We study the regularity of weak solutions for the Stefan and Hele- Shaw problems with Gibbs-Thomson law under special conditions. The main result says that whenever the free boundary is Lipschitz in space and time it becomes (instantaneously) C[superscript 2,alpha] in space and its mean curvature is Hölder continuous. Additionally, a similar model related to the Signorini problem is introduced, in this case it is shown that for large times weak solutions converge to a stationary configuration. / text

O paradigma forma segue a função, originado na biologia, indica uma invariável dependência entre a origem anatômica de partes de plantas e animais com as funções desempenhadas por estas partes. Embora este paradigma, na biologia, tenha sido superado após Lamarck, a arquitetura e o design ainda se utilizam de analogias biológicas para justificar escolhas estéticas. Neste sentido, as formas mais belas seriam parametrizadas pela eficácia máxima de suas partes na distribuição de esforços. Esta analogia levou à adoção, na arquitetura de edifícios, de padrões geométricos demasiadamente homogêneos, sem vínculo com a complexidade ou linguagem das formas naturais, porém fortemente associados à lógica estrutural. Esta dissertação sugere um caminho alternativo em que a lógica estrutural de duas categorias de esforços (tração e compressão) não comprometa a linguagem presente ou a inspiração gerada pelas formas naturais. Para tal, fundamenta um processo de projeto de superfícies mínimas com base na identificação e parametrização de formas emergentes da natureza. O método proposto utiliza modelos de representação associando a evolução do projeto à aferição, sob o ponto de vista estrutural, da gramática da forma emergente. Os resultados obtidos confirmam as possibilidades de obtenção de eficácia estrutural originada em padrões naturais, sem que haja comprometimento da linguagem de inspiração. / The paradigm form follows function, originated in biology, shows an invariable connection between the anatomical origin of parts of plants and animals with the functions performed by these parts. Although this paradigm, in biology, has been overcome after Lamarck, architecture and design still apply biological analogies to justify aesthetic choices. In this sense, the most beautiful forms would be parameterized by their maximum efficiency at load distribution. This analogy led to the adoption, as a matter of building architecture, of geometric patterns too homogeneous, not linked with the complexity and language of natural forms, but strongly associated with its structural logic. This research suggests an alternative way, in which the structural logic of two load categories (tension and compression) does not change the language or inspiration taken from natural forms. Thus, it is proposed a design process of minimal surfaces, upon identification and parameterization of natural emergent shapes. The proposed method relies on representation by computer models, linking the design evolution to evaluation, under the structural point of view, of emergent shape grammar. The results confirm the possibilities of obtaining structural efficiency originated in natural patterns, without compromising its inspiring language.

O paradigma forma segue a função, originado na biologia, indica uma invariável dependência entre a origem anatômica de partes de plantas e animais com as funções desempenhadas por estas partes. Embora este paradigma, na biologia, tenha sido superado após Lamarck, a arquitetura e o design ainda se utilizam de analogias biológicas para justificar escolhas estéticas. Neste sentido, as formas mais belas seriam parametrizadas pela eficácia máxima de suas partes na distribuição de esforços. Esta analogia levou à adoção, na arquitetura de edifícios, de padrões geométricos demasiadamente homogêneos, sem vínculo com a complexidade ou linguagem das formas naturais, porém fortemente associados à lógica estrutural. Esta dissertação sugere um caminho alternativo em que a lógica estrutural de duas categorias de esforços (tração e compressão) não comprometa a linguagem presente ou a inspiração gerada pelas formas naturais. Para tal, fundamenta um processo de projeto de superfícies mínimas com base na identificação e parametrização de formas emergentes da natureza. O método proposto utiliza modelos de representação associando a evolução do projeto à aferição, sob o ponto de vista estrutural, da gramática da forma emergente. Os resultados obtidos confirmam as possibilidades de obtenção de eficácia estrutural originada em padrões naturais, sem que haja comprometimento da linguagem de inspiração. / The paradigm form follows function, originated in biology, shows an invariable connection between the anatomical origin of parts of plants and animals with the functions performed by these parts. Although this paradigm, in biology, has been overcome after Lamarck, architecture and design still apply biological analogies to justify aesthetic choices. In this sense, the most beautiful forms would be parameterized by their maximum efficiency at load distribution. This analogy led to the adoption, as a matter of building architecture, of geometric patterns too homogeneous, not linked with the complexity and language of natural forms, but strongly associated with its structural logic. This research suggests an alternative way, in which the structural logic of two load categories (tension and compression) does not change the language or inspiration taken from natural forms. Thus, it is proposed a design process of minimal surfaces, upon identification and parameterization of natural emergent shapes. The proposed method relies on representation by computer models, linking the design evolution to evaluation, under the structural point of view, of emergent shape grammar. The results confirm the possibilities of obtaining structural efficiency originated in natural patterns, without compromising its inspiring language.

Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-09-01T13:15:28Z No. of bitstreams: 1 arquivototal.pdf: 612605 bytes, checksum: 21376fa219dbfadac44b0c5d02d91cd3 (MD5) / Approved for entry into archive by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2017-09-01T15:55:26Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 612605 bytes, checksum: 21376fa219dbfadac44b0c5d02d91cd3 (MD5) / Made available in DSpace on 2017-09-01T15:55:26Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 612605 bytes, checksum: 21376fa219dbfadac44b0c5d02d91cd3 (MD5) Previous issue date: 2017-03-20 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / In this work we detail the results submitted by Ho man and Meeks in \The strong half-space theorem for minimal surfaces". The rst results are half-space theorems for minimal surfaces in R3 which have been generalized for other ambients, as have been done by Daniel, B./ Hauswirth, L., e Daniel, B./ Meeks, W. H. III. The third and last one result, caracterize convex hull in n- dimensional Euclidean spaces. / Neste trabalho detalhamos os resultados apresentados por William H. Meeks e David A. Ho man em \The strong half-space theorem for minimal surfaces", . Os primeiros resultados s~ao teoremas de semiespa co para superf cies m nimas no R3, os quais tem sido generalizados para outros ambientes como foi feito por Daniel, B./ Hauswirth, L., e Daniel, B./ Meeks, W. H. III. O terceiro e ultimo resultado, caracteriza fechos convexos no espa co euclidiano n-dimensional.

Made available in DSpace on 2014-07-29T16:02:16Z (GMT). No. of bitstreams: 1 Dissertacao Leonardo Antonio Souto.pdf: 432603 bytes, checksum: cab235c5136d13c6ddcc4340d691a745 (MD5) Previous issue date: 2008-02-29 / The theory of Ribaucour transformations for hypersurfaces in space forms is presented. A method to obtaining linear Weingarten surfaces in a three-dimensional space form is showed. By applying the theory to the cylinder, we obtain a two-parameter family of linear Weingarten surfaces. A new one-parameter family of complete constant mean curvature surfaces in the unit sphere, locally associated to the flat torus, is obtained. We construct new families of constant mean curvature 1 (cmc-1) surfaces which are locally associated to Enneper cousin. / A teoria da transformação de Ribaucour para hipersuperfícies em formas espaciais é apresentada. É mostrado um método para obter superfícies linear Weingarten em formas espaciais tridimensionais. Aplicando a teoria da transformações de Ribaucour ao cilindro, obtemos uma família à dois parâmetros de superfícies linear Weingarten. Uma nova família à um parâmetro de superfícies com curvatura média constante completas na esfera unitária, localmente associada ao toro plano é obtida. Construimos uma família de superfícies com curvatura média constante igual a 1 no espaço hiperbólico tridimensional que são localmente associadas a prima da superfície de Enneper.

[pt] O presente trabalho, desdobramento da pesquisa desenvolvida entre 2007 e 2009, relatada na dissertação de mestrado intitulada Design de estruturas reticuladas de bambu geradas a partir de superfícies mínimas, tem como objetivo principal a aplicação de alguns dos modelos de estruturas de cobertura desenvolvidos pelo LILD (Laboratório de Investigação em Livre Desenho), em escala e contexto real para uso comunitário. Isso ocorre através do ensino de técnicas simples e de baixo impacto ambiental, em processos de construção coletiva utilizando materiais e mão de obra locais. Por meio da elaboração de desenhos, modelos físicos reduzidos e da prática construtiva coletiva em si, obtém-se uma dinâmica de troca de saberes entre mestres e aprendizes, onde o conhecimento flui de maneira multidirecional, se retroalimenta. O aprendizado obtido fica evidente em dois momentos: no desenvolvimento das estruturas em laboratório, pois ampliam o repertório de unidades estruturais do LILD, e na construção das mesmas fora dos muros da universidade, pois trazem resultados reais tanto sobre os saberes trocados entre os envolvidos quanto à ação do meio físico e social sobre o experimento. / [en] The present work, unfolding of the research developed between 2007 and 2009, reported in the master dissertation entitled Design of bamboo frame structures generated from minimal surfaces, has as main objective the implementation of models of roof structures developed by LILD (Laboratory Research in Free Design) on a scale and real context for community use. It happens by teaching simple and low environmental impact techniques in processes of collective construction using local materials and labor. Through the development of drawings, reduced physical models and collective constructive practice itself, we can get a dynamic exchange of knowledge between teachers and learners in which knowledge flows multidirectional way, feeds itself. The knowledge gained is evident in two phases: in the development of structures in the laboratory, it expands the repertoire of structural units of the LILD, and building them outside the walls of the university, because they bring real results both on the knowledge exchanged between those involved as the action of the physical and social environment on them.

Cette thèse est consacrée à l'étude des valeurs propres de l'opérateur de Laplace et de l'opérateur de Steklov sur des variétés riemanniennes. On cherche à donner des bornes optimales parmi l'ensemble des métriques, dans une classe conforme donnée ou non, et à caractériser, si elles existent, les métriques qui atteignent ces bornes. Ces métriques extrémales ont des propriétés qui s'inscrivent dans la théorie des surfaces minimales. On s'intéresse d'abord à la borne supérieure des valeurs propres de Laplace parmi des métriques conformes entre elles, appelées valeurs propres conformes. Dans le chapitre 1, on estime la deuxième valeur propre conforme de la sphère standard. Dans les chapitres 2 et 3, on montre que la première valeur propre conforme d'une variété riemannienne est plus grande que celle de la sphère standard de même dimension avec égalité seulement pour la sphère standard. Ensuite, on cherche à démontrer l'existence et la régularité de métriques qui maximisent les valeurs propres sur des surfaces, dans une classe conforme donnée ou non. Dans les chapitres 3 et 4, on démontre un résultat d'existence pour les valeurs propres de Laplace. Dans le chapitre 6, le travail est fait pour les valeurs propres de Steklov. Enfin, dans le chapitre 5, fruit d'un travail réalisé en collaboration avec Paul Laurain, on démontre un résultat de régularité et de quantification des applications harmoniques à bord libre sur une surface Riemannienne. C'est un élément clé pour le chapitre 6 / This thesis is devoted to the study of the Laplace eigenvalues and the Steklov eigenvalues on Riemannian manifolds. We look for optimal bounds among the set of metrics, lying in a conformal class or not. We also characterize, if they exist the metrics which reach these bounds. These extremal metrics have properties from the theory of minimal surfaces. First, we are interested in the upper bound of Laplace eigenvalues in a class of conformal metrics, called the conformal eigenvalues. In Chapter 1, we estimate the second conformal eigenvalue of the standard sphere. In Chapters 2 and 3, we prove that the first conformal eigenvalue of a Riemannian manifold is greater than the one of the standard sphere of same dimension, with equality only for the standard sphere. Then, we look for existence and regularity results for metrics which maximize eigenvalues on surfaces, in a given conformal class or not. In Chapters 3 and 4, we prove an existence result for Laplace eigenvalues. In Chapter 6, the work is done for Steklov eigenvalues. Finally, in Chapter 5, obtained in collaboration with Paul Laurain, we prove a regularity and quantification result for harmonic maps with free boundary on a Riemannian surface. It is a key component for Chapter 6

This thesis focuses on the use of biomolecular assemblies for creating materials with novel properties. Several aspects of biomimetic materials have been investigated, from fundamental studies on membrane shaping molecules to the integration of biomolecules with inorganic materials. Triply periodic minimal surfaces (TPMS) are mathematically defined surfaces that partition space and present a large surface area in a confined space. These surfaces have analogues in many physical systems. The endoplasmic reticulum (ER) can form intricate structures and it acts as a replica for the wing scales of the butterfly C. rubi, which is characterized by electron microscopy and reflectometry. It was shown to contain a photonic crystal and an analogue to a TPMS. These photonic crystals have been replicated in silica and titania, leading to blue scales with replication on the nanometer scale. Replicas analyzed with left and right handed polarized light are shown be optically active. A macroporous hollow core particle was synthesized using a double templating method where a swollen block copolymer was utilized to create polyhedral nanofoam. Emulsified oil was used as a secondary template which gave hollow spheres with thin porous walls. The resulting material had a high porosity and low thermal conductivity. The areas of inorganic materials and functional biomolecules were combined to create a functional nanoporous endoskeleton. The membrane protein ATP synthase were incorporated in liposomes which were deposited on nanoporous silica spheres creating a tight and functional membrane. Using confocal microscopy, it was possible to follow the transport of Na+ through the membrane. Yop1p is a membrane protein responsible for shaping the ER. The protein was purified and reconstituted into liposomes of three different sizes. The vesicles in the 10-20 nm size range resulted in tubular structures. Thus, it was shown that Yop1p acts as a stabilizer of high curvature structures. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 2: Manuscript. Paper 3: Submitted. Paper 4: Submitted. Paper 5: Submitted.</p>

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

Orientador: João Peres Vieira / Banca: Eliris Cristina Rizziolli / Banca: Laércio Aparecido Lucas / Resumo: 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 / Abstract: 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 / Mestre