The amount of total and relative sway of a framed or a composite (frame-shear wall) building is of utmost importance in assessing the seismic resistance of the building. Therefore, the design engineer must calculate the sway profile of the building several times during the design process. However, it is not a simple task to calculate the sway of a three-dimensional structure. Of course, computer programs can do the job, but developing the three-dimensional model becomes necessary, which is obviously tedious and time consuming. An easy to apply analytical method is developed, which enables the determination of sway profiles of framed and composite buildings subject to seismic loading. Various framed and composite three-dimensional buildings subject to lateral seismic loads are solved by SAP2000 and the proposed analytical method. The sway profiles are compared and found to be in very good agreement. In most cases, the amount of error involved is less than 5 %. The analytical method is applied to determine sway magnitudes at any desired elevation of the building, the relative sway between two consecutive floors, the slope at any desired point along the height and the curvature distribution of the building from foundation to roof level. After sway and sway-related properties are known, the requirements of the Turkish Earthquake Code can be evaluated and / or checked. By using the analytical method, the amount of shear walls necessary to satisfy Turkish Earthquake Code requirements are determined. Thus, a vital design question has been answered, which up till present time, could only be met by rough empirical guidelines. A mathematical derivation is presented to satisfy the strength requirement of a three-dimensional composite building subject to seismic loading. Thus, the occurrence of shear failure before moment failure in the building is securely avoided. A design procedure is developed to satisfy the stiffness requirement of composite buildings subject to lateral seismic loading. Some useful tools, such as executable user-friendly programs written by using &ldquo / Borland Delphi&rdquo / , have been developed to make the analysis and design easy for the engineer. A method is also developed to satisfy the ductility requirement of composite buildings subject to lateral seismic loading based on a plastic analysis. The commonly accepted sway ductility of &amp / #956 / &amp / #916 / =5 has been used and successful seismic energy dissipation is thus obtained.

Made available in DSpace on 2014-06-11T19:27:10Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-09-21Bitstream added on 2014-06-13T19:47:36Z : No. of bitstreams: 1 batista_ra_me_rcla.pdf: 818880 bytes, checksum: 6293c2c753e3d0bd5a6900cfc890944f (MD5) / O principal objetivo deste trabalho é confeccionar um texto para alunos de gradua ção na área de Ciências Exatas e da Terra concernente ao estudo da Curvatura Gaussiana e Aplicação de Gauss, Superfícies Mínimas, Teorema Egregium de Gauss e o Teorema de Gauss- Bonnet para curvas simples fechadas / The main objective from this work is to make a text for students of graduation in the area of exact sciences and of the land concerning to the study of the Gaussian Curvature and the Gauss Map, Minimal Surfaces, Gauss's Theorem Egregium and the Gauss-Bonnet Theorem for Simple Closed Curves

Nous développons une nouvelle approche éléments finis pour des équations aux dérivées partielles elliptiques de type élasticité linéaire ou Stokes sur une surface fermée de R3. La surface considérée est décrite par le zéro d'une fonction de niveau assez régulière. Le problème se ramène à la minimisation d'une fonctionnelle énergie pour le champ de vitesse sous contraintes. Les contraintes sont de deux types : (i) la vitesse est tangentielle à la surface, (ii) la surface est inextensible. Cette deuxième contrainte équivaut à l'incompressibilité surfacique du champ de vitesse. Nous abordons ce problème de deux façons : la pénalisation et l'introduction de deux multiplicateurs de Lagrange. Cette dernière méthode a l'avantage de traiter le cas de la limite incompressible d'un écoulement en surface dont nous présentons pour la première fois l'analyse théorique et numérique. Nous montrons des estimations d'erreurs sur la solution discrète et les tests numériques confirment l'optimalité des ces estimations. Pour cela, nous proposons plusieurs approches pour le calcul numérique de la normale et la courbure de la surface. L'implémentation utilise la librairie libre d'éléments finis Rheolef. Nous présentons aussi des résultats de simulations numériques pour une application en biologie : la morphogenèse de l'embryon de la drosophile, durant laquelle des déformations tangentielles d'une monocouche de cellules avec une faible variation d'aire. Ce phénomène est connu sous le nom de l'extension de la bande germinale. / We develop a novel finite element approach for linear elasticity or Stokes-type PDEs set on a closed surface of $mathbb{R}^3$. The surface we consider is described as the zero of a sufficiently smooth level-set function. The problem can be written as the minimisation of an energy function over a constrained velocity field. Constraints areof two different types: (i) the velocity field is tangential to the surface, (ii) the surface is inextensible. This second constraint is equivalent to surface incompressibility of the velocity field. We address thisproblem in two different ways: a penalty method and a mixed method involving two Lagrange multipliers. This latter method allows us to solve the limiting case of incompressible surface flow, for which we present a novel theoretical and numerical analysis. Error estimates for the discrete solution are given andnumerical tests shows the optimality of the estimates. For this purpose, several approaches for the numerical computation of the normal and curvature of the surface are proposed. The implementation relies on the Rheolef open-source finite element library. We present numerical simulations for a biological application: the morphogenesis of Drosophila embryos, duringwhich tangential flows of a cell monolayer take place with a low surface-area variation. This phenomenon is known as germ-band extension.

Si dans les caméras actuelles, les matrices de photodétection sont planes, dans la nature, aucune surface focale n'est plane : la rétine est soit concave (œil humain), soit convexe (œil d'insecte). Ces architectures offrent deux solutions de miniaturisation et de simplification des systèmes de détection, qui ont fait l'objet des travaux de cette thèse. La courbure concave du détecteur permet de supprimer l'aberration de courbure de champ qui est particulièrement présente dans les instruments grand champ. L'étude théorique de cette solution, étayée par des applications concrètes, a permis de démontrer la simplification des architectures accessibles par cette approche, ainsi que les améliorations en termes de performances optiques. La courbure convexe permet quant à elle de miniaturiser les systèmes grand champ, en s'inspirant de l'œil composé des petits invertébrés. Cette architecture, constituée de groupes de pixels reliés par une métallisation souple, a été réalisée sur une matrice de détecteurs infrarouge en CdHgTe. Les composants obtenus sont fonctionnels et comparables en termes de performances aux valeurs standard. Ils ouvrent à la voie à des architectures grand champ extrêmement compactes. L'originalité du travail a porté sur la mise en forme sphérique de composants monolithiques, dont la couche active n'est pas modifiée, permettant ainsi de produire des systèmes avec un taux de remplissage de 100%. Après une étude de la souplesse d'échantillons de silicium aminci, le procédé de courbure a été transféré sur des composants fonctionnels: circuit de lecture Si-CMOS et matrice de micro-bolomètres infrarouge. La courbure concave des matrices de détection infrarouge de type micro-bolomètres, a mené à la réalisation de deux caméras. La première, constituée de deux lentilles du commerce, a permis de comparer les systèmes composés des détecteurs plan et courbe. Le gain lié à la courbure sphérique de la rétine sur l'uniformité de la réponse impulsionnelle a été prouvé grâce aux mesures de la fonction de transfert de contrastes (FTC). Enfin, à l'image d'un œil humain, un œil infrarouge composé d'une seule lentille et d'une matrice de micro-bolomètres courbée en concave a été réalisée. La qualité des images obtenues, ainsi que la FTC mesurée, ont mis en évidence le potentiel des plans focaux courbés pour des systèmes ultra-compacts, inenvisageables jusqu'à ce jour. / In natural world, plane retina, on which are based our cameras does not exist. The focal plane is either concave for human beings or convex in insects' eyes. Both curvatures offer novel solution to miniaturize and simplify the optical design, and both of them have been studied in this work.The concave curving of the focal plane suppresses one aberration, the field curvature, on which depends the image quality of large field of view instruments. Advantages in image quality and optical design have been studied by theoretical analysis and by real cases of instruments. The convex curvature results in a miniaturization achieved by reproducing the compound eye of small invertebrates. This design, which is composed of several groups of pixels interconnected by metallic lines, has been realized with cooled infrared detecting device. The performed detectors are still electrically functional with a comparable behaviour than conventional sensors. The originality of this work is the spherical curvature of monocrystalline and monolithic components; the active layer is not modified for this purpose. The process of curvature has been developed on thinned square silicon bare dies and then transferred to thinned functional devices: Si-CMOS and micro-bolometers. The concave curvature of bolometers leads to the realization of two cameras. The first one, composed of two commercial lenses, was dedicated to the comparison between a planar traditional camera and a curved detector system. Optical advantages, and especially the response uniformity, have been proved thanks to measures of the contrast modulation function (CMF). Finally, I have realized an infrared eye composed of a unique lens and a curved concave bolometer. Both the image quality obtained and CMF experiments proved the interest of the curved focal plane in miniaturized optical systems.

Sejam M uma variedade de Hadamard com curvatura seccional KM ≤ −k2 < 0 e ∂ M sua fronteira assintótica. Dizemos que M satisfaz a condição de convexidade estrita se, dados x ∈ ∂∞M e W ⊂ ∂∞M aberto relativo contendo x, existe um aberto Ω ⊂ M de classe C2 tais que x ∈ Int (∂ Ω) ⊂ W e M \ Ω ´e convexo. Provamos que a condição de convexidade estrita implica que M éregular no infinito com relação ao operador Q[u] := div a(|∇u|) \ |∇u| ∇u definido no espa¸co de Sobolev W 1,p(M ), onde a ∈ C1([0, +∞)) satisfaz a(0) = 0, at(s) > 0 para todo s > 0, a(s) ≤ C (sp−1 + 1), ∀s ≥ 0, onde C > 0 é uma constante, e a(s) ≥ sq para algum q > 0 e para s ≈ 0 e supomos que é possível resolver problemas de Dirichlet em bolas (compactas) de M com dados contínuos no bordo. Segue disto que sob a condição de convexidade estrita, os problemas de Dirichlet para equação de hipersuperfície mínima e para o p-laplaciano, p > 1, são solúveis para qualquer dado contínuo prescrito no bordo assintótico. Também provamos que se M é rotacionalmente simétrica ou se inf BR+1 KM ≥ −e 2kR /R2+2 , R ≥ R∗, para certos R∗ e E > 0, então M satisfaz a condição de convexidade estrita. / Let M be Hadamard manifold with sectional curvature KM ≤ −k2, k > 0 and ∂∞M its asymptotic boundary. We say that M satisfies the strict convexity condition if, given x ∈ ∂∞M and a relatively open subset W ⊂ 2 ∂∞M containing x, there exists a C open subset Ω ⊂ M such that x ∈ Int (∂∞Ω) ⊂ W and M \ Ω is convex. We prove that the strict convexity condition implies that M is regular at infinity relative to the operator Q [u] := div a(|∇u|) \ |∇u| ∇u , defined on the Sobolev space W 1,p(M ), where a ∈ C 1 ([0, ∞)) satisfies a(0) = 0, at(s) > 0 for all s > 0, a(s) ≤ C (s p−1 + 1), ∀s ≥ 0, where C > 0 is a constant, and a(s) ≥ sq , for some q > 0 and for s ≈ 0 and we suppose that it is possible to solve Dirichlet problems on (compact) balls of M with continuous boundary data. It follows that under the strict convexity condition, the Dirichlet problems for the minimal hypersurface and the p-Laplacian, p > 1, equations are solvable for any prescribed continuous asymptotic boundary data. We also prove that if M is rotationally symmetric or if inf BR+1 KM ≥ −e2kR/R2+2 , R ≥ R∗, for some R∗ and E > 0, then M satisfies the SC condition.

This work introduces a time adaptive strategy that uses a refinement estimator based on the geometric indicator of curvature. The developed methodology is suitable for problems of numerical time integration present, for example, in the study of bodies subjected to dynamical loads. The refinement estimator demands low computational resources, being easily applied to several direct integration methods. Trying to interact these methods, an object oriented library that uses the developed scheme of adaptation is built. The main idea of this tool is to incorporate this scheme, in an easy way, in existing computational codes that employ direct integration methods. Examples of dynamic solid bodies are presented, ilustrating the technique and library usage in existing applications. / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho introduz uma estratégia de adaptação no tempo que utiliza um estimador de refinamento baseado no indicador geométrico curvatura. A metodologia desenvolvida é aplicada ao problema de integração numérica temporal, presente, por exemplo, no estudo do comportamento de corpos submetidos a cargas dinâmicas. O estimador de refinamento formulado demanda pouco esforço computacional, sendo facilmente aplicado aos diversos métodos de integração direta existentes. Visando a interação com esses métodos, constrói-se uma biblioteca orientada a objetos que incorpora a técnica de adaptação desenvolvida. A idéia principal desta ferramenta é prover, de forma fácil, a técnica de adaptação concebida a códigos computacionais existentes e que fazem uso dos referidos métodos de integração. Apresentam-se exemplos de dinâmica de corpos sólidos que ilustram o potencial de utilização da técnica e o uso da biblioteca em aplicações existentes.

In this work we demonstrate a theorem obtained by F. Hang and X. Wang, which ensures that a compact Riemannian manifold (Mn,g) with nonempty boundary, Ricci curvature greater or equal to (n-1)g, boundary isometric to the (n-1)-dimensional sphere and second fundamental form nonnegative, is isometric to the hemisphere . That result was published in this year in Journal of Geometric Analysis with the title Rigidity Theorems for Compact Manifolds with Boundary and Positive Ricci Curvature. / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Nesta dissertação apresentamos a demonstração de um teorema obtido por F. Hang e X. Wang, o qual estabelece que uma variedade (Mn,g) Riemanniana compacta com bordo não-vazio, curvatura de Ricci maior ou igual a (n-1)g, e com bordo isométrico à esfera (n-1)-dimensional e segunda forma fundamental não-negativa, é isométrica ao hemisfério . Este artigo foi publicado em 2009 no Journal of Geometric Analysis, com o título Rigidity Theorems for Compact Manifolds with Boundary and Positive Ricci Curvature.

This dissertation has as base Jocelino Sato and Vicente de Souza Neto's paper called Complete and Stable O(p + 1) x O(q + 1)-Invariant Hypersurfaces with Zero Scalar Curvature in Euclidean Space Rp+q+2, published on the Annals of Global Analysis and Geometry - 29 in 2006. The main result of this dissertation is the Classi_cation Theorem, which states: The O(p+1) x O(q+1)-Invariant Hypersurfaces in Rp+q+2, p; q > 1, with zero scalar curvature belong to one of the following classes: (1) Cones with a singularity at the orign of Rp+q+2; (2) Hypersurfaces having one orbit of singularity and asymptoting both of the cones C&#945; and C&#946;; (3) Regular hypersurfaces asymptoting the cone C&#945;; (4) Regular hypersurfaces asymptoting the cone C&#946;; (5) Regular hypersurfaces asymptoting both of the cones C&#945; and C&#946;. It was reached by the studies of the ordinary differential equation on R2, involving the coordenate curves that generate these hypersurfaces. Such differential equation, in its turn, is associated with a vector field X : R22 &#8594; R2 on the plan. The study of the orbits space in this field is essential; after all, because of it, it was possible to translate the X orbits' behavior into information concerning the profile curves and, finally, reach the theorem. / Fundação de Amparo a Pesquisa do Estado de Alagoas / Esta dissertação está baseada no artigo de Jocelino Sato e Vicente de Souza Neto intitulado Complete and Stable O(p+1) x O(q+1) - Invariant Hypersurfaces with Zero Scalar Curvature in Euclidean Space Rp+q+2, publicado na revista Annals of Global Analysis and Geometry, volume 29, em 2006. O principal resultado desta dissertação é o Teorema de Classicação, que afirma o seguinte: Uma hipersuperfície Mp+q+1 que é invariante pela açãoao do grupo O(p + 1) x O(q + 1), p; q > 1, com curvatura escalar identicamente nula deve pertencer a uma das seguintes classes: (1) Cones com uma singularidade na origem de Rp+q+2; (2) Hipersuperfícies possuindo uma órbita de singularidades e assintotando ambos os cones C&#945; e C&#946;; (3) Hipersuperfícies regulares que assintotam o cone C&#945;; (4) Hipersuperfícies regulares que assintotam o cone C&#946;; (5) Hipersuperfícies regulares que assintotam ambos os cones C&#945; e C&#946;. A demonstração do teorema requer um estudo de uma equação diferencial ordinária envolvendo as coordenadas das curvas, no plano, que geram estas hipersuperfícies. Esta equação diferencial, por sua vez, está associada a um campo de vetores X : R2 &#8594; R2 no plano. O estudo do retrato de fase deste campo é fundamental. Através dele, foi possível traduzir o comportamento das trajetórias de X em informações com respeito às curvas geratrizes e desta maneira obter o teorema.

Submitted by Sofia Meirelles (sofiaksm@gmail.com) on 2015-02-11T16:47:40Z No. of bitstreams: 1 Estratégias de imunização de carteiras de renda fixa no Brasil - Sofia Meirelles.pdf: 1823249 bytes, checksum: c9dbdd216cfecbe8d0f18ca7f411d3cd (MD5) / Approved for entry into archive by Renata de Souza Nascimento (renata.souza@fgv.br) on 2015-02-11T17:06:46Z (GMT) No. of bitstreams: 1 Estratégias de imunização de carteiras de renda fixa no Brasil - Sofia Meirelles.pdf: 1823249 bytes, checksum: c9dbdd216cfecbe8d0f18ca7f411d3cd (MD5) / Made available in DSpace on 2015-02-11T17:07:50Z (GMT). No. of bitstreams: 1 Estratégias de imunização de carteiras de renda fixa no Brasil - Sofia Meirelles.pdf: 1823249 bytes, checksum: c9dbdd216cfecbe8d0f18ca7f411d3cd (MD5) Previous issue date: 2015-01-23 / This paper aims to statistically compare the performance of two hedging strategies for Brazilian fixed income portfolios, with discrete rebalancing. The first hedging strategy matches duration, and hence it considers only small parallel changes in the yield curve. The alternative methodology ponders level, curvature and convexity shifts through a factor model. We first estimate the yield curve using the polynomial model of Nelson & Siegel (1987) and Diebold & Li (2006) and then immunize the fixed income portfolio using Litterman & Scheinkman’s (1991) hedging procedure. The alternative strategy for portfolio immunization outperforms duration matching in the empirical exercise we contemplate. Additionally, we show that rebalancing the hedging portfolio every month is more efficient than at other frequencies. / Este trabalho visa comparar, estatisticamente, o desempenho de duas estratégias de imunização de carteiras de renda fixa, que são recalibradas periodicamente. A primeira estratégia, duração, considera alterações no nível da estrutura a termo da taxa de juros brasileira, enquanto a abordagem alternativa tem como objetivo imunizar o portfólio contra oscilações em nível, inclinação e curvatura. Primeiro, estimamos a curva de juros a partir do modelo polinomial de Nelson & Siegel (1987) e Diebold & Li (2006). Segundo, imunizamos a carteira de renda fixa adotando o conceito de construção de hedge de Litterman & Scheinkman (1991), porém assumindo que as taxas de juros não são observadas. O portfólio imunizado pela estratégia alternativa apresenta empiricamente um desempenho estatisticamente superior ao procedimento de duração. Mostramos também que a frequência ótima de recalibragem é mensal na análise empírica.

SILVA, Adam Oliveira da. Rigidez de métricas críticas para funcionais riemannianos. 2017. 78 f. Tese (Doutorado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017. / Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-09-19T19:08:04Z No. of bitstreams: 1 2017_tese_aosilva.pdf: 481005 bytes, checksum: 2bdfc6ab68b042a5cfd4f67caf1e21e4 (MD5) / Rejected by Rocilda Sales (rocilda@ufc.br), reason: Bom dia, Estou devolvendo a Tese de ADAM OLIVEIRA DA SILVA, para que o arquivo seja substituído, pois o aluno já veio na BCM e orientei quais eram as correções a serem feitas. Atenciosamente, on 2017-09-20T14:03:26Z (GMT) / Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-09-20T16:47:21Z No. of bitstreams: 1 2017_tese_aosilva.pdf: 480774 bytes, checksum: a1267dd82f8a82a19f79902004e1afb5 (MD5) / Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2017-09-21T12:26:34Z (GMT) No. of bitstreams: 1 2017_tese_aosilva.pdf: 480774 bytes, checksum: a1267dd82f8a82a19f79902004e1afb5 (MD5) / Made available in DSpace on 2017-09-21T12:26:35Z (GMT). No. of bitstreams: 1 2017_tese_aosilva.pdf: 480774 bytes, checksum: a1267dd82f8a82a19f79902004e1afb5 (MD5) Previous issue date: 2017-09-15 / The aim of this work is to study metrics that are critical points for some Riemannian functionals. In the first part, we investigate critical metrics for functionals which are quadratic in the curvature on closed Riemannian manifolds. It is known that space form metrics are critical points for these functionals, denoted by F t,s (g). Moreover, when s = 0, always Einstein metrics are critical to F t (g). We proved that under some conditions the converse is true. For instance, among others results, we prove that if n ≥ 5 and g is a Bach-flat critical metric to F −n/4(n−1) , with second elementary symmetric function of the Schouten tensor σ 2 (A) > 0, then g should be Einstein. Furthermore, we show that a locally conformally flat critical metric with some additional conditions are space form metrics. In the second part, we study the critical metrics to volume functional on compact Riemannian manifolds with connected smooth boundary. We call such critical points of Miao-Tam critical metrics due to the variational study making by Miao and Tam (2009). In this work, we show that the geodesics balls in space forms Rn , Sn and Hn have the maximum possible boundary volume among Miao-Tam critical metrics with connected boundary provided that the boundary be an Einstein manifold. In the same spirit, we also extend a rigidity theorem due to Boucher et al. (1984) and Shen (1997) to n-dimensional static metrics with positive constant scalar curvature, which give us another way to get a partial answer to the Cosmic no-hair conjecture already obtained by Chrusciel (2003). / Este trabalho tem como principal objetivo estudar métricas que são pontos críticos de alguns funcionais Riemannianos. Na primeira parte, investigaremos métricas críticas de funcionais que são quadráticos na curvatura sobre variedades Riemannianas fechadas. É de conhecimento que métricas tipo formas espaciais são pontos críticos para tais funcionais, denotados aqui por F t,s (g). Além disso, no caso s = 0, métricas de Einstein são sempre críticas para F t (g). Provamos que sob algumas condições, a recíproca destes fatos são verdadeiras. Por exemplo, dentre outros resultados, provamos que se n ≥ 5 e g é uma métrica Bach-flat crìtica para F−n/4(n−1) com segunda função simétrica elementar do tensor de Schouten σ 2 (A) > 0, então g tem que ser métrica de Einstein. Ademais, mostramos que uma métrica crítica localmente conformemente plana, com algumas hipóteses adicionais, tem que ser tipo forma espacial. Na segunda parte, estudamos as métricas críticas do funcional volume sobre variedades Riemannianas compactas com bordo suave conexo. Chamamos tais pontos críticos de métricas críticas de Miao-Tam, devido ao estudo variacional feito por Miao e Tam (2009). Neste trabalho provamos que as bolas geodésicas das formas espaciais Rn , S n e H n possuem o valor máximo para o volume do bordo dentre todas as métricas críticas de Miao-Tam com bordo conexo, desde que o bordo seja uma variedade de Einstein. No mesmo sentido, também estendemos um teorema de rigidez devido à Boucher et al. (1984) e Shen (1997) para métricas estáticas de dimensão n e com curvatura escalar constante positiva, o qual nos fornece outra maneira para obter uma resposta parcial para a Cosmic no-hair conjecture já obtida por Chrusciel (2003).