O principal objetivo desta tese é estudar o número de rotação de fins primos de homeomorfismos planares que pertencem a uma classe de homeomorfismos H. Tal número de rotação é devido à Carathéordory e semelhante à teoria de Poincaré para homeomorfismos do crculo. Para todo irracional (0, 1), denotando por (h, U ) o número de rotação de fins primos de h H em U , com U a bacia de repulsão do infinito, construiremos um homeomorfismo h H satisfazendo (h, U ) = e que possui uma sela periódica com intersecção homoclnica transversal em U . Além disso, quando h é de classe C 2 e det(Dh| x ) < 1 em todo ponto, mostraremos que existe ponto periódico acessvel em U se, e somente se, (h, U ) é racional. Também será provado que, quando h é uma ferradura de Smale, o número de rotação (h, U ) é racional. Finalizando, provaremos que se for possvel a existência de um difeomorfismo C r , r 1, em um conjunto genérico a ser definido, com U = W u (p) para p uma sela homoclnica com intersecção transversal e tal que o número de rotação (h, U ) é irracional, necessariamente, h deve satisfazer uma propriedade que não é válida para ferraduras de Smale. / The main objective of this thesis is to study the prime ends rotation number of planar homeomorphisms belonging to a class of homeomorphisms H. Such rotation number is due to Carathéordory and similar to the Poincarés theory of homeomorphisms of the circle. For all irrational (0, 1), denoting by (h, U ) the prime end rotation number of h H in U , with U the infinity repulsion basin, we will construct a homeomorphism h H satisfying (h, U ) = and having a homoclinic saddle with transverse intersection in U . Also, when h is class C 2 and det (Dh| x ) < 1 at every point, we will show that there is accessible periodic point in U if, and only if, (h, U ) is rational. It will also be proved that when h is a Smales horseshoe, the rotation number (h, U ) is rational. To conclude, we will prove that if there exists a C r -diffeomorphism, in a generic set to be defined, with U = W u (p) for a saddle point p with transverse homoclinal intersection and such that the rotation number (h, U ) is irrational, then h must satisfy a property that is not valid for Smales horseshoes.

Nesse trabalho, propomos uma modificação da técnica de caracterização de filmes conhecida por m-line para o desenvolvimento de um refratômetro para gases e líquidos. O principio dessa técnica consiste no acoplamento de ondas evanescentes em guias de ondas planares obtidos via o fenômeno da reflexão total interna frustrada através de dispositivos acopladores. Observa-se experimentalmente, após incidir um feixe de laser contínuo na base do acoplador óptico, uma grande atenuação da radiação refletida para determinados ângulos de incidência, que é justamente a radiação acoplada nos modos permitidos pelo guia de onda. Medindo-se os valores desses ângulos e usando a teoria de acoplamento, é possível determinar as características desconhecidas do sistema. Esse sistema consiste de um acoplador óptico semicircular de alto índice de refração em cuja base foram depositados, via evaporação, um filme de dióxido de silício (SiO2) e outro de dióxido de zircônio (ZrO2). Ou seja, o sistema resume-se a dois meios finitos (filmes) prensados entre dois meios semi-infinitos (prisma e amostra). Como a espessura dos filmes e os índices de refração complexos dos filmes e do prisma são conhecidos, a única variável é o índice de refração do quarto meio, que é a amostra da qual se deseja medir o índice de refração. Estudamos a influência que cada um dos parâmetros externos exerce sobre o perfil refletido, tais como comprimento de onda e polarização da radiação incidente, espessuras e índices de refração dos filmes e o formato dos dispositivos acopladores. Descrevemos o comportamento do sistema quando o feixe incidente possui perfil gaussiano, que é perfil dos lasers usualmente usados em pesquisa. As espessuras das camadas de SiO2 e de ZrO2 foram otimizadas tendo em vista a faixa dos valores do índice de refração das amostras que se deseja medir. A otimização do sistema é obtida via teoria de guiamento de radiação em guias de ondas planares para o caso de quatro meios. Para a aquisição e tratamento dos dados desenvolvemos um programa na plataforma LabVIEW&reg; que processa a imagem detectada por uma câmera CCD no visível, possibilitando o acompanhamento da variação do feixe refletido em função da variação do índice de refração da amostra. Assim, além de determinar ponto a ponto a variação do perfil refletido, é possível determinar a dinâmica em que esse efeito se realiza, gerando possibilidades de aplicação da técnica em áreas relacionadas à dinâmica química e bioquímica. Para confirmação da efetividade da técnica, realizamos medidas da variação do índice de refração do ar em função da umidade relativa, temperatura, pressão e para soluções de glicose. O sistema demonstrou sensitividade suficiente para acompanhar mudanças do índice de refração do ar da ordem de 10-6. / In this work, we propose a modification of the technique for characterization of films known as the m-line for the development of a refractometer for liquids and gases. The principle of this technique is coupling evanescent waves in planar waveguides obtained by the phenomenon of frustrated total internal reflection devices through devices couplers. It is experimentally observed, after focusing a continuous laser beam at the base of the coupler, a large attenuation of the reflected radiation for certain angles of incidence, which is precisely the radiation coupled in the modes allowed by the waveguide. Measuring the values of these angles and using the coupling theory, it is possible to determine the unknown characteristics of the system. This system consists of a semicircular optocoupler high refractive index which in the base was deposited, via evaporation, a film of silicon dioxide (SiO2) and a zirconium dioxide (ZrO2). In other words, the system is similar to a two finite media (films) pressed between two semi-infinite media (prism and sample). As the film thickness and complex refractive indices of the film and the prism are known, the only variable is the index of refraction of the fourth medium that is the sample from which it is aimed to measure the refractive index. We studied the influence that each of the external parameters has on the reflected profile, such as wavelength and polarization of the incident radiation, thicknesses and refractive indices of the films and the format of the devices couplers. We describe the system behavior when the incident beam has a Gaussian profile, which is usually the profile of the lasers usually used in researches. The thicknesses of the layers of SiO2 and ZrO2 were optimized in function of the range of the refractive index values of the samples to be measured. System optimization is obtained via the guiding theory of radiation in planar waveguides for the case of four mediums. For acquisition and data processing, a program were developed in LabVIEW&reg; platform that processes the image detected by a CCD camera in visible light, allowing us to relate the variation of the reflected beam to the value of the refractive index of the sample. Thus, besides determining the variation of the profile reflected, it is possible to determine the dynamic in which this effect takes place, generating opportunities for application of the technique in areas related to the dynamic chemistry and biochemistry. To confirm the effectiveness of the technique, we performed measurements of the variation of the refractive index of air as a function of relative humidity, temperature, pressure and glucose solutions. The system shows sufficient sensitivity to follow changes in the refractive index of air in the order of 10-6.

Cette thèse se compose de deux parties qui peuvent être considérées comme deux aspects différents de l'électronique moléculaire avec pour point commun les moyens de nanofabrication mis en jeu pour réaliser des dispositifs de mesures électriques à bas courant. La première partie de la thèse concerne l'assemblage de nano-aimants entre électrodes à nanogap. Le besoin croissant de processeurs toujours plus performants et celui d’une densité de stockage toujours plus grande ont poussé la technologie CMOS couramment utilisée dans l'industrie à ses limites physiques vis-à-vis de sa miniaturisation. L'électronique moléculaire et la spintronique moléculaire se révèlent être des alternatives prometteuses à cette technologie pour les futurs dispositifs nanoélectroniques. Mes principaux travaux dans ce domaine ont porté sur l'assemblage entre des électrodes à nanogap, de nano-aimants moléculaires à base de bleu de Prusse ou de son analogue Cs–Co–Cr. Le but était ainsi de faire les premiers pas vers la construction de dispositifs en spintronique moléculaire. Des nanogaps de ~ 7 à 50 nm ont été fabriqués en palladium ou en or sur un substrat Si/SiO₂ par lithographie électronique et lift-off. Les nano-aimants ont été placés dans le gap par diélectrophorèse à courant alternatif (AC DEP). À température ambiante, un courant négligeable a été mesuré sur les jonctions utilisant des nanoparticules de Cs–Co–Cr alors qu’un courant de ~ 30 pA a été mesuré sur celles avec les nanoparticules en bleu de Prusse pour une tension de ~ 1 V. J’ai montré qu‘en fait, l’eau piégée dans les nanogaps altérait sérieusement les mesures de courants et nécessitait un recuit préalable. Pour optimiser la localisation des nanoparticules entre les électrodes, j’ai proposé un programme de simulation de la DEP ne tenant pas compte du mouvement brownien et de la dynamique des fluides. La deuxième partie de la thèse concerne la fabrication de dispositifs de type nanopatch-clamp planaire pour l'enregistrement de courants ioniques à travers les canaux ioniques des protéines membranaires. Les canaux de ces protéines incorporées dans les membranes cellulaires sont des composantes essentielles de toutes les cellules vivantes et sont à la base de divers processus physiologiques tels que ceux dans la communication nerveuse, la contraction musculaire, la sensation tactile, etc. Les mesures de transport d'ions sont maintenant utilisées dans diverses applications telles que le criblage de médicaments dans l'industrie pharmaceutique et les biocapteurs médicaux. La méthode classique pour effectuer des mesures de transport d'ions consiste à utiliser un système patch-clamp. Cependant, cette méthode nécessite d’importantes compétences, des équipements lourds et coûteux et présente une faible efficacité de mesure. Pour pallier ces inconvénients, une solution est de développer des patch-clamps planaires, qui sont modulables, automatisés et faciles d’utilisation. La fabrication du dispositif a consisté en la réalisation d’une piste conductrice constituée d’un empilement de couches Au/Ag sur un substrat de silicium oxydé. Cette piste a été passivée et isolée électriquement par une couche de Si₃N₄/SiO₂ dans laquelle j’ai gravé des micro-trous et j’ai ensuite converti la couche d’Ag en AgCl pour les mesures électriques. Afin de valider le fonctionnement du dispositif sans la membrane, j’ai procédé à des mesures de courant en fonction du temps pour diverses tensions, ce qui m’a ensuite permis de proposer un schéma équivalent électrique. / This thesis consists of two parts. The two parts correspond to two different subjects but with a common feature which is the fabrication of nanometer scale devices for low current measurements. The first part investigated the assembly of Prussian blue and Cs–Co–Cr Prussian blue analogue molecular nanomagnets into nano-patterned electrodes. The ever growing need for higher performance processors and higher storage densities has pushed the CMOS technology commonly used in industry to its physical limitations toward its miniaturization. Molecular electronics and molecular spintronics prove to be promising alternatives for the CMOS in future nanoelectronic devices. Pd or Au gaps with ~ 7–50 nm width were fabricated on a Si/SiO₂ substrate using standard electron beam lithography, metal deposition and lift-off. Nanomagnets were positioned between the gaps via AC dielectrophoresis (DEP). At room temperature, the Cs–Co–Cr Prussian blue analogue nanoparticles exhibited negligible current whereas junction with Prussian blue nanoparticles exhibited ~ 30 pA at ~ 1 V. Water trapped in nanogaps was found to seriously alter current measurements. This problem was solved by heating samples prior to measurements. A simplified DEP simulation program using Delphi was developed, which neglected Brownian motion and fluid dynamics but allowed us to better understand the DEP process. The second part of the thesis investigated the fabrication of devices for measuring electrical currents through membrane protein channels. Membrane-embedded protein channels are the basis of various physiological processes like nervous communication, muscular contraction, tactile sensation, and so on. Electrical measurements are used in different applications such as drug screening in pharmaceutical industry and biosensors. The standard method to perform such measurements is the use of patch-clamp. However, this method requires intense skill and heavy equipment while it exhibits low measurement efficiency. A solution to these drawbacks is the development of planar patch clamps, which are scalable, automated and easier to use. The first device fabrication step was the patterning of Au/Ag electrodes on thermally oxidized Si substrate by optical lithography, metallization and lift-off. Secondly, a passivation layer of Si₃N₄/SiO₂ was deposited on top of electrodes by PECVD. Then micro-holes were formed inside the Si₃N₄/SiO₂ passivation layer stack using Raith-150 e-beam lithography and reactive ion etching. Finally, Ag layer was converted to AgCl using bleach. The test of electrical current was done using Axopatch patch-clamp amplifier. Current versus time measurements for different voltages were recorded without membrane covering the holes, and an electrical model has been developed for the fabricated devices.

The development of Laser-Induced Thermal Grating Spectroscopy (LITGS) for diagnostics of combusting and non-combusting flows is described. The first use of LITGS to provide in situ calibration of 2-Dimensional temperature distributions generated using Two-Colour Planar Laser-Induced Fluorescence (TC-PLIF) is reported. Time-resolved measurements of temperature distributions in a firing GDI optical engine obtained by TC-PLIF were made during the compression stroke and calibrated to the absolute temperature scale by simultaneous LITGS measurements. The accuracy and precision of the temperatures derived from LITGS data are evaluated using alternative methods of data analysis - Fast Fourier Transform and Fitting to theoretical models of the experimental data. The relative merits of the two methods are examined for analysis of weak LITGS signals obtained under engine conditions of low pressure and high temperature. The combined TC-PLIF and LITGS system was demonstrated by performing repeated single-shot measurements for 1 in every 10 four-stroke cycles showing excellent correlation of the temperatures derived from both techniques. Direct measurement of the effect of 'charge cooling', of order 5 K, for operation with direct injection is reported. Inhomogeneous temperature distributions were observed during the compression stroke for fired operation with Port Fuel Injection (PFI) and also with Gasoline Direct Injection (GDI). The effects of varying the relative concentrations of toluene and iso-octane in the two-component fuel were investigated. Extension of the LITGS technique to multi-point measurements along a 1-D line is described. By recording signals from 4 points on separate detectors using a fibre-coupled photodiode array the limitations of Streak Cameras used previously for 1-D LITGS measurements were overcome. Demonstration of principle experiments are reported in which simultaneous 4-point measurements were made with 1 mm spatial resolution and a precision of 0.7 % in temperature gradients in gas flows and in boundary layers at surfaces.

Silylamide ligands have been used throughout the Periodic Table since the 1960s. They have delivered landmark complexes by providing the first three co-ordinate f-element complexes, the first trigonal planar f-element complexes and the first near-linear f-element complexes. This area is reviewed in Chapter 2.Herein, this work presents the first uses of several novel bis-silylamide ligands developed at Manchester which take the form {N(SiR3)2} where R = Me, iPr or tBu to afford four novel ligands: N ʹ, {N(SiMe3)(SiiPr3)}; N**, {N(SitBuMe2)2}; N* {N(SitBuMe2)(SiiPr3)}; and N , {N(SiiPr3)2}. Group 1 and 2 complexes of all of these ligands are presented along with the previously reported N*ʹ [N*ʹ = {N(SitBuMe2)(SiMe3)}]; which show variable bonding motifs based on the steric bulk. The N** and N ligands have formed the bulk of the work presented and were used to stabilise the first trigonal planar actinide complex [U(N**)3], as well as the first near-linear Ln(II) (Ln = lanthanide) complexes [Ln(N )2] (Ln = Sm, Eu, Yb, Tm). Additionally the trigonal planar Ln(II) complexes [K(2.2.2-cryptand)][Ln(N**)3] (Ln = Sm, Eu, Yb, Tm) have also been synthesised to compare the physicochemical properties of trigonal planar and near-linear geometries on the same elements with similar ligands.

Neuromesodermal progenitors (NMPs) are bipotent progenitors, located at the caudal end of the embryo and are essential for axis formation. These stem cell-like progenitors possess the ability to self-renew and differentiate to both mesodermal and neural lineages, such as skeletal muscle and spinal cord derivatives. These progenitors arise at E8.5 and are localised in the caudal lateral epiblast (CLE), a posterior region of the embryo near the primitive streak. Later in development, they reside in the tail bud until cessation of axial elongation at E13.5. Throughout these stages NMPs are characteristically marked by co-expression of T(Bra) (Brachyury) and Sox2. This characteristic is also present in in vitro NMPs, which can be derived from Epiblast Stem Cells (EpiSCs) through treatment with Wnt/β-catenin signalling agonists and Fgf2, which simulates their in vivo environment. Protein and mRNA profiling of NMPs and mutant phenotypes in vivo supports the hypothesis that a non-canonical Wnt pathway, the Wnt/Planar Cell Polarity pathway (PCP) could be involved in NMP fate decision and/or maintenance. This thesis focuses on understanding more about the role of PCP by aiming to identify the spatio-temporal profile of Wnt/PCP pathway components in NMP regions during axial elongation, as well as determining its role in NMP behaviour through manipulation of this pathway via in vivo and in vitro assays Employing in situ hybridisation and immunohistochemistry techniques, key Wnt/PCP components, including Pk1, Vangl2 and Ptk7, were confirmed to be present in in vivo and in vitro NMPs, thus, providing strong evidence that Wnt/PCP may be involved regulating NMP behaviour. Disruption of Wnt/PCP signalling through overexpression of Wnt/PCP components was tested in refined in vivo and in vitro assays. Overexpression of Vangl2 and Ptk7, but not Pk1 in NMPs regions in vivo resulted in loss of contribution to neural lineages, as well as lower contribution to NMP regions themselves. Similarly, Wnt/PCP components were disrupted in vitro through generation of dox-inducible overexpression cells lines for Wnt/PCP components. These lines were used to generate NMPs from an optimised novel alternative source Epiblast-Like Cells (EpiLCs), however no clear affect to lineage was observed. Overall this work has successfully advanced our knowledge of Wnt/PCP mediated control of NMP differentiation and maintenance, and provided a finer grained description of the relationships between them.

As curvas limite de conformação (CLC) permitem representar de maneira abrangente a estampabilidade de uma chapa e tem sido empregadas largamente como critério na otimização do processo de estampagem e no projeto de matrizes. Os ensaios simulativos Nakazima são comumente utilizados na determinação das curvas CLC mas suas posições são afetadas devido ao atrito do punção com a chapa e desta com a matriz. Adicionalmente, são demorados e dispendiosos porque exigem 10 corpos de prova (c.p.) de dimensões diferentes e pelo menos três c.p. de cada uma destas dimensões para fins estatísticos perfazendo a quantidade mínima recomendada de 30 corpos de prova. A necessidade da gravação de rede de círculos nas superfícies de todas as amostras bem como as leituras ópticas das elipses após as deformações oneram e atrasam mais a obtenção das CLC. A presente pesquisa baseou-se no aço da qualidade livre de intersticiais (IF) e no aço SAE 1050 coalescido e buscou determinar o ponto CLC0, raiz das curvas CLC e crítico para a estampagem, de modo mais rápido e barato que os ensaios simulativos. Assim, o ensaio intrínseco de tração uniaxial em estado plano de deformação foi aplicado utilizando menor quantidade de amostras. O ensaio Nakazima e Análises por Elementos Finitos (FEM) também foram executados nos aços sob estudo, de modo a permitir comparações dos valores CLC0. Os resultados de CLC0 obtidos pelos ensaios de tração uniaxiais em estado plano de deformação mostraram-se inferiores àqueles apresentados pela análise por elementos finitos e pelo ensaio não planar Nakazima, especialmente em relação a este último. A influência de trações unidirecionais e também ortogonais em estado plano de deformação sobre a rugosidade superficial das chapas, CLC0 e seu estado de tensões (CLT0) e sobre a textura também foi analisada. Desta forma, CLC0 e rugosidade mostraram-se dependentes da trajetória de deformação ao contrario de CLT0. A textura do aço IF, forte no estado recozido, foi fortalecida na direção DL e enfraquecida na direção DT em qualquer das duas trajetórias de deformação. / The forming limit curves (FLC) are used to reveal sheet metal formability and it is largely used in the stamping process optimization and in the project of dies. The measurements of FLC points are made by simulative tests (for example, the one named after Nakazima) which are very complex and costly procedures: around thirty specimens with different measures; engraving of circles grid in metallics surfaces and also, plastics strains and optical lectures are required. The present work used interstitial free (IF) and SAE 1050 spheroidized steel sheets. The aim was to investigate the precision of a simplified test, called near plane tensile test, wich is simpler and less dispendious, allowing the determination of the critical value to formability called FLC0 by a intrinsic plane strain test, which uses smaller sample numbers. The FLC0 value was obtained also by Nakazima simulative test and Finite Elements Analysis (FEM) to allow comparisons with plane strain tests. The results of FLC0 obtained by plane strain tension tests are smaller that similar values provided through FEM and Nakazima tests, but these differences can be attributed to deficiencies in these procedures, so the plane strain tensile values are presumably more reliable. The numerical analysis FEM ignores texture evolution during plastic strain, which is a possible factor to explain the differences. The Nakazima test showed largest FLC0 parameter in all cases, which is attributed to geometric factors. Evolution of sheet roughness, crystallographic texture and their correlation with the obtained FLC0 values were also investigated in addition to applying plain strain uniaxial and orthogonal tensile tests. The type of deformation trajectory influenced the FLC0 point and roughness, but the tension point FLSC0 associated to FLC0 was invariant. Texture depends on deformation trajectory and its intensity increases with the deformation along rolling direction.

A primeira parte deste trabalho é dedicada ao estudo de sistemas dinâmicos contínuos e discretos bidimensionais com um único ponto de equillíbrio que é do tipo sela hiperbólica. No caso contínuo, obtemos condições sufiientes para que um campo vetorial planar seja topologicamente equivalente à sela linear L(x; y) = (-x; y). No caso em que o campo vetorial é um difeomorfismo local, a injetividade do campo jogará um papel fundamental na obtenção de tal equivalência topológica. Além disto, apresentamos uma descrição das folheações do plano associadas a campos de vetores com uma única singularidade do tipo sela hiperbólica. No âmbito dos sistemas discretos, apresentamos condições para que um difeomorfismo, possuindo uma sela hiperbólica como único ponto fixo, satisfaça as propriedades básicas de um sistema linear com um ponto fixo que é do tipo sela hiperbólica: as quatro separatrizes do ponto fixo se acumulam só no infinito e os iterados dos pontos que não estão nas variedades invariantes deste ponto fixo se acumulam no infinito tanto no passado quanto no futuro. A segunda parte deste texto, se dedica a problemas de injetividade de difeomorfismos locais em \'R POT. n\'. Mais especificamente, obtemos versões fracas da Conjetura Jacobiana Real de Jelonek e de uma Conjetura apresentada por Nollet e Xavier. Ambos problemas estão intimamente ligados à famosa Conjetura Jacobiana, que foi considerada por Smale em 1998 como um dos dezoito problemas matemáticos mais relevantes ainda em aberto / The first part of this work is dedicated to the study of continuous and discrete twodimensional dynamical systems with a unique equilibrium point which is a hyperbolic saddle. In the continuous case, we obtain sufficient conditions for a planar vector field be topologically equivalent to the linear saddle L(x; y) = (-x; y). In the case where the vector field is a local diffeomorphism, the injectivity of the field will play a key role in obtaining such a topological equivalence. Furthermore, we provide a description of foliations of the plane vector fields associated with a unique singularity of hyperbolic saddle type. In the context of discrete systems, we present conditions for a diffeomorphism, possessing a hyperbolic saddle as the single fixed point, to satisfy the basic properties of a linear system with a fixed point of saddle type which is hyperbolic: the four separatrices of the fixed point accumulate only at infinity and iterated the points that are not in invariant manifolds of this fixed point accumulate in infinity in both the past and future. The second part of this text is devoted to problems of injectivity of local diffeomorphisms on \'R POT. n\'. More specifically, we obtain weaker versions of the Jelonek\'s Real Jacobian Conjecture and a Conjecture given by Nollet and Xavier. Both problems are closely linked to the famous Jacobian Conjecture, which was considered by Smale in 1998 as one of eighteen mathematical problems even more important in open

As curvas limite de conformação (CLC) permitem representar de maneira abrangente a estampabilidade de uma chapa e tem sido empregadas largamente como critério na otimização do processo de estampagem e no projeto de matrizes. Os ensaios simulativos Nakazima são comumente utilizados na determinação das curvas CLC mas suas posições são afetadas devido ao atrito do punção com a chapa e desta com a matriz. Adicionalmente, são demorados e dispendiosos porque exigem 10 corpos de prova (c.p.) de dimensões diferentes e pelo menos três c.p. de cada uma destas dimensões para fins estatísticos perfazendo a quantidade mínima recomendada de 30 corpos de prova. A necessidade da gravação de rede de círculos nas superfícies de todas as amostras bem como as leituras ópticas das elipses após as deformações oneram e atrasam mais a obtenção das CLC. A presente pesquisa baseou-se no aço da qualidade livre de intersticiais (IF) e no aço SAE 1050 coalescido e buscou determinar o ponto CLC0, raiz das curvas CLC e crítico para a estampagem, de modo mais rápido e barato que os ensaios simulativos. Assim, o ensaio intrínseco de tração uniaxial em estado plano de deformação foi aplicado utilizando menor quantidade de amostras. O ensaio Nakazima e Análises por Elementos Finitos (FEM) também foram executados nos aços sob estudo, de modo a permitir comparações dos valores CLC0. Os resultados de CLC0 obtidos pelos ensaios de tração uniaxiais em estado plano de deformação mostraram-se inferiores àqueles apresentados pela análise por elementos finitos e pelo ensaio não planar Nakazima, especialmente em relação a este último. A influência de trações unidirecionais e também ortogonais em estado plano de deformação sobre a rugosidade superficial das chapas, CLC0 e seu estado de tensões (CLT0) e sobre a textura também foi analisada. Desta forma, CLC0 e rugosidade mostraram-se dependentes da trajetória de deformação ao contrario de CLT0. A textura do aço IF, forte no estado recozido, foi fortalecida na direção DL e enfraquecida na direção DT em qualquer das duas trajetórias de deformação. / The forming limit curves (FLC) are used to reveal sheet metal formability and it is largely used in the stamping process optimization and in the project of dies. The measurements of FLC points are made by simulative tests (for example, the one named after Nakazima) which are very complex and costly procedures: around thirty specimens with different measures; engraving of circles grid in metallics surfaces and also, plastics strains and optical lectures are required. The present work used interstitial free (IF) and SAE 1050 spheroidized steel sheets. The aim was to investigate the precision of a simplified test, called near plane tensile test, wich is simpler and less dispendious, allowing the determination of the critical value to formability called FLC0 by a intrinsic plane strain test, which uses smaller sample numbers. The FLC0 value was obtained also by Nakazima simulative test and Finite Elements Analysis (FEM) to allow comparisons with plane strain tests. The results of FLC0 obtained by plane strain tension tests are smaller that similar values provided through FEM and Nakazima tests, but these differences can be attributed to deficiencies in these procedures, so the plane strain tensile values are presumably more reliable. The numerical analysis FEM ignores texture evolution during plastic strain, which is a possible factor to explain the differences. The Nakazima test showed largest FLC0 parameter in all cases, which is attributed to geometric factors. Evolution of sheet roughness, crystallographic texture and their correlation with the obtained FLC0 values were also investigated in addition to applying plain strain uniaxial and orthogonal tensile tests. The type of deformation trajectory influenced the FLC0 point and roughness, but the tension point FLSC0 associated to FLC0 was invariant. Texture depends on deformation trajectory and its intensity increases with the deformation along rolling direction.

This dissertation focuses on the study of spectral stability in traveling waves, with a special interest in planar detonations in the multidimensional reactive Navier-Stokes equations. The chief tool is the Evans function, combined with STABLAB, a numerical library devoted to calculating the Evans function. Properly constructed, the Evans function is an analytic function in the right half-plane whose zeros correspond in multiplicity and location to the spectrum of the traveling wave. Thus the Evans function can be used to verify stability, or to locate precisely any unstable eigenvalues. We introduce a new method that uses numerical continuation to follow unstable eigenvalues as system parameters vary. We also use the Evans function to track instabilities of viscous detonations in the multidimensional reactive Navier-Stokes equations, building on recent results for detonations in one dimension. Finally, we introduce a Python implementation of STABLAB, which we hope will improve the accessibility of STABLAB and aid the future study of large, multidimensional systems by providing easy-to-use parallel processing tools.