CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior / O som produzido por um tambor à determinado atravÃs de um conjunto de frequÃncias vibracionais. Essas frequÃncias chamadas de autovalores dependem da forma do tambor. Conhecendo os autovalores serà possÃvel determinar o formato de um tambor? Em outras palavras, serà que pode-se ouvir a forma de um tambor? Essa pergunta foi colocada por Mark Kac(KAC) em 1966 e foi um problema que levou uma boa quantidade de anos para ser resolvido. Um resultado relevante provado mais cedo foi de que pode-se ouvir a Ãrea de um tambor. Em 1910 o grande fÃsico H. A. Lorentz deu cinco palestras sob o tÃtulo geral: âVelhos e novos problemas da FÃsica" - e no final da quarta palestra, ele mostrou um problema em aberto, que em nossos termos dita uma relaÃÃo entre os autovalores e a Ãrea de um tambor. Hà um relatÃrio que Hilbert previu que esse problema nÃo seria resolvido em seu tempo de vida. Mas ele estava muito enganado, em menos de dois anos, Hermann Weyl(WEYL), que estava presente na palestra de Lorentz, prova o problema, o qual ficou conhecido por Lei de Weyl. O objetivo deste trabalho à provar a Lei de Weyl e dar um contraexemplo para o problema posto por Mark Kac. / The sound produced by a drum is determined through a set of frequencies vibrational. These frequencies eigenvalues calls depend on the shape of the drum. Knowing the eigenvalues you can determine the shape of a drum? In other words, you can hear the shape of a drum? This question was posed by Mark Kac (KAC) in 1966 and was a problem that took a good amount of years to resolved. An important result was proved earlier that you can hear the area of a drum. In 1910 the great physicist H. A. Lorentz gave five lectures under the title general: "Old and new problems of physics" - and at the end of the fourth lecture, he showed an open problem, which in our terms dictates a relationship between the eigenvalues and the area of a drum. There is a report that Hilbert predicted that this problem would not settled in their lifetime. But was very mistaken, in less than two years, Hermann Weyl (WEYL), that was present at the lecture of Lotentz, proves the problem, which was known for Weylâs law. The objective of this work is to prove the Weylâ law and give a counterexample to the problem posed by Mark Kac.

Chapas de aço elétrico (0,7% Si e 0,3% Al) foram laminadas a diferentes graus de deformação e recozidas (760º C, 2h) de modo a obter diferentes tamanhos de grão por recristalização. Um outro conjunto de chapas do mesmo material foi recozido a tempos e temperaturas diferentes de modo a obter tamanho de grão variado por crescimento de grão. Os tamanhos de grão foram medidos pelo método dos interceptos e os parâmetros da distribuições de tamanho de grão determinados por um método semi-analítico que se baseia na medição das áreas individuais de cada grão na micrografia. A partir do ensaio quase-estático de histerese magnética no quadro de Epstein obtiveram-se os campos coercivos de cada amostra, a diferentes induções máximas (0,6 0,8 1,0 1,2 1,4 e 1,5T). Notou-se que o conjunto dos dados se enquadra com menos de 4% de desvio médio absoluto uma lei fenomenológica do tipo: Hc aBmax^c /TG bBmax^d Na qual Hc é o campo coercivo, TG é o tamanho de grão, Bmax é a indução máxima do ensaio de histerese e a, b, c e d são os parâmetros de ajuste. A partir da inserção do efeito do campo desmagnetizante no contorno de grão no modelo físico de Mager obteve-se uma boa estimativa para os valores dos parâmetros independentes da indução a e b, além de propor um significado físico para os mesmos. Com a integração dos modelos Mager e Preisach, determinou-se uma equação diferente para o ajuste dos dados, a qual oferece um valor aproximado de c. Para que o modelo físico explique completamente a relação fenomenológica resta ainda elucidar o parâmetro d. / Electrical steel sheets (0,7% Si and 0,3% Al) were cold-rolled and annealed (760º C, 2h) in order to obtain different grain sizes through recrystallization. Another set of sheets from the same material were annealed at different temperatures and time-frames, so as to produce different grain sizes through grain growth. Grain size was measured through the intercept method and grain size distribution parameters were determined via a semi-analytical method based on measurement of individual grain areas upon micrographs. From quasistatic hysteresis measurements in an Epstein frame, the coercive field of each sample was determined at various maximum induction values (0,6 0,8 1,0 1,2 1,4 e 1,5T). The data set fits with less than 4% average deviation a phenomenological law of the type: Hc aBmax^c /TG bBmax^d In which Hc is the coercive field, TG is the grain size, Bmax is the maximum induction value and a, b, c and d are the fitting parameters. By introducing the grain boundary demagnetizing field effect on Magers physical model, a good estimate of the values of a and b was obtained, as well as a reasonable explanation to their physical meaning. Integrating Mager and Preisach models, a different equation for the data was obtained, which offered an approximate value of c. In order for physical models do fully explain the phenomenological equation, there is still need to understand the parameter d.

Hoje eu vou morrer para nascer de novo. E como escrever histórias que existem em voz alta e que nunca quiseram estar nesta dissertação? Escrevo aqui uma dramaturgia a partir da alteridade, transformo o texto de um outro pela minha autoria. Procuro, assim, problematizar os usos de um discurso alheio ao escritor, como fundamento para o teatro. Para tanto, apresento três ações artísticas que realizei, Consulta, Fim da Fila e Jogo do Gênero, que são o motor para se pensar como a apropriação do real pode culminar na construção de um texto, processo que chamo de rubricagem. A presença física do dramaturgo em diálogo com o outro possibilita a construção de uma dramaturgia situada em campos expandidos do teatro, evidencia a performatividade do gesto, tanto no processo quanto na obra, e permite pensar caminhos da dramaturgia a partir da aproximação a alguém desconhecido. / Today I will die in order to be reborn. How to write spoken-word stories that never wanted to appear in this thesis? I describe here a dramaturgy of alterity, transforming the text of another into my own words. I thus seek to problematize the uses of a discourse foreign to the author as a foundation for theater. Therefore, I present three performances I have realized-- Consulta, Fim da Fila, and Jogo do Gênero--which drive my consideration about how the appropriation of the real can culminate in the construction of a text, a process I term rubricagem-- rubrication. The physical presence of the playwright in dialogue with another enables the construction of a text set in expanded domains of theatre, demonstrating the gesture\'s performativity--both in the process and final piece--and allowing us to conceive a dramaturgy that emanates from the approximation of someone unknown.

This thesis is motivated by some of the recent results of the solvability of elliptic PDE in Lipschitz domains and the relationships between the solvability of different boundary value problems. The parabolic setting has received less attention, in part due to the time irreversibility of the equation and difficulties in defining the appropriate analogous time-varying domain. Here we study the solvability of boundary value problems for second order linear parabolic PDE in time-varying domains, prove two main results and clarify the literature on time-varying domains. The first result shows a relationship between the regularity and Dirichlet boundary value problems for parabolic equations of the form Lu = div(A∇u)−ut = 0 in Lip(1, 1/2) time-varying cylinders, where the coefficient matrix A = [aij(X, t)] is uniformly elliptic and bounded. We show that if the Regularity problem (R)p for the equation Lu = 0 is solvable for some 1 < p < then the Dirichlet problem (D*) 1 p, for the adjoint equation L*v = 0 is also solvable, where p' = p/(p − 1). This result is analogous to the one established in the elliptic case. In the second result we prove the solvability of the parabolic Lp Dirichlet boundary value problem for 1 < p ≤ ∞ for a PDE of the form ut = div(A∇u)+B ·∇u on time-varying domains where the coefficients A = [aij(X, t)] and B = [bi(X, t)] satisfy a small Carleson condition. This result brings the state of affairs in the parabolic setting up to the current elliptic standard. Furthermore, we establish that if the coefficients of the operator A and B satisfy a vanishing Carleson condition, and the time-varying domain is of VMO-type then the parabolic Lp Dirichlet boundary value problem is solvable for all 1 < p ≤ ∞. This is related to elliptic results where the normal of the boundary of the domain is in VMO or near VMO implies the invertibility of certain boundary operators in Lp for all 1 < p < ∞. This then (using the method of layer potentials) implies solvability of the Lp boundary value problem in the same range for certain elliptic PDE. We do not use the method of layer potentials, since the coefficients we consider are too rough to use this technique but remarkably we recover Lp solvability in the full range of p's as the elliptic case. Moreover, to achieve this result we give new equivalent and localisable definitions of the appropriate time-varying domains.

L’objectif de cette étude est de modéliser et de simuler numériquement des phénomènes d’interaction fluide-structure dans un cadre compressible pour des écoulements non-visqueux. La modélisation proposée repose sur une formulation monolithique du couplage fluide-structure en considérant une unique équation permettant de résoudre simultanément le mouvement du fluide et du solide. Un terme supplémentaire dans l’équation de quantité de mouvement traduit la présence de l’obstacle dans l’écoulement. La contribution de ce terme de pénalisation est étudiée à travers l’analogie avec une formulation variationnelle et un intérêt est porté à la rigueur physique, mathématique et numérique de l’unification des deux milieux, en particulier à l’interface. L’approche numérique correspond à une méthode à pas fractionnaire, en tout point identique aux méthodes de prédiction correction utilisées en incompressible. Quelques résultats numériques clôturent ce travail et permettent de préciser les conditions d’application de ce modèle d’interaction fluide-structure en régime compressible. / This study deals with the modeling and simulation of fluid-structure interactions in a compressible framework for inviscid flows. A monolithic approach has been chosen for treating the coupling between the fluid and the solid through a single equation that solves the motion of both simultaniously. An additionnal term in the momentum equation allows to take into account the obstacle in the flow. A weak formulation is derived from previous similar works that confirms the unification problem is mathematically well-posed, especially on the interface. The numerical procedure relies on a time-splitting method similar to prediction-correction methods for incompressible flows. Some numerical examples illustrate this work and allows to conclude on the feasibility of this fluid-structure interaction model for compressible flows.

More than a decade has passed since Agnew (2005) introduced his General Theory of Crime and Delinquency (GTCD). Despite this interval, GTCD remains a relatively untested theory. Drawing on previous testing efforts, the current research provides a systematic assessment of Agnew's theoretical propositions. It also provides only the second empirical examination of Cochran's (2015) extension of GTCD, which incorporates religion as a sixth distinct life domain. Nested negative binomial regression modeling and Poisson regression modeling are used to assess the effects of life domains on several diverse forms of self-reported criminal behavior at two distinct stages of development: adolescence and adulthood. Data are drawn from two waves of the second generation of the Kaplan Longitudinal and Multigenerational Study. Consistent with prior empirical tests, results provide mixed support for theoretical propositions, highlighting the complexity of Agnew’s initial theory. Specifically, general support is provided for the direct effects of both theories’ variables, indicating they are important to the explanation of crime. Also, in line with Cochran's findings, initial observed effects of religious variables on criminal behavior are reduced to non-significance when all other predictors are introduced in most regression models, hinting that the incorporation of such variables may be incongruous with Agnew's chosen method of theoretical integration. However, religious variables emerge as significant predictors of general crime during adulthood, suggesting that the relationship between these variables and crime is more complex than anticipated. Additionally, strong support is found for the proposition that the effects of life domains are primarily contemporaneous. Results offer weaker support, however, for the assertion that life domain effects are largely mediated by constraints against crime and motivations towards it. Policy implications for the creation of theoretically-informed crime prevention and intervention strategies tailored to specific developmental stage are discussed.

We studied some semilinear elliptic equations on the entire space R^N. Our approach was variational, and the major obstacle was the breakdown in compactness due to the unboundedness of the domain. First, we considered an asymptotically linear Scltrodinger equation under the presence of a steep potential well. Using Lusternik-Schnirelmann theory, we obtained multiple solutions depending on the interplay between the linear, and nonlinear parts. We also exploited the nodal structure of the solutions. For periodic potentials, we constructed infinitely many homoclinic-type multibump solutions. This recovers the analogues result for the superlinear case. Finally, we introduced weights on the linear and nonlinear parts, and studied how their interact ion affects the local and global compactness of the problem. Our approach is based on the Caffarelli-Kohn-Nirenberg inequalities.

Amorphous and nanocrystalline transition metal magnetic alloys (TMMAs) have been the subjects of fundamental and applied study due to their unique structure. The lack of long-range order in these materials sets the stage for their soft magnetic properties to be tuned for a variety of technological applications, such as sensitive magnetic field sensors, high frequency transformers, and stress sensors. Fundamental investigation of the magnetic and structural properties of these materials is also motivated by their unique amorphous or nanocrystalline-embedded amorphous matrix morphology, which has consequences on both the magnetism seen from both the atomic and macro-scale. The surfaces of these materials become important to their high frequency applications, where the skin depth of the excitation field is distributed near the surface. In conjunction with high frequency magnetoimpedance measurements, surface sensitive probes of magnetism and structure must be employed to provide a complete picture of the relationship between the surface and dynamic magnetism. This dissertation focuses on the surface impact of chemical composition, annealing conditions, and coatings on TMMAs on their magnetoimpedance response through multiple surface sensitive techniques such as atomic/magnetic force microscopy, magneto-optical Kerr effect, and scanning/transmission electron microscopy. These tools provide a view into the relationship between the nanostructure, microstructure and soft magnetic properties that make these materials highly desired for fundamental study and technological application.

The importance of plates, with discontinuities in boundary supports in aeronautical and marine structures, have led to various techniques to solve plate problems with mixed edge support conditions. The domain decomposition method is one of the most effective of these techniques, providing accurate numerical solutions. This method is used to investigate the vibration and buckling of flat, isotropic, thin and elastic plates with mixed edge support conditions. Two practical approaches have been developed as an extension of the domain decomposition method, namely, the primary-secondary domain (PSD) approach and the line-domains (LD) approach. The PSD approach decomposes a plate into one primary domain and one/two secondary domain(s). The LD approach considers interconnecting boundaries as dominant domains whose basic functions take a higher edge restraint from the neighbouring edges. Convergence and comparison studies are carried out on a number of selected rectangular plate cases. Extensive practical plate problems with various shapes, combinations of mixed boundary conditions and different inplane loading conditions have been solved by the PSD and LD approaches. / Master of Engineering (Hons)

An analysis of the correspondence between Charles Lyell and Gideon Mantell from 1821 to 1852, in conjunction with other manuscript material, highlights the contrasting backgrounds and geological careers of the two men. It is also characterised by two underlying themes: the nature and timing of their geological work; and the influence of various social factors on their career plans and desire to achieve high social and scientific status. In turn, these points raise several wider issues and inter-related questions concerning the following aspects of English geology in the first half of the nineteenth century. When, why and how did an elite group of geologists emerge in England during this period? Who were its members and what were their characteristics in common? What was the nature and scope of the geological work carried out by the identified elite? In what way did it differ from Mantell's? What social and other barriers did Mantell encounter in his search for scientific and social status? What were the critical factors? In this thesis these issues are examined on a decade-by-decade basis, in three main chapters, as a prelude to examining the central question of why Mantell, unlike Lyell, did not achieve the status of an elite geologist. First, an elite group of English geologists is identified through a series of prosopographic and 'screening' analyses of all members of council of the Geological Society of London (GSL). Geologists who did not meet the prescribed criteria are taken into account. Thirteen geologists are identified in the penultimate and final stages of screening over the four decades. Mantell was the only provincial identified, but he did not attain a position in the final list, which consisted exclusively of a distinctive group of 'gentleman-specialists'. Second, the concept of a geological 'domain' is introduced to analyse the nature and scope of the geological work carried out by the identified group. A critical finding is that all members identified in the final 'screening' list established a 'domain' in one of four categories of the concept and were recognised as the leading authority or exponent of the domain they had fashioned. Finally, the impact and relative importance of specific social and other factors on the careers of Lyell and Mantell are examined. When the findings from each decade of the three chapters are brought together it is shown that by the end of the 1820s it was necessary for a future elite geologist to be so 'positioned' in terms of basic geological experience, location, income and available time that he was able to identify and subsequently fashion an appropriate geological 'domain'. 'Gentleman-specialists', such as Lyell, who were able to follow this strategy, constituted a clearly defined elite that dominated the GSL in the 1830s and 1840s. Mantell's failure to achieve elite geological status stemmed from the fact that he placed too much emphasis on fashioning his image and social status, rather than his scientific career. In doing so, he let the opportunity slip of establishing a major domain - British fossil reptiles - in the early 1830s.