In der Dissertation werden Schranken für Abschätzungen des Kommutators in verschiedenen Normen gegeben. Den Ausgangspunkt bildet die Frobenius-Norm, für die eine überraschend kleine Schranke bewiesen werden kann. Auf diesem Resultat aufbauend lassen sich über eine spezielle Adaption der Interpolationsmethode von Riesz-Thorin scharfe Schranken bei Verwendung von Schatten- und Vektornormen weitestgehend bestimmen. Es werden ferner die Fälle untersucht, in denen die obere Abschätzung erreicht wird (sog. Maximalität). Eine wichtige Rolle spielen verschiedene Darstellungen der Ungleichung, welche vielfältige Interpretationsmöglichkeiten eröffen und Verbindungen der algebraischen Abschätzung zu einem wichtigen Satz der Differentialgeometrie über die Krümmung von Mannigfaltigkeiten aufzeigen.

No description available.

Afin de surmonter les difficultés de la méthode des éléments finis (MEF) liées à la forte dépendance de la solution au maillage, des méthodes sans maillage ont été développées durant les 20 dernières années. Ces techniques ont l’avantage de procurer des approximations très régulières, capables de répondre de manière plus satisfaisante aux exigences croissantes des applications. Cependant, certaines caractéristiques intrinsèques à la plupart de ces approches rendent leur mise en œuvre difficile : souvent des techniques supplémentaires spécifiques doivent être mises en place pour imposer les conditions aux limites et traiter les discontinuités physiques. Récemment, la méthode des éléments naturels (MEN) est apparue, se basant sur les concepts de diagramme de Voronoï et de voisins naturels. C’est une approche capable d’associer les avantages d’une approximation très régulière propre aux méthodes sans maillage et une mise en œuvre quasiment identique à la MEF. Cette thèse porte sur l’étude et le développement de la MEN dédiée aux applications du génie électrique. Le but principal de ce travail exploratoire est l’étude des limitations ainsi que des avantages et du potentiel de la MEN et ses concepts sous-jacents. Les analyses de performances de la méthode sont présentées. Sur les points ouverts tels que l’intégration numérique, la montée en ordre et l’interpolation vectorielle, des développements originaux sont proposés. / In order to overcome the limitations related to the finite element method’s (FEM) narrow dependency of the solution on the mesh, meshless or meshfree methods were developed over the last 20 years. These techniques present the advantage of yielding very smooth approximations, being able to respond more adequately to the increasing demands of applications. However, some intrinsic features of most of these approaches make the implementation difficult, often requiring additional specific techniques for the imposition of the boundary conditions and the treatment of physical discontinuities. Recently, the natural element method (NEM) was developed. This approach, based on the Voronoi diagram and the “natural neighbors” concepts, combines the advantages of very smooth approximations and a FEM-like implementation. This thesis focuses on the study and development of the NEM, dedicated to electrical engineering applications. The main purpose of this exploratory work is the study of the limitations, benefits and the potential of the NEM and its underlying concepts. Several analyses of NEM’s performance are presented. As far as the numerical integration, higher order approximations and the vector interpolation are concerned, original developments are proposed.

A presente tese trata da representação e da visualização volumétrica de dados espaciais, através das quais novas possibilidades para visualizar tridimensionalmente as propriedades dos solos são apresentadas. O uso de volumes nos processos avaliativos dos solos permite ver e explorar a estrutura complexa do fenômeno como um corpo contínuo no espaço, incorporando dessa forma a terceira dimensão na cartografia de solos. A metodologia de trabalho adotada compreende a aquisição, organização e codificação dos dados, como também a interpolação, formação e visualização de volumes, através da utilização de um Sistema de Informações Geográficas Tridimensional em conjunto com um programa para visualização de volumes. Os dados de solos são de natureza qualitativa e quantitativa e foram interpolados para sua representação contínua no espaço tridimensional. Os resultados obtidos para as representações volumétricas das propriedades físicas, químicas e morfológicas são uma nova forma de visualizar os solos e se constituem em uma fonte de novos conhecimentos para o estudo deste fenômeno. / This dissertation is on volume representation and visualization of spatial data. It aims at showing new possibilities to visualize soil’s properties on 3D. The use of volumes in soil’s evaluation processes allows one to visualize and to explore the phenomenon as a continuous body in the space bringing third dimension to soil cartography. The methodology of this research entails the acquisition, organization and coding of data, as well as volume interpolation, formation and visualization by means of 3D-GIS environment. Soil’s data are either qualitative or quantitative and they were interpolated in order to be continuously represented in 3D space. The outcome of volume representations of physical, chemical and morphological properties is a new way to visualize the soil and a new source of knowledge to the study of this phenomenon.

Dans cette thèse, nous proposons de construire de meilleurs modèles Processus Gaussiens (GPs) en intégrant les connaissances antérieures avec des données expérimentales. En raison du coût élevé de l’exécution d’expériences sur les systèmes physiques, les modèles numériques deviennent un moyen évident de concevoir des systèmes physiques. Traditionnellement, ces modèles ont été construits expérimentalement et itérativement; une méthode plus rentable de construction de modèles consiste à utiliser des algorithmes d’apprentissage automatique. Nous démontrons comment créer des modèles en intégrant une connaissance antérieure en modifiant les fonctions de covariance. Nous proposons des modèles GP pour différents phénomènes physiques en mécanique des fluides.De même, les lois physiques entre plusieurs sorties peuvent être appliquées en manipulant les fonctions de covariance. Pour chaque application, nous comparons le modèle proposé avec le modèle de l’état de l’art et démontrons les gains de coût ou de performance obtenus. / In this thesis, we propose to build better Gaussian Process (GP) modelsby integrating the prior knowledge of Aircraft design with experimental data. Due tothe high cost of performing experiments on physical systems, models become an efficientmeans to designing physical systems. We demonstrate how to create efficient models byincorporating the prior information from engineering design, mainly by changing the covariancefunctions of the GP.We propose GP models to detect onset of non-linearity, detectmodal parameters and interpolate position of shock in aerodynamic experiments. Similarly,physical laws between multiple outputs can be enforced by manipulating the covariancefunctions, we propose to integrate flight-mechanics to better identify loads using thesemodels. For each application we compare the proposed model with the state-of-the-artmodel and demonstrate the cost or performance gains achieved.

A presente tese trata da representação e da visualização volumétrica de dados espaciais, através das quais novas possibilidades para visualizar tridimensionalmente as propriedades dos solos são apresentadas. O uso de volumes nos processos avaliativos dos solos permite ver e explorar a estrutura complexa do fenômeno como um corpo contínuo no espaço, incorporando dessa forma a terceira dimensão na cartografia de solos. A metodologia de trabalho adotada compreende a aquisição, organização e codificação dos dados, como também a interpolação, formação e visualização de volumes, através da utilização de um Sistema de Informações Geográficas Tridimensional em conjunto com um programa para visualização de volumes. Os dados de solos são de natureza qualitativa e quantitativa e foram interpolados para sua representação contínua no espaço tridimensional. Os resultados obtidos para as representações volumétricas das propriedades físicas, químicas e morfológicas são uma nova forma de visualizar os solos e se constituem em uma fonte de novos conhecimentos para o estudo deste fenômeno. / This dissertation is on volume representation and visualization of spatial data. It aims at showing new possibilities to visualize soil’s properties on 3D. The use of volumes in soil’s evaluation processes allows one to visualize and to explore the phenomenon as a continuous body in the space bringing third dimension to soil cartography. The methodology of this research entails the acquisition, organization and coding of data, as well as volume interpolation, formation and visualization by means of 3D-GIS environment. Soil’s data are either qualitative or quantitative and they were interpolated in order to be continuously represented in 3D space. The outcome of volume representations of physical, chemical and morphological properties is a new way to visualize the soil and a new source of knowledge to the study of this phenomenon.

La SER, est la grandeur qui permet de quantifier le pouvoir réflecteur d'un objet, ou a contrario sa discrétion électromagnétique. Maîtriser la SER, voire la diminuer, est un enjeu majeur dans le domaine aéronautique de défense. C'est en particulier un gage de survivabilité pour les aéronefs. Historiquement, les fréquences RADAR d'intérêt étaient celles de la bande Super Haute Fréquence, ce qui équivaut à des longueurs d'onde de 2 à 30 centimètres. Des outils d'analyse adaptés ainsi que des moyens de mesure ou de caractérisation de la SER ont été mis au point. Ils se sont révélés extrêmement performants. On peut citer par exemple la chambre anéchoïque CAMELIA du CESTA. En revanche, dans le domaine des basses fréquences, il est plus délicat de réaliser des mesures précises. Pour des longueurs d'onde de 1 à 5 mètres, l'épaisseur des absorbants est souvent trop faible ; même les dimensions des chambres anéchoïques ne représentent que quelques longueurs d'onde. Notre objectif, lors de cette thèse, était de proposer et d'étudier des algorithmes nouveaux permettant d'améliorer ou de faciliter la caractérisation de la SER en basse fréquence. La notion de courants caractéristiques, introduite par Harrington et Mautz dans les années 70, puis reprise par Y. Morel dans le cas d'objets parfaitement conducteurs, permet la décomposition d'un courant induit quelconque en courants élémentaires. Les modes caractéristiques sont obtenus en faisant rayonner ces courants caractéristiques. Cependant, il n'existe pas d'outil de détermination des modes lorsque l'objet n'est plus parfaitement conducteur. Nous nous sommes donc dotés d'un tel outil, que nous avons construit et validé. Pour cela, nous avons repris dans un premier temps le cadre mathématique qui permet de définir l'opérateur de Perturbation, ses propriétés mathématiques et sa décomposition en éléments propres. Nous avons montré que cet opérateur discrétisé conserve ses propriétés mathématiques. Nous avons ensuite validé notre méthode de calcul direct des modes caractéristiques, issus de la diagonalisation de l'opérateur de perturbation discrétisé. Dans un deuxième temps, nous avons mené des études phénoménologiques. Nous avons tout d'abord observé l'évolution des éléments propres de l'opérateur de perturbation en fonction de l'impédance, et nous nous sommes intéressés au cas particulier de l'impédance égale à 1. Nous avons ensuite observé les phénomènes lorsque la fréquence évolue. En nous concentrant sur les valeurs propres, nous avons pu différencier deux types de modes. Enfin, nous avons détaillé quelques exemples d'applications concrètes de cette méthode de détermination des modes, qui permettent d'améliorer ou de faciliter la caractérisation de la SER en basse fréquence. L'outil ORFE (Outil de Reformulation, Filtrage et Extrapolation de données) permet d'atténuer les termes d'erreurs inhérents à toute caractérisation, et d'extrapoler des données existantes à des cas de figure non acquis ou non accessibles en mesure. Il a donné lieu à un brevet. Un outil d'interpolation de SER en basse fréquence a aussi été construit. Il permet d'obtenir de meilleurs résultats que l'interpolation linéaire de la SER. Nous avons aussi mis en place une méthode d'imagerie basse fréquence. Elle permet de localiser d'éventuels défauts de métallisation de l'objet considéré, en utilisant la base des courants caractéristiques. Enfin, nous avons présenté une méthodologie de caractérisation de SER qui intègre les limites des moyens de mesure. Nous avons mis en évidence que cette caractérisation donne une information absolue sur la SER de l'objet, dans un périmètre de validité. Un brevet a été déposé sur cette méthode. / This work focuses on RADAR Cross Section (RCS) measurements in the low frequency domain. Radar Cross Section (RCS) is a description of how an object reflects an incident electromagnetic wave. Quantitatively, RCS is the effective surface area that intercepts the incident wave and isotropically scatters the energy. Controlling RCS is a real challenge for aeronautic defence. In the past, RCS interest frequencies used to be in the Super High Frequency domain (wavelengths between 2 and 30 centimetres). RCS is mastered in this frequency domain, due to the use of bright point model and large anechoic chamber. On the other hand, RCS measurements cannot be entirely and accurately obtained in the low frequency domain because of experimental constraints. Indeed, absorbing coatings are too thin (compared to the wavelength) to be efficient, and the anechoic chamber is too small. The aim of the thesis was to suggest new algorithms that improve RCS low frequency characterization. The Characteristic Currents were first introduced by Harrington and Mautz in the early 70's and then studied by Y. Morel in his PhD thesis. This work highlights that the current of any Perfectly Electrically Conducting (PEC) object can be split into elementary currents. The characteristic modes are obtained by radiating the characteristic currents. However, there is no tool to determine the characteristic modes for non PEC object. In this thesis, such a tool has been built and validated. We _rst needed to set the mathematical framework. We defined the Perturbation Operator, its eigenvalues decomposition and its mathematical properties. We proved that the discrete Perturbation Operator keeps its properties. This method of modes determination has then been validated. We then presented two phenomenology studies. The first one deals with the impact of impedance on the eigenvalues and eigenvectors of the perturbation operator. We get particularly interested in the case of the impedance equal to 1. The second focuses on the impact of frequency, which led us to distinguish two kinds of modes. When finally listed some concrete applications of our method of modes determination, that led to improve RCS characterizations. The first tool named ORFE (it stands for Reformulation, Filtering and Extrapolation Tool), consists in reducing errors that are inherent in RCS measurements, and extrapolating data out of measurement range. This tool has been patented. A RCS frequency interpolation algorithm has also been built. We then implemented a low frequency imagery method. It consists in localizing some perturbation of metallization, by using the characteristic current basis. We finally presented a way to characterize RCS while taking low frequency experimental constraints into account. We show that this characterization gives information of the RCS of the object in a validity perimeter. This method has been patented too.

A presente tese trata da representação e da visualização volumétrica de dados espaciais, através das quais novas possibilidades para visualizar tridimensionalmente as propriedades dos solos são apresentadas. O uso de volumes nos processos avaliativos dos solos permite ver e explorar a estrutura complexa do fenômeno como um corpo contínuo no espaço, incorporando dessa forma a terceira dimensão na cartografia de solos. A metodologia de trabalho adotada compreende a aquisição, organização e codificação dos dados, como também a interpolação, formação e visualização de volumes, através da utilização de um Sistema de Informações Geográficas Tridimensional em conjunto com um programa para visualização de volumes. Os dados de solos são de natureza qualitativa e quantitativa e foram interpolados para sua representação contínua no espaço tridimensional. Os resultados obtidos para as representações volumétricas das propriedades físicas, químicas e morfológicas são uma nova forma de visualizar os solos e se constituem em uma fonte de novos conhecimentos para o estudo deste fenômeno. / This dissertation is on volume representation and visualization of spatial data. It aims at showing new possibilities to visualize soil’s properties on 3D. The use of volumes in soil’s evaluation processes allows one to visualize and to explore the phenomenon as a continuous body in the space bringing third dimension to soil cartography. The methodology of this research entails the acquisition, organization and coding of data, as well as volume interpolation, formation and visualization by means of 3D-GIS environment. Soil’s data are either qualitative or quantitative and they were interpolated in order to be continuously represented in 3D space. The outcome of volume representations of physical, chemical and morphological properties is a new way to visualize the soil and a new source of knowledge to the study of this phenomenon.

Bien que les méthodes de calcul peuvent donner de bons résultats, ils ne sont généralement pas en accord avec exactement les données d'essais en vol en raison des incertitudes dans les modelé de calcul de structure et aérodynamiques. Une méthode efficace est nécessaire pour la mise à jour des modelé aeroelastiques en utilisant les données d'essais en vol, les données d'essais de vibration au sol ( GVT ) et les données de soufflerie. Tout d'abord tous les développements ont été valides sur une section de l'aile 2D et sur un modèle 3D simple et après l'approche POD a été applique= a une configuration industrielle (modèle de soufflerie aile-fuselage et modèle d' avions complète). / Although computational methods can provide good results, they usually do not agree exactly with the flight test data due to uncertainties in structural and aerodynamic computational models. An effective method is required for updating computational aeroelastic models using the flight test data along with Ground Vibration Test (GVT) data and wind tunnel data. Firstly all developments have been validated on a 2D wing section and on a simple 3D model and after the POD approach has been applied to an industrial configuration (wing-fuselage wind tunnel model and complete aircraft model).

Deciphering the activity of chemical molecules against a pathogenic organism is an essential task in drug discovery process. Virtual screening, in which few plausible molecules are selected from a large set for further processing using computational methods, has become an integral part and complements the expensive and time-consuming in vivo and in vitro experiments. To this end, it is essential to extract certain features from molecules which in the one hand are relevant to the biological activity under consideration, and on the other are suitable for designing fast and robust algorithms. The features/representations are derived either from physicochemical properties or their structures in numerical form and are known as descriptors. In this work we develop two new molecular-fragment descriptors based on the critical analysis of existing descriptors. This development is primarily guided by the notion of coding degeneracy, and the ordering induced by the descriptor on the fragments. One of these descriptors is derived based on the simple graph representation of the molecule, and attempts to encode topological feature or the connectivity pattern in a hierarchical way without discriminating atom or bond types. Second descriptor extends the first one by weighing the atoms (vertices) in consideration with the bonding pattern, valence state and type of the atom. Further, the usefulness of these indices is tested by ranking and classifying molecules in two previously studied large heterogeneous data sets with regard to their anti-tubercular and other bacterial activity. This is achieved by developing a scoring function based on clustering using these new descriptors. Clusters are obtained by ordering the descriptors of training set molecules, and identifying the regions which are (almost) exclusively coming from active/inactive molecules. To test the activity of a new molecule, overlap of its descriptors in those cluster (interpolation) is weighted. Our results are found to be superior compared to previous studies: we obtained better classification performance by using only structural information while previous studies used both structural features and some physicochemical parameters. This makes our model simple, more interpretable and less vulnerable to statistical problems like chance correlation and over fitting. With focus on predictive modeling, we have carried out rigorous statistical validation. New descriptors utilize primarily the topological information in a hierarchical way. This can have significant implications in the design of new bioactive molecules (inverse QSAR, combinatorial library design) which is plagued by combinatorial explosion due to use of large number of descriptors. While the combinatorial generation of molecules with desirable properties is still a problem to be satisfactorily solved, our model has potential to reduce the number of degrees of freedom, thereby reducing the complexity.