This thesis considers two broad categories of shape-preserving transformations: physical transformations, in which the chemistry of the as-grown material remains constant but some structural change is introduced (i.e., conversion of dense silicon nanowires into porous silicon nanowires); and chemical transformations, in which the physical structure of the as-grown material remains constant but the chemical composition is changed (i.e., conversion of SiO2 photonic crystal fibers into MgF¬2 photonic crystal fibers). Part I of this thesis focuses on the development of a process which allows for the introduction of porosity into dense silicon nano- and microstructures (a shape preserving net physical transformation, albeit by chemical means), while Part II focuses on conversion of SiO2-based photonic structures, including three dimensional photonic crystals and hollow-core photonic crystal fibers into Mg2Si or MgF2 replicas with more desirable chemical compositions (a shape preserving net chemical transformation) possessing enhanced optical characteristics.

Non-Uniform Rational B-Splines (NURBS) curve has acquired great significance in the field of Computer Aided Design and Machining due to their ability to draw a large variety of shapes in an interactive computer graphics environment. A biarc curve is a composition of two circular arcs such that they are tangent continuous at the point of join. Biarcs have replaced traditionally used line segments in approximating curves and surfaces for generating tool paths of Computerised cutting machines called CNC (Computerised Numerical Controlled) machines. This is due to their ability to be at a greater proximity to the original curve with fewer number of segments. Since most of the machining tools can move only in straight lines and circular arcs, it is desirable that the tool paths be composed of biarcs and/or straight line segments. Shape preserving interpolation is a technique of drawing a curve through a set of points such that the shape represented by the data points are preserved. Both NURBS and biarc curves are not essentially shape preserving curves; however, if certain constraints are imposed on them, they are able to preserve the shape represented by the data points. This work proposes a technique that incorporates both NURBS and biarcs to perform the interpolation. The advantages are twofold; it acts as a common platform for the two techniques to operate together, which is novel, and the fitted NURBS curve can be approximated by biarcs, which has applications in the machining industry.

Non-Uniform Rational B-Splines (NURBS) curve has acquired great significance in the field of Computer Aided Design and Machining due to their ability to draw a large variety of shapes in an interactive computer graphics environment. A biarc curve is a composition of two circular arcs such that they are tangent continuous at the point of join. Biarcs have replaced traditionally used line segments in approximating curves and surfaces for generating tool paths of Computerised cutting machines called CNC (Computerised Numerical Controlled) machines. This is due to their ability to be at a greater proximity to the original curve with fewer number of segments. Since most of the machining tools can move only in straight lines and circular arcs, it is desirable that the tool paths be composed of biarcs and/or straight line segments. Shape preserving interpolation is a technique of drawing a curve through a set of points such that the shape represented by the data points are preserved. Both NURBS and biarc curves are not essentially shape preserving curves; however, if certain constraints are imposed on them, they are able to preserve the shape represented by the data points. This work proposes a technique that incorporates both NURBS and biarcs to perform the interpolation. The advantages are twofold; it acts as a common platform for the two techniques to operate together, which is novel, and the fitted NURBS curve can be approximated by biarcs, which has applications in the machining industry.

This research develops and applies nonparametric estimation tools in two sectors of interest of financial econometrics: risk management and market microstructure. In the first part we address the problem of estimating conditional quantiles in financial and economic time series. Research in this field received great impulse since quantile based risk measures such as Value at Risk (VaR) have become essential tools to assess the riskiness of trading activities. The great amounts of data available in financial time series allows building nonparametric estimators that are not subject to the risk of specification error of parametric models. A wavelet based estimator is developed. With this approach, minimum regularity conditions of the underlying process are required. Moreover the specific choice of the wavelets in this work leads to the constructions of shape preserving estimators of probability functions. In other words, estimates of probability functions, both densities and cumulative distribution functions, are probability functions themselves. This method is compared with competing methods through simulations and applications to real data. In the second part we carry out a nonparametric analysis of financial durations, that is of the waiting times between particular financial events, such as trades, quote updates, volume accumulation, that happen in financial markets. These data display very peculiar stylized facts one has to take into account when attempting to model them. We make use of an existing algorithm to describe nonparametrically the dynamics of the process in terms of its lagged realizations and of a latent variable, its conditional mean. The estimation devices needed to effectively apply the algorithm to our dataset are presented in this part of the work.

Shape-preserving silica magnesiothermic reduction is a gas-solid reaction used to convert complex, 3-dimensional SiO₂ structures into replicas composed of a two-phase product of MgO and Si. The MgO/Si components of this reaction are found to form an interwoven aggregate product structure, which is suitably robust that the MgO phase can be selectively dissolved to yield porous Si. Here, the kinetics and mechanisms of growth of this robust product structure have been studied. The aggregate product structure was deduced to result because stacked layers of MgO/Si product phases with planar interfaces are geometrically unstable, owing to the growth kinetics of the products. The interwoven nature of the aggregate may be explained by the presence of an amorphous magnesium silicate phase ahead of the MgO/Si product during reaction. Complex composition gradients in the magnesium silicate can lead to tortuous and branching growth of MgO and Si phases as the magnesium silicate is consumed by reaction. In addition, a large residual stress (> 5 GPa) was measured in the MgO/Si product layer formed during reaction of planar quartz. Despite the presence of such a large stress, no distortion or cracking of reacted structures was found to occur after reaction in the temperature range 650-900 °C. XRD-based residual stress measurements and morphological observations of product films on reacted quartz substrates were used to evaluate possible mechanisms of stress relief in the structure. It was found that the migration of MgO to the external surface of the product layer could be correlated to the rate of stress relaxation that occurred in annealed product films. Finally, applications of silica magnesiothermic reduction and derivative processes were studied in the fields of chemical catalysis and optical chemical sensing.

No description available.

Le rendu photo-réaliste traditionnel exige un effort manuel et des calculs intensifs pour créer des scènes et rendre des images réalistes. C'est principalement pour cette raison que la création de contenus pour l’imagerie numérique de haute qualité a été limitée aux experts et le rendu hautement réaliste nécessite encore des temps de calcul significatifs. Le rendu basé image (IBR) est une alternative qui a le potentiel de rendre les applications de création et de rendu de contenus de haute qualité accessibles aux utilisateurs occasionnels, puisqu'ils peuvent générer des images photo-réalistes de haute qualité sans subir les limitations mentionnées ci-dessus. Nous avons identifié trois limitations importantes des méthodes actuelles de rendu basé image : premièrement, chaque algorithme possède des forces et faiblesses différentes, en fonction de la qualité de la reconstruction 3D et du contenu de la scène, et un seul algorithme ne permet souvent pas d’obtenir la meilleure qualité de rendu partout dans l’image. Deuxièmement, ces algorithmes présentent de forts artefacts lors du rendu d’objets manquants ou partiellement reconstruits. Troisièmement, la plupart des méthodes souffrent encore d'artefacts visuels significatifs dans les régions de l’image où la reconstruction est de faible qualité. Dans l'ensemble, cette thèse propose plusieurs améliorations significatives du rendu basé image aussi bien en termes de vitesse de rendu que de qualité d’image. Ces nouvelles solutions sont basées sur le rendu sélectif, la substitution de modèle basé sur l'apprentissage, et la prédiction et la correction des erreurs de profondeur. / Traditional photo-realistic rendering requires intensive manual and computational effort to create scenes and render realistic images. Thus, creation of content for high quality digital imagery has been limited to experts and highly realistic rendering still requires significant computational time. Image-Based Rendering (IBR) is an alternative which has the potential of making high-quality content creation and rendering applications accessible to casual users, since they can generate high quality photo-realistic imagery without the limitations mentioned above. We identified three important shortcomings of current IBR methods: First, each algorithm has different strengths and weaknesses, depending on 3D reconstruction quality and scene content and often no single algorithm offers the best image quality everywhere in the image. Second, such algorithms present strong artifacts when rendering partially reconstructed objects or missing objects. Third, most methods still result in significant visual artifacts in image regions where reconstruction is poor. Overall, this thesis addresses significant shortcomings of IBR for both speed and image quality, offering novel and effective solutions based on selective rendering, learning-based model substitution and depth error prediction and correction.

Numerous organisms produce ornately detailed inorganic structures (often known as shells) with features on length scales from 50 nm to several centimeters. One class of such organisms are the diatoms; microscopic algae that form silica frustules. Another group of algae, the coccolithophorids, produce similar calcium carbonate structures. Over 100,000 species comprise these two classes of algae, every one of which is endowed with a unique cytoskeleton structure. Using various types of displacement reactions, the chemistry of the original structure can be modified to produce a new material. Magnesium vapor has been found to displace the silicon in diatom frustules to yield an MgO structure. The conversion has been reported at temperatures from 650°C to 900°C. In the current work, the conversion and processing of silica frustules to MgO was examined in depth. The effect of reaction temperature on grain size and extent of conversion was evaluated. With the goal of obtaining high purity MgO structures, various methods for removing the silicon products of reaction were investigated. Wet chemistry and high temperature vapor etches were evaluated. The MgO reaction served as an intermediate step in the production of magnesium tungstate diatoms, which were imbued with photoluminescent properties. Reactions were identified to allow the conversion of calcium carbonate (calcite) structures to alternative chemistries. Calcite sand-dollars were converted to calcium tungstate or calcium molybdate by aqueous solution chemistry. In this process, sand dollar tests (shells) and coccolithophore frustules were reacted with ammonium para-molybdate or ammonium para-tungstate. The reactions were evaluated for shape preservation, phase purity, and photoluminescence of the structures.