This thesis attempts to resolve the contradictory relationship between the ecological merits of wood construction and the significant material intensity of recent free form timber surface structures. The building industry is now adept in the design and construction of freeform surface architecture, however new challenges have been introduced with the environmentally conscious desire to build these structures in wood. Lacking the formal versatility of steel and concrete, wood introduces a great deal of difficulty in the realization of complex form at an architectural scale. Powerful digital design and fabrication tools have recently made it possible to model, analyze and construct these buildings, but at the cost of heavy structural solutions that involve energy intensive fabrication processes and significant material waste. This approach contradicts the ecological benefits of wood, and raises the question of whether it is possible to achieve free and expressive form in timber surface architecture while maintaining an economy of means and material. This question is addressed through the development of a generative design tool for the creation of material conscious free form timber surface architecture. The formation of the tool is informed by the field of computational morphogenesis, which draws from the natural growth processes of biological structures in the virtual synthesis of form. The tool is conceived as a morphogenetic material system, which consists of a generative algorithm that integrates material, structure and form in a single computational process. Specific material saving techniques deployed in the algorithm draw from existing research in timber shell design and material optimization. Established methods in the use of geodesic lines for the structural patterning of wood shells and stress driven material distribution make up the core concepts deployed in the algorithm. The material system is developed, refined and tested through the design and construction of an experimental free form timber lattice.

In this thesis we discuss possible ways to give quantitative measurement for two spaces not being quasi-isometric. From this quantitative point of view, we reconsider the definition of quasi-isometries and propose a notion of ''quasi-isometric distortion growth'' between two metric spaces. We revise our article [32] where an optimal upper-bound for Morse Lemma is given, together with the dual variant which we call Anti-Morse Lemma, and their applications.Next, we focus on lower bounds on quasi-isometric distortion growth for hyperbolic metric spaces. In this class, $L^p$-cohomology spaces provides useful quasi-isometry invariants and Poincaré constants of balls are their quantitative incarnation. We study how Poincaré constants are transported by quasi-isometries. For this, we introduce the notion of a cross-kernel. We calculate Poincaré constants for locally homogeneous metrics of the form $dt^2+\sum_ie^{2\mu_it}dx_i^2$, and give a lower bound on quasi-isometric distortion growth among such spaces.This allows us to give examples of different quasi-isometric distortion growths, including a sublinear one (logarithmic).

This thesis attempts to resolve the contradictory relationship between the ecological merits of wood construction and the significant material intensity of recent free form timber surface structures. The building industry is now adept in the design and construction of freeform surface architecture, however new challenges have been introduced with the environmentally conscious desire to build these structures in wood. Lacking the formal versatility of steel and concrete, wood introduces a great deal of difficulty in the realization of complex form at an architectural scale. Powerful digital design and fabrication tools have recently made it possible to model, analyze and construct these buildings, but at the cost of heavy structural solutions that involve energy intensive fabrication processes and significant material waste. This approach contradicts the ecological benefits of wood, and raises the question of whether it is possible to achieve free and expressive form in timber surface architecture while maintaining an economy of means and material. This question is addressed through the development of a generative design tool for the creation of material conscious free form timber surface architecture. The formation of the tool is informed by the field of computational morphogenesis, which draws from the natural growth processes of biological structures in the virtual synthesis of form. The tool is conceived as a morphogenetic material system, which consists of a generative algorithm that integrates material, structure and form in a single computational process. Specific material saving techniques deployed in the algorithm draw from existing research in timber shell design and material optimization. Established methods in the use of geodesic lines for the structural patterning of wood shells and stress driven material distribution make up the core concepts deployed in the algorithm. The material system is developed, refined and tested through the design and construction of an experimental free form timber lattice.

[pt] Neste trabalho provamos que o fluxo geodésico de uma variedade Finsler de dimensão n compacta, sem pontos conjugados e que é uma variedade de visibilidade uniforme é transitivo. Para isso, introduzimos versões Finsler dos conceitos de hiperbolicidade de Gromov e visibilidade de Eberlein e estudamos suas consequências. Como aplicação da transitividade, provamos que superfícies Finsler k-básicas compactas de gênero maior que um, sem pontos conjugados e com fibrados de Green contínuos são Riemannianas. / [en] In this work we prove that the geodesic flow of a compact, n-dimensional Finsler manifold without conjugate points and which is an uniform visibility manifold is transitive. For this, we introduce Finsler versions of Gromov s hyperbolicity and Eberlein s visibility concepts and study its consequences. As an application of the transitivity, we prove that compact, k-basic Finsler surfaces without conjugate points, with genus greater than one and with continuous Green bundles are Riemannian.

Dans ce mémoire, nous étudions les propriétés génériques satisfaites par des mesures invariantes par l’action du flot géodésique {∅t}t∈R sur des variétés M non compactes de courbure sectionnelle négative pincée. Nous nous intéressons dans un premier temps au cas des variétés hyperboliques. L’existence d’une représentation symbolique du flot géodésique pour les variétés hyperboliques convexes cocompactes ainsi que la propriété de mélange topologique du flot géodésique nous permet de démontrer que l’ensemble des mesures de probabilité ∅t−invariantes, faiblement mélangeantes est résiduel dans l’ensemble M1 des mesures de probabilité invariantes par l’action du flot géodésique. Si nous supposons que la courbure de M est variable, nous ignorons si le flot géodésique est topologiquement mélangeant. Ainsi les méthodes utilisées précédemment ne peuvent plus s’adapter à notre situation. Afin de généraliser le résultat précédent, nous faisons appel à des outils issus du formalisme thermodynamique développés récemment par F.Paulin, M.Pollicott et B.Schapira. Plus précisément, la démonstration de notre résultat repose sur la possibilité de construire, pour toute orbite périodique Op une suite de mesures de Gibbs mélangeantes, finies, convergeant faiblement vers la mesure de Dirac supportée sur Op. Nous montrons que ce fait est possible lorsque M est géométriquement finie. Dans le cas contraire, il n’existe pas d’exemple de variétés géométriquement infinies possédant une mesure de Gibbs finie. Cependant, nous conjecturons que ce fait est possible pour toute variété M. Afin de supporter cette affirmation, nous démontrons dans la dernière partie de ce manuscrit un critère de finitude pour les mesures de Gibbs. / In this work, we study the properties satisfied by the probability measures invariant by the geodesic flow {∅t}t∈R on non compact manifolds M with pinched negative sectional curvature. First, we restrict our study to hyperbolic manifolds. In this case, ∅t is topologically mixing in restriction to its non-wandering set. Moreover, if M is convex cocompact, there exists a symbolic representation of the geodesic flow which allows us to prove that the set of ∅t-invariant, weakly-mixing probability measures is a dense Gδ−set in the set M1 of probability measures invariant by the geodesic flow. The question of the topological mixing of the geodesic flow is still open when the curvature of M is non constant. So the methods used on hyperbolic manifolds do not apply on manifolds with variable curvature. To generalize the previous result, we use thermodynamics tools developed recently by F.Paulin, M.Pollicott et B.Schapira. More precisely, the proof of our result relies on our capacity of constructing, for all periodic orbits Op a sequence of mixing and finite Gibbs measures converging to the Dirac measure supported on Op. We will show that such a construction is possible when M is geometrically finite. If it is not, there are no examples of geometrically infinite manifolds with a finite Gibbs measure. We conjecture that it is always possible to construct a finite Gibbs measure on a pinched negatively curved manifold. To support this conjecture, we prove a finiteness criterion for Gibbs measures.

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).

Submitted by Caroline Periotto (carol@ufscar.br) on 2016-10-03T20:28:29Z No. of bitstreams: 1 DissCASfr.pdf: 1220679 bytes, checksum: 34316f04f7e4dda72c5fb929a51099d8 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-20T19:18:17Z (GMT) No. of bitstreams: 1 DissCASfr.pdf: 1220679 bytes, checksum: 34316f04f7e4dda72c5fb929a51099d8 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-20T19:18:22Z (GMT) No. of bitstreams: 1 DissCASfr.pdf: 1220679 bytes, checksum: 34316f04f7e4dda72c5fb929a51099d8 (MD5) / Made available in DSpace on 2016-10-20T19:18:28Z (GMT). No. of bitstreams: 1 DissCASfr.pdf: 1220679 bytes, checksum: 34316f04f7e4dda72c5fb929a51099d8 (MD5) Previous issue date: 2016-03-04 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / The present thesis is devoted to the study of closed geodesics in some types of orbifolds. First, we present the notion of Riemannian foliation and their equivalent definitions using foliation atlas and Riemannian submersions. Aiming to understand the leaf space of certain foliations, we introduce the concept of orbifold. Also, the notion of orbifolds will be addressed via pseudogroups. For compact Riemannian good orbifolds, we will prove the existence of non-trivial closed geodesics. The main objective of this work is to obtain closed geodesics in compact Riemannian orbifolds by employing the shortening process with respect to Riemannian foliations. Following the approach of Alexandrino and Javaloyes [5], we also discuss the existence of closed geodesics in the leaf spaces for some classes of singular Riemannian foliations. / A presente dissertação é devotada ao estudo de geodésicas fechadas em alguns tipos de orbifolds. Primeiro, é apresentada a noção de folheação Riemanniana bem como suas equivalentes definições via atlas folheados e submersões Riemannianas. Visando compreender o espaço das folhas de certas folheações, é introduzido o conceito de orbifold. Também será abordada a noção de orbifolds via pseudogrupos. Para orbifolds riemannianos compactos bons, é provada a existência de geodésicas fechadas de comprimento positivo. O principal objetivo deste trabalho é empregar o processo de encurtamento com relação às folheações Riemannianas para obter geodésicas fechadas em orbifolds riemannianos compactos. Seguindo a abordagem de Alexandrino e Javaloyes [5], também discutimos sobre a existência de geodésicas fechadas no espaço das folhas de algumas classes de folheações Riemannianas singulares.

Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2017-01-02T14:12:29Z No. of bitstreams: 2 Dissertação - Eduardo Silva Lira - 2016.pdf: 6831540 bytes, checksum: 4fe7b9bd7a7a3584d1cb48239b390f70 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-01-03T09:39:46Z (GMT) No. of bitstreams: 2 Dissertação - Eduardo Silva Lira - 2016.pdf: 6831540 bytes, checksum: 4fe7b9bd7a7a3584d1cb48239b390f70 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-01-03T09:39:46Z (GMT). No. of bitstreams: 2 Dissertação - Eduardo Silva Lira - 2016.pdf: 6831540 bytes, checksum: 4fe7b9bd7a7a3584d1cb48239b390f70 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-12-01 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / From Carathéodory’s theorem arises the definition of the Carathéodory number for graphs. This number is well-known for monophonic and triangle-path convexities. It is limited for some classes of graphs on P3 and geodesic convexities but is known to be unlimited only on P3-convexity. Driven by open questions in geodesic convexity, in this work we study the Carathéodory number in this convexity. For general graphs and cartesian product, we prove that the Carathéodory number is unlimited. We characterize the Carathéodory number for trees, cographs, for the complementary prisms of cographs and simple graphs Kn, Pn and Cn, for the complement and the complementary prism of the graph KnKn and for the cartesian products PnxPm, KnxKm and PnxKm. / Do Teorema de Carathéodory da geometria surge a definição do número de Carathéodory para grafos. Este número é bem determinado na convexidade monofônica e na convexidade de caminho de triângulos. Ele é limitado para algumas classes de grafos nas convexidades P3 e geodésica, mas só foi provado ser ilimitado na convexidade P3. Motivados pelas questões em aberto na convexidade geodosésica, neste trabalho estudamos o número de Carathéodory nesta convexidade. Para grafos gerais e para produtos cartesianos, provamos que o número de Carathéodory é ilimitado. Determinamos o número de Carathéodory para árvores, cografos, para o prisma complementar de cografos e dos grafos simples Kn, Pn e Cn, para o complemento e prisma complementar do grafo KnKn e para os produtos cartesianos PnxPm, KnxKm e PnxKm.

Let M be a possibly non compact smooth manifold. We study genericity in the C^k topology (3<=k<=+infty) of nondegeneracy properties of semi-Riemannian geodesic flows on M. Namely, we prove a new version of the Bumpy Metric Theorem for a such M and also genericity of metrics that do not possess any degenerate geodesics satisfying suitable endpoints conditions. This extends results of Biliotti, Javaloyes and Piccione for geodesics with fixed endpoints to the case where endpoints lie on a compact submanifold P of MxM that satisfies an admissibility condition. Immediate consequences are generic non conjugacy between two points and non focality between a point and a submanifold (or also between two submanifolds). / Seja M uma variedade suave possivelmente não compacta. Estuda-se a genericidade na topologia C^k (3<=k<=+infty) de propriedades de não degenerescência de fluxos geodésicos semi-Riemannianos em M. A saber, provase uma nova versão do Teorema de Métricas Bumpy para uma tal M e também a genericidade de métricas que não possuem geodésicas degeneradas cujos pontos finais satisfazem certas condições. Isso estende resultados anteriores de Biliotti, Javaloyes and Piccione para geodésicas com extremos fixos para o caso onde os extremos variam em uma subvariedade compacta P de M ×M que satisfaz uma condição de admissibilidade. Consequências imediatas são genericidade de não conjugação entre dois pontos e não focalidade entre um ponto e uma subvariedade (ou também entre duas subvariedades).

Orientador : Maria Margaret Lopes / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Geociencias / Made available in DSpace on 2018-08-04T02:34:20Z (GMT). No. of bitstreams: 1 Heizer_AldaLucia_D.pdf: 6141642 bytes, checksum: 0983ba3a2e79903ed8c65ba8fac199e2 (MD5) Previous issue date: 2005 / Resumo: A presente pesquisa tem por finalidade contribuir para a História das Grandes Exposições da segunda metade do século XIX, sublinhando a participação do Império do Brasil nesses grandes eventos, em particular na Exposição Universal de Paris de 1889. Consideramos possível, ao analisar os catálogos de instrumentos científicos, relatórios, memórias, revistas científicas, entre outras fontes, identificar pistas que nos revelam que o Império do Brasil pretendia desfazer a imagem de flor exótica nos trópicos. A partir da constatação de que os trabalhos acadêmicos realizados no Brasil sobre estes grandes eventos, dos anos de 1980 para cá, não se ocuparam da participação dos países da América Latina, este trabalho pretende se desenvolver na confluência de linhas de pesquisa que, embora plenamente articuláveis, permanecem, até hoje, em grande parte dissociadas na produção historiográfica nacional. Trata-se de pesquisas em História das Exposições Universais e a História dos Instrumentos Científicos / Abstract: This present research has the purpose to contribute for the history of the Great Expositions of the second half of the XIX century, underlining the participation of the Brazilian Empire on these events, in particular in the Paris Universal Exposition in 1889. We found it possible, when analyzing the scientific instrument¿s catalogues, reports, memories, scientific magazines, among other sources, to identify tracks that reveal to us that the Brazilian Empire intended to appear under the image of the ¿Exotic flower of the tropics¿. After discover that the academic works that were made in Brazil about these great events, from 1980 until today, disregard the participation of the Latin American countries, this work intend to be developed in the confluence of the lines of research , although they can be articulated, remains until today dissociated in the national history production. It¿s about research on the history of the Great Universal Expositions and the History of Scientific Instruments / Doutorado / Doutor em Ensino e História de Ciências da Terra