Made available in DSpace on 2015-05-15T11:46:20Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1326144 bytes, checksum: 8caf7598b3ff31900cccda592a06981f (MD5) Previous issue date: 2014-07-25 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we investigate monotonicity and symmetry properties of of solutions to equations involving the p-Laplace-Beltrami operator in hyperbolic space and sphere. The main tools used to obtain the result is a variant of the method of moving planes and a careful use of the maximum and comparison principles / Neste trabalho investigamos propriedades de simetria e monotonicidade de soluções para equações envolvendo o operador de p-Laplace-Beltrami no espaço hiperbólico e na esfera. As principais ferramentas empregadas para obtenção do resultado é uma variante do método dos planos móveis e um cuidadoso uso de princípios do máximo e de comparação

Les textures directionnelles forment la classe particulière des images texturées représentant des hypersurfaces (lignes dermiques, fibres de matériaux, horizons sismiques, etc.). Pour ce type de textures, la reconstruction d'hypersurfaces permet ainsi d'en décrire la géométrie et la structure. À partir du calcul préalable du champ d'orientation, des reconstructions peuvent être obtenues au moyen de la minimisation d'une équation aux dérivées partielles sous contraintes, linéarisée et résolue itérativement de manière optimale dans le domaine de Fourier.Dans ce travail, les reconstructions d'hypersurfaces sont considérées comme un moyen de description à la fois amont et aval de la géométrie des textures directionnelles. Dans une démarche amont, la reconstruction de faisceaux locaux et denses d'hypersurfaces conduit à un modèle de transformation d'espace permettant de déplier localement la texture ou son champ de gradient et d'améliorer l'estimation du champ d'orientation par rapport au classique tenseur de structure. Dans une démarche aval, des reconstructions d'hypersurfaces effectuées sur des supports polygonaux quelconques, isolés ou imbriqués, permettent d'obtenir des reconstructions plus pertinentes que par les méthodes existantes. Les démarches proposées mettent en œuvre des chaînes de transformations d'espace conformes (transformation de Schwarz-Christoffel, de Möbius, etc.) afin de respecter les contraintes et d'accéder à des schémas de résolution rapide. / Directional textures are the particular class of textured images representing hypersurfaces (dermal lines, material fibers, seismic horizons, etc.). For this type of textures, the reconstruction of hypersurfaces describes their geometry and structure. From the preliminary estimation of the orientation field, reconstructions can be obtained by means of the minimization of a partial differential equation under constraints, linearized and iteratively resolved in the Fourier domain.In this work, the reconstructions of hypersurfaces are considered as means of description both upstream and downstream of the geometry of the directional textures. In an upstream approach, the reconstruction of local and dense streams of hypersurfaces leads to a spatial transformation model to locally unfold the texture or its gradient field and to improve the estimation of the orientation field compared with the classic tensor structure. In a downstream approach, reconstructions of hypersurfaces carried out on any polygonal supports, either isolated or imbricated, lead to more accurate reconstructions than existing methods. The proposed approaches implement chains of conformal space transformations (transformation of Schwarz-Christoffel, Möbius, etc.) in order to respect the constraints and to access fast PDE solution schemes.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Based on the article “Hyperbolic Main Cycles on Hypersurface of R4”, Garcia, see [4], we will study the bending lines in the vicinity of a main loop, closed bending line, a hypersurface immersed in R4. For this, we will define the Poincaré transformation associated with the cycle and calculate its derivative. With this analysis, we show under what conditions we can become hyperbolic, with a small deformation in the immersion, a major cycle given. Finally, we will build an example of a hypersurface containing a hyperbolic primary cycle, based on the article “Surfaces Around Closed Main Curvature Lines, an Inverse Problem." Garcia, Mello and Sotomayor, see [5]. / Tomando como base o artigo “Hyperbolic Principal Cycles on Hyper-surface of R4", de Garcia, ver [4], estudaremos as linhas de curvatura na vizinhança de um ciclo principal, linha de curvatura fechada, de uma hipersuperfície imersa no R4. Para isso, definiremos a transformação de Poincaré associada ao ciclo e calcularemos a sua derivada. Com essa análise, mostraremos sob quais condições podemos tornar hiperbólico, com uma pequena deformação na imersão, um ciclo principal dado. E por fim, construiremos um exemplo de uma hipersuperfície contendo um ciclo principal hiperbólico, baseando-nos no artigo “Surfaces Around Closed Principal Curvature Lines, an Inverse Problem." de Garcia, Mello e Sotomayor, ver [5].

This work concerns the interrelationship between thermodynamic, kinetic and structural aspects of crystal polymorphism. It is both experimental and theoretical, and limited with respect to compounds to substituted monocyclic aromatics. Two polymorphs of the compound m-aminobenzoic acid have been experimentally isolated and characterized by ATR-FTIR spectroscopy, X-ray powder diffraction and optical microscopy. In addition, two polymorphs of the compound m-hydroxybenzoic acid have been isolated and characterized by ATR-FTIR spectroscopy, high-temperature XRPD, confocal Raman, hot-stage and scanning electron microscopy. For all polymorphs, melting properties and specific heat capacity have been determined calorimetrically, and the solubility in several pure solvents measured at different temperatures with a gravimetric method. The solid-state activity (ideal solubility), and the free energy, enthalpy and entropy of fusion have been determined as functions of temperature for all solid phases through a thermodynamic analysis of multiple experimental data. It is shown that m-aminobenzoic acid is an enantiotropic system, with a stability transition point determined to be located at approximately 156°C, and that the difference in free energy at room temperature between the polymorphs is considerable. It is further shown that m-hydroxybenzoic acid is a monotropic system, with minor differences in free energy, enthalpy and entropy. 1393 primary nucleation experiments have been carried out for both compounds in different series of repeatability experiments, differing with respect to solvent, cooling rate, saturation temperature and solution preparation and pre-treatment. It is found that in the vast majority of experiments, either the stable or the metastable polymorph is obtained in the pure form, and only for a few evaluated experimental conditions does one polymorph crystallize in all experiments. The fact that the polymorphic outcome of a crystallization is the result of the interplay between relative thermodynamic stability and nucleation kinetics, and that it is vital to perform multiple experiments under identical conditions when studying nucleation of polymorphic compounds, is strongly emphasized by the results of this work. The main experimental variable which in this work has been found to affect which polymorph will preferentially crystallize is the solvent. For m-aminobenzoic acid, it is shown how a significantly metastable polymorph can be obtained by choosing a solvent in which nucleation of the stable form is sufficiently obstructed. For m-hydroxybenzoic acid, nucleation of the stable polymorph is promoted in solvents where the solubility is high. It is shown how this partly can be rationalized by analysing solubility data with respect to temperature dependence. By crystallizing solutions differing only with respect to pre-treatment and which polymorph was dissolved, it is found that the immediate thermal and structural history of a solution can have a significant effect on nucleation, affecting the predisposition for overall nucleation as well as which polymorph will preferentially crystallize. A set of polymorphic crystal structures has been compiled from the Cambridge Structural Database. It is found that statistically, about 50% crystallize in the crystallographic space group P21/c. Furthermore, it is found that crystal structures of polymorphs tend to differ significantly with respect to either hydrogen bond network or molecular conformation. Molecular mechanics based Monte Carlo simulated annealing has been used to sample different potential crystal structures corresponding to minima in potential energy with respect to structural degrees of freedom, restricted to one space group, for each of the polymorphic compounds. It is found that all simulations result in very large numbers of predicted structures. About 15% of the predicted structures have excess relative lattice energies of <=10% compared to the most stable predicted structure; a limit verified to reflect maximum lattice energy differences between experimentally observed polymorphs of similar compounds. The number of predicted structures is found to correlate to molecular weight and to the number of rotatable covalent bonds. A close study of two compounds has shown that predicted structures tend to belong to different groups defined by unique hydrogen bond networks, located in well-defined regions in energy/packing space according to the close-packing principle. It is hypothesized that kinetic effects in combination with this structural segregation might affect the number of potential structures that can be realized experimentally. The experimentally determined crystal structures of several compounds have been geometry-optimized (relaxed) to the nearest potential energy minimum using ten different combinations of common potential energy functions (force fields) and techniques for assigning nucleus-centred point charges used in the electrostatic description of the energy. Changes in structural coordinates upon relaxation have been quantified, crystal lattice energies calculated and compared with experimentally determined enthalpies of sublimation, and the energy difference before and after relaxation computed and analysed. It is found that certain combinations of force fields and charge assignment techniques work reasonably well for modelling crystal structures of small aromatics, provided that proper attention is paid to electrostatic description and to how the force field was parameterized. A comparison of energy differences for randomly packed as well as experimentally determined crystal structures before and after relaxation suggests that the potential energy function for the solid state of a small organic molecule is highly undulating with many deep, narrow and steep minima. / QC 20110527