No description available.

In this master thesis, the goal was to devise design patterns and a fabrication processfor manufacturing a 3-D rotationally symmetric converging-diverging cold gasmicronozzle in silicon.The report explains the theory of etching and the methods involved. The work beginswith calculations and simulations of the etching processes. The chosen etch techniqueutilizes so called microloading and reactive ion etching lag effects, which essentially arephenomena where the etch rate can be adjusted by breaking up mask features intosubpatterns, and the etch depth for a given recipe and time can be made to differlocally. The subpatterns consisted of very small rectangles and triangles withalternating concentration. Five different recipes for the reactive ion etching weretried, where the coil power, platen power, pressure, temperature and time wasvaried.Etch rates could be made to differ locally depending on the concentration ofsubpatterns within the mask feature. The etch rates were also affected by the recipeparameters such as coil power, platen power, and pressure. High coil and platenpower increased the etch rate, while high pressure reduced the etch rate. The platenpower also affected the surface roughness.A solution for reducing misalignment problems in the future for the fusion bondingprocess resulted in the proposed moiré patterns that were made to showmisalignments down to 0.2 μm.Through scanning electron microscopy, the Nozzle 5_4_2 was concluded to have themost rotationally symmetric cross section at both the throat and the outlet. It hasthroat diameter of 31.1 μm with a depth of 34.2 μm and an outlet diameter of146.4 μm with a depth of 113.2 μm

The optical design for a dual modality endoscope based on piezo scanning fiber technology is presented including a novel technique to combine forward-viewing navigation and side viewing OCT. Potential applications include navigating body lumens such as the fallopian tube, biliary ducts and cardiovascular system. A custom cover plate provides a rotationally symmetric double reflection of the OCT beam to deviate and focus the OCT beam out the side of the endoscope for cross-sectional imaging of the tubal lumen. Considerations in the choice of the scanning fiber are explored and a new technique to increase the divergence angle of the scanning fiber to improve system performance is presented. Resolution and the necessary scanning density requirements to achieve Nyquist sampling of the full image are considered. The novel optical design lays the groundwork for a new approach integrating side-viewing OCT into multimodality endoscopes for small lumen imaging.

Este trabalho trata de estimativas inferiores para o primeiro autovalor do problema de Dirichlet para o Laplaciano para domínios relativamente compactos contidos em variedades riemannianas. Essas estimativas são obtidas com hipóteses sobre a curvatura seccional ou a curvatura de Ricci radial e a curvatura do bordo do domínio. / This paper deals of lower estimates for the first eigenvalue of the Dirichlet problem for the Laplacian for relatively compact domains contained in Riemannian manifolds. These estimates are obtained with assumptions on the sectional or Ricci radial curvature and the curvature of the boundary of the domain.

Este trabalho trata de estimativas inferiores para o primeiro autovalor do problema de Dirichlet para o Laplaciano para domínios relativamente compactos contidos em variedades riemannianas. Essas estimativas são obtidas com hipóteses sobre a curvatura seccional ou a curvatura de Ricci radial e a curvatura do bordo do domínio. / This paper deals of lower estimates for the first eigenvalue of the Dirichlet problem for the Laplacian for relatively compact domains contained in Riemannian manifolds. These estimates are obtained with assumptions on the sectional or Ricci radial curvature and the curvature of the boundary of the domain.

Este trabalho trata de estimativas inferiores para o primeiro autovalor do problema de Dirichlet para o Laplaciano para domínios relativamente compactos contidos em variedades riemannianas. Essas estimativas são obtidas com hipóteses sobre a curvatura seccional ou a curvatura de Ricci radial e a curvatura do bordo do domínio. / This paper deals of lower estimates for the first eigenvalue of the Dirichlet problem for the Laplacian for relatively compact domains contained in Riemannian manifolds. These estimates are obtained with assumptions on the sectional or Ricci radial curvature and the curvature of the boundary of the domain.

Dans cette thèse, nous nous intéressons au problème de tester en grande dimension l'uniformité sur la sphère-unité $S^{p_n-1}$ (la dimension des observations, $p_n$, dépend de leur nombre, $n$, et être en grande dimension signifie que $p_n$ tend vers l'infini en même temps que $n$). Nous nous restreignons dans un premier temps à des contre-hypothèses ``monotones'' de densité croissante le long d'une direction ${\pmb \theta}_n\in S^{p_n-1}$ et dépendant d'un paramètre de concentration $\kappa_n>0$. Nous commençons par identifier le taux $\kappa_n$ auquel ces contre-hypothèses sont contiguës à l'uniformité ;nous montrons ensuite grâce à des résultats de normalité locale asymptotique, que le test d'uniformité le plus classique, le test de Rayleigh, n'est pas optimal quand ${\pmb \theta}_n$ est connu mais qu'il le devient à $p$ fixé et dans le cas FvML en grande dimension quand ${\pmb \theta}_n$ est inconnu.Dans un second temps, nous considérons des contre-hypothèses ``axiales'', attribuant la même probabilité à des points diamétralement opposés. Elles dépendent aussi d'un paramètre de position ${\pmb \theta}_n\in S^{p_n-1}$ et d'un paramètre de concentration $\kappa_n\in\R$. Le taux de contiguïté s'avère ici plus élevé et suggère un problème plus difficile que dans le cas monotone. En effet, le test de Bingham, le test classique dans le cas axial, n'est pas optimal à ${\pmb \theta}_n$ inconnu et $p$ fixé, et ne détecte pas les contre-hypothèses contiguës en grande dimension. C'est pourquoi nous nous tournons vers des tests basés sur les plus grande et plus petite valeurs propres de la matrice de variance-covariance et nous déterminons leurs distributions asymptotiques sous les contre-hypothèses contiguës à $p$ fixé.Enfin, à l'aide d'un théorème central limite pour martingales, nous montrons que sous certaines conditions et après standardisation, les statistiques de Rayleigh et de Bingham sont asymptotiquement normales sous l'hypothèse d'invariance par rotation des observations. Ce résultat permet non seulement d'identifier le taux auquel le test de Bingham détecte des contre-hypothèses axiales mais aussi celui auquel il détecte des contre-hypothèses monotones. / In this thesis we are interested in testing uniformity in high dimensions on the unit sphere $S^{p_n-1}$ (the dimension of the observations, $p_n$, depends on their number, and high-dimensional data are such that $p_n$ diverges to infinity with $n$).We consider first ``monotone'' alternatives whose density increases along an axis ${\pmb \theta}_n\in S^{p_n-1}$ and depends on a concentration parameter $\kappa_n>0$. We start by identifying the rate at which these alternatives are contiguous to uniformity; then we show thanks to local asymptotic normality results that the most classical test of uniformity, the Rayleigh test, is not optimal when ${\pmb \theta}_n$ is specified but becomes optimal when $p$ is fixed and in the high-dimensional FvML case when ${\pmb \theta}_n$ is unspecified.We consider next ``axial'' alternatives, assigning the same probability to antipodal points. They also depend on a location parameter ${\pmb \theta}_n\in S^{p_n-1}$ and a concentration parameter $\kappa_n\in\R$. The contiguity rate proves to be higher in that case and implies that the problem is more difficult than in the monotone case. Indeed, the Bingham test, the classical test when dealing with axial data, is not optimal when $p$ is fixed and ${\pmb \theta}_n$ is not specified, and is blind to the contiguous alternatives in high dimensions. This is why we turn to tests based on the extreme eigenvalues of the covariance matrix and establish their fixed-$p$ asymptotic distributions under contiguous alternatives.Finally, thanks to a martingale central limit theorem, we show that, under some assumptions and after standardisation, the Rayleigh and Bingham test statistics are asymptotically normal under general rotationally symmetric distributions. It enables us to identify the rate at which the Bingham test detects axial alternatives and also monotone alternatives. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Neste trabalho estudamos o problema de Dirichlet assintótico para a equação das superfícies mínimas em uma superfície de Cartan-Hadamard rotacionalmente simétrica e mostramos que o problema e unicamente solúvel para qualquer dado contínuo em seu bordo assintótico. / In this work we study the asymptotic Dirichlet problem for the minimal surface equation on rotationally symmetric Cartan-Hadamard surfaces. We prove that the problem is uniquely solvave for any continuous asymptotic boundary data.

Neste trabalho estudamos o problema de Dirichlet assintótico para a equação das superfícies mínimas em uma superfície de Cartan-Hadamard rotacionalmente simétrica e mostramos que o problema e unicamente solúvel para qualquer dado contínuo em seu bordo assintótico. / In this work we study the asymptotic Dirichlet problem for the minimal surface equation on rotationally symmetric Cartan-Hadamard surfaces. We prove that the problem is uniquely solvave for any continuous asymptotic boundary data.

Neste trabalho estudamos o problema de Dirichlet assintótico para a equação das superfícies mínimas em uma superfície de Cartan-Hadamard rotacionalmente simétrica e mostramos que o problema e unicamente solúvel para qualquer dado contínuo em seu bordo assintótico. / In this work we study the asymptotic Dirichlet problem for the minimal surface equation on rotationally symmetric Cartan-Hadamard surfaces. We prove that the problem is uniquely solvave for any continuous asymptotic boundary data.