equações parabólicas não lineares e para um problema parabólico com expoente variável. Em ambos os casos, consideramos um domínio arbitrário de RN com fronteira regular e com condições de Dirichlet na fronteira. Como consequência destes resultados é possível determinar o coe ciente de Fujita destes problemas. / We study conditions for existence and non existence of global solutions for a nonlinear coupled parabolic systems and for parabolic problem with variable exponent. In both cases, we consider an arbitrary domain of RN with smooth boundary and Dirichlet condition on the boundary. As consequence of these results is possible to determinate the Fujita's exponent of ones.

Submitted by Geyciane Santos (geyciane_thamires@hotmail.com) on 2015-08-06T15:11:15Z No. of bitstreams: 1 Dissertação - Celso Ricardo Caldeira Rêgo.pdf: 2481181 bytes, checksum: f162815b3f4a2d2e2f18c79b501aeacf (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2015-08-07T13:46:03Z (GMT) No. of bitstreams: 1 Dissertação - Celso Ricardo Caldeira Rêgo.pdf: 2481181 bytes, checksum: f162815b3f4a2d2e2f18c79b501aeacf (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2015-08-07T13:43:56Z (GMT) No. of bitstreams: 1 Dissertação - Celso Ricardo Caldeira Rêgo.pdf: 2481181 bytes, checksum: f162815b3f4a2d2e2f18c79b501aeacf (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2015-08-07T13:47:14Z (GMT) No. of bitstreams: 1 Dissertação - Celso Ricardo Caldeira Rêgo.pdf: 2481181 bytes, checksum: f162815b3f4a2d2e2f18c79b501aeacf (MD5) / Made available in DSpace on 2015-08-07T13:47:14Z (GMT). No. of bitstreams: 1 Dissertação - Celso Ricardo Caldeira Rêgo.pdf: 2481181 bytes, checksum: f162815b3f4a2d2e2f18c79b501aeacf (MD5) Previous issue date: 2012-01-06 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Many time series exihibit multifractal scale properties with important physical implications. We use the method for the multifractal characterization the MF-DFA (Mutifractal- Detrended Fluctuation Analysis) to calculate the generalized Hurst exponent [11] of water levels series of sixteen hydrological stations of the main Brazilian rivers, located in the cities of Manaus, Obidos, Lad ario, Porto Velho, Fonte Boa, Tucuru , Marab a, Santar em, Cruzeiro do Sul, Xambio a, Concei c~ao do Araguaia, Gua ra, Altamira, C aceres, Barra e Piranhas. These stations are placed in cities with di erent climate zones in Brazil. From this analysis, we concluded that all series exhibit multifractality and non-stationary behavior. We also show that the type of multifractality involved in this process is mainly due to the presence of di erent types of correlations in hydrological time series. We derive an analytic equation that generates the multifractal spectra for all the stations studied, with maximum errors of 1%, from the generalization of the d-Process Multiplied Multinomial. It suggests the existence of a universal multifractality in the hydrologic cycle of the Brazilian rivers and why not of the planet? This work shows that it is possible to treat the time series of water levels of the Brazilian rivers from a multifractal perspective, and therewith to have a better understanding of the complex aspects of the scale properties that these series exhibit. / Muitas séries temporais exibem propriedades de escala multifractais com importantes implicações físicas. Neste trabalho usamos o método para a caracterização multifractal MF-DFA para calcular o expoente de Hurst generalizado [11], das séries de níveis de água de dezesseis estações hidrológicas dos principais rios brasileiros, sediadas nas cidades de Manaus, Óbidos, Porto Velho, Fonte Boa, Tucuruí, Marabá,Santarém, Cruzeiro do Sul, Xambio á, Conceição do Araguaia, Guaíra, Altamira, Caceres, Ladario, Barra e Piranhas. Essas estações estão localizadas em cidades de diferentes zonas climáticas do Brasil. Dessa ánalise, pudemos constatar que todas as séries exibem multifractalidade e comportamento não estacionário. Mostramos ainda, que o tipo de multifractalidade envolvido nesse processo e devido, essencialmente, a presença de diferentes tipos de correlações nas séries hidrológicas. Conseguimos exibir, de modo anal tico, uma equa ção que gera todos os espectros multifractais nas estacões trabalhadas, com erros máximos de 1%, a partir da generaliza c~ao do d-Processo Multiplicativo Multinomial, sugerindo a existência de uma multifractalidade universal no ciclo hidrológico dos rios brasileiros e por que não do planeta? Este trabalho mostra que e possível tratar as séries dos níveis de água dos rios brasileiros a partir da perspectiva multifractal e, disso, compreender melhor os aspectos complexos das propriedades de escalas que essas séries apresentam.