Disertační práce se zabývá soustavou lineárních diskrétních rovnic se zpožděním a řeší Cauchyovu úlohu s danou počáteční podmínkou užitím zde definovaných maticových funkcí. Odvozený vzorec je pak použit při řešení úlohy relativní řiditelnosti této soustavy. Je dokázáno kritérium řiditelnosti soustavy, nalezena množina všech řídicí funkcí a minimální funkce vyhovující dané úloze.

Dans cette thèse, nous nous intéressons à l’étude des courbes discrètes bruitées qui correspondent aux contours d’objets dans des images. Nous avons proposé plusieurs outils permettant de les analyser. Les points dominants (points dont l’estimation de la courbure est localement maximale) jouent un rôle très important dans la reconnaissance de formes et, nous avons développé une méthode non heuristique, rapide et fiable pour les détecter dans une courbe discrète. Cette méthode est une amélioration d’une méthode existante introduite par Nguyen et al. La nouvelle méthode consiste à calculer une mesure d’angle. Nous avons proposé aussi deux approches pour la simplification polygonale : une méthode automatique minimisant, et une autre fixant le nombre de sommets du polygone résultant. Ensuite, nous avons introduit un nouvel outil géométrique, nommé couverture tangentielle adaptative (ATC), reposant sur la détection des épaisseurs significatives introduites par Kerautret et al. Ces épaisseurs calculées en chaque point du contour à analyser, permettent d’estimer localement le niveau de bruit. Dans ce contexte notre algorithme de construction de la couverture tangentielle adaptative prend en considération les différents niveaux de bruits présents dans la courbe à étudier et ne nécessite pas de paramètre. Deux applications de l’ATC sont proposées en analyse d’images : d’une part la décomposition des contours d’une forme dans une image en arcs et en segments de droite et d’autre part, dans le cadre d’un projet avec une université d’Inde, autour du langage des signes et la reconnaissance des gestes de la main. Premièrement, la méthode de décomposition des courbes discrètes en arcs et en segments de droite est basée sur deux outils : la détection de points dominants en utilisant la couverture tangentielle adaptative et la représentation dans l’espace des tangentes du polygone, issue des points dominants détectés. Les expériences montrent la robustesse de la méthode w.r.t. le bruit. Deuxièmement, à partir des contours des mains extraits d’images prises par une Kinect, nous proposons différents descripteurs reposant sur des points dominants sélectionnés du contour des formes dans les images. Les descripteurs proposés, qui sont une combinaison entre descripteurs statistiques et descripteurs géométriques, sont efficaces et conviennent à la reconnaissance de gestes / In this thesis, we are interested in the study of noisy discrete curves that correspond to the contours of objects in images. We have proposed several tools to analyze them. The dominant points (points whose curvature estimation is locally maximal) play a very important role in pattern recognition and we have developed a non-heuristic, fast and reliable method to detect them in a discrete curve. This method is an improvement of an existing method introduced by Nguyen et al. The new method consists in calculating a measure of angle. We have also proposed two approaches for polygonal simplification: an automatic method minimizing, and another fixing the vertex number of the resulting polygon. Then we proposed a new geometric tool, called adaptive tangential cover ATC, based on the detection of meaningful thickness introduced by Kerautret et al. These thicknesses are calculated at each point of the contours allow to locally estimate the noise level. In this context our construction algorithm of adaptive tangential cover takes into account the different levels of noise present in the curve to be studied and does not require a parameter. Two applications of ATC in image analysis are proposed: on the one hand the decomposition of the contours of a shape in an image into arcs and right segments and on the other hand, within the framework of a project with an Indian university about the sign language and recognition of hand gestures. Firstly, the method to decompose discrete curves into arcs and straight segments is based on two tools: dominant point detection using adaptive tangential cover and tangent space representation of the polygon issued from detected dominant points. The experiments demonstrate the robustness of the method w.r.t. noise. Secondly, from the outlines of the hands extracted from images taken by a Kinect, we propose several descriptors from the selected dominant points computed from the adaptive tangential cover. The proposed descriptors, which are a combination of statistical descriptors and geometrical descriptors, are effective and suitable for gesture recognition

High power Gallium Nitride (GaN) based field effect transistors are used in many high power applications from RADARs to communications. These devices dissipate a large amount of power and sustain high electric fields during operation. High power dissipation occurs in the form of heat generation through Joule heating which also results in localized hot spot formation that induces thermal stresses. In addition, because GaN is strongly piezoelectric, high electric fields result in large inverse piezoelectric stresses. Combined with residual stresses due to growth conditions, these effects are believed to lead to device degradation and reliability issues. This work focuses on studying these effects in detail through modeling of Heterostructure Field Effect Transistors (HFETs) and metal oxide semiconductor hetero-structure field effect transistor (MOSHFETs) under various operational conditions. The goal is to develop a thorough understanding of device operation in order to better predict device failure and eventually aid in device design through modeling. The first portion of this work covers the development of a continuum scale model which couples temperature and thermal stress to find peak temperatures and stresses in the device. The second portion of this work focuses on development of a micro-scale model which captures phonon-interactions at the device scale and can resolve local perturbations in phonon population due to electron-phonon interactions combined with ballistic transport. This portion also includes development of phonon relaxation times for GaN. The model provides a framework to understand the ballistic diffusive phonon transport near the hotspot in GaN transistors which leads to thermally related degradation in these devices.

This thesis introduces spatial filtering, which is a technique to extend the time step size beyond the conventional stability limit for the Finite-Difference Time-Domain (FDTD) method, at the expense of transforming field nodes between the spatial domain and the discrete spatial-frequency domain and removing undesired spatial-frequency components at every FDTD update cycle. The spatially-filtered FDTD method is demonstrated to be almost as accurate as and more efficient than the conventional FDTD method via theories and numerical examples. Then, this thesis combines spatial filtering and an existing subgridding scheme to form the spatially-filtered subgridding scheme. The spatially-filtered subgridding scheme is more efficient than existing subgridding schemes because the former allows the time step size used in the dense mesh to be larger than the dense mesh CFL limit. However, trade-offs between accuracy and efficiency are required in complicated structures.

This thesis introduces spatial filtering, which is a technique to extend the time step size beyond the conventional stability limit for the Finite-Difference Time-Domain (FDTD) method, at the expense of transforming field nodes between the spatial domain and the discrete spatial-frequency domain and removing undesired spatial-frequency components at every FDTD update cycle. The spatially-filtered FDTD method is demonstrated to be almost as accurate as and more efficient than the conventional FDTD method via theories and numerical examples. Then, this thesis combines spatial filtering and an existing subgridding scheme to form the spatially-filtered subgridding scheme. The spatially-filtered subgridding scheme is more efficient than existing subgridding schemes because the former allows the time step size used in the dense mesh to be larger than the dense mesh CFL limit. However, trade-offs between accuracy and efficiency are required in complicated structures.

No description available.

The general scope of this thesis is aimed at investigating certain classes of discrete equations through the analysis of certain characteristics of the solutions of these equations. We construct new methods of analysis based on the growth of these characteristics that let us single out known integrable discrete equations from certain class of equations. These integrable discrete equations are discrete analogues of the famous Painleve equations.

Thesis (MScEng)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: The increased necessity to obtain power from other sources than conventional fossil fuels has led to the growing interest in solar power. The problem with the proposed technology is that it can only provide power during the day and therefore requires some sort of storage system, if power is to be supplied throughout the day and night. A number of storage systems exist, but the one of particular interest for this research, is packed rock beds. Rock beds have the advantage that if designed right, they have the potential to be one of the most cost effective means of storing thermal energy for solar power plants. Discrete Element Models (DEM) of rock beds were therefore developed through both experimental and numerical procedures, by conducting a series of sensitivity, calibration and verification studies. The developed models were then used to study various aspects associated with rock beds, which were either too impractical, impossible or too expensive to conduct through actual experimental work. This research focused specifically on the potential of constructing self-supporting tunnels within the rock beds in order to improve the air flow uniformity through the bed, while minimizing the pressure drop. It was observed that if the appropriate steps were followed, stable self-supporting tunnels could be formed. Valuable information such as the rock orientations resulting from different packing directions could also be derived from the models and finally, a method to convert the DEM models into the appropriate format such that it could be imported into a CFD preprocessor for future CFD studies, was developed. / AFRIKAANSE OPSOMMING: Die verhoogde noodsaaklikheid om energie te verkry uit ander bronne as konvensionele fossielbrandstowwe, het gelei tot die groeiende belangstelling in sonkrag energie. Die probleem met die voorgestelde tegnologie is dat dit net energie gedurende die dag kan voorsien en dus word daar ’n stoorstelsel benodig indien energie deur beide die dag en nag voorsien moet word. Tans bestaan daar wel ’n aantal van hierdie stoorstelsels, maar die een wat van besondere belang is in hierdie navorsing, is verpakte klip beddens. Klip beddens het die voordeel dat, indien dit reg ontwerp is, dit oor die potensiaal beskik om een van die mees koste-doeltreffende middels te wees vir die stoor van termiese energie vir sonkragstasies. Diskreet Element Modelle (DEM) van die klip beddens is ontwikkel deur gebruik te maak van beide experimentele en numeriese metodes waartydens ’n reeks sensitiwiteits-, kalibrasie- en verifiëring studies uitgevoer is. Die ontwikkelde modelle is gebruik om verskeie aspekte van klip beddens te ondersoek, wat of te onprakties, onmoontlik of te duur is vanuit ’n eksperimentele oogpunt. Hierdie navorsing het spesifiek gefokus op die potensiaal om self-ondersteunende tonnels binne in die klip beddens te vorm, ten einde die egaligheid van die lugvloei deur die bed te verbeter, terwyl die drukval geminimeer word. Daar is waargeneem dat stabiele self-ondersteunende tonnels wel gevorm kon word indien die toepaslike stappe gevolg is. Waardevolle inligting soos die klip oriëntasies wat as gevolg van die verskillende verpakkings rigtings onstaan kon ook vanuit die model verkry word. Ten slotte is ’n metode ontwikkel om die DEM modelle na die toepaslike formaat te omskep sodat dit ten einde gebruik kan word in numeriese vloeidinamika studies.

In a proposed design for a concentrated solar power tower, sand is irradiated by solar energy and transfers its energy to another fluid stream by means of a finned tube heat exchanger. To maximize heat transfer and minimize potential damage to the heat exchanger, it is desired to have a very uniform flow through the heat exchanger. However, performing full scale flow tests can be expensive, impractical, and depending upon the specific quantities of interest, unsuitable for revealing the details of what it happening inside of the flow stream. Thus, the discrete element method has been used to simulate and study particulate flows. In this project, the flow of small glass beads through a square pyramid shaped hopper and a wedge shaped hopper were studied at the lab scale. These flows were also simulated using computers running two versions of discrete element modeling software – EDEM and LIGGGHTS. The simulated results were compared against the lab scale flows and against each other. They show that, in general, the discrete element method can be used to simulate lab scale particulate flows as long as certain material properties are well known, especially the friction properties of the material. The potential for increasing the accuracy of the simulations, such as using better material property data, non-uniform particle size distributions, and non-spherical particle shapes, as well as simulating heat transfer within a granular flow are also discussed.

Dans cette thèse, nous étudions les transformations rigides dans le contexte de l'imagerie numérique. En particulier, nous développons un cadre purement discret pour traiter ces transformations. Les transformations rigides, initialement définies dans le domaine continu, sont impliquées dans de nombreuses applications de traitement d'images numériques. Dans ce contexte, les transformations rigides digitales induites présentent des propriétés géométriques et topologiques différentes par rapport à leurs analogues continues. Afin de s'affranchir des problèmes inhérents à ces différences, nous proposons de formuler ces transformations rigides dans un cadre purement discret. Dans ce cadre, les transformations rigides sont regroupées en classes correspondant chacune à une transformation digitale donnée. De plus, les relations entre ces classes de transformations peuvent être modélisées par une structure de graphe. Nous prouvons que ce graphe présente une complexité spatiale polynômiale par rapport à la taille de l'image. Il présente également des propriétés structurelles intéressantes. En particulier, il permet de générer de manière progressive toute transformation rigide digitale, et ce sans approximation numérique. Cette structure constitue un outil théorique pour l'étude des relations entre la géométrie et la topologie dans le contexte de l'imagerie numérique. Elle présente aussi un intérêt méthodologique, comme l'illustre son utilisation pour l'évaluation du comportement topologique des images sous des transformations rigides / In this thesis, we study rigid transformations in the context of computer imagery. In particular, we develop a fully discrete framework for handling such transformations. Rigid transformations, initially defined in the continuous domain, are involved in a wide range of digital image processing applications. In this context, the induced digital rigid transformations present different geometrical and topological properties with respect to their continuous analogues. In order to overcome the issues raised by these differences, we propose to formulate rigid transformations on digital images in a fully discrete framework. In this framework, Euclidean rigid transformations producing the same digital rigid transformation are put in the same equivalence class. Moreover, the relationship between these classes can be modeled as a graph structure. We prove that this graph has a polynomial space complexity with respect to the size of the considered image, and presents useful structural properties. In particular, it allows us to generate incrementally all digital rigid transformations without numerical approximation. This structure constitutes a theoretical tool to investigate the relationships between geometry and topology in the context of digital images. It is also interesting from the methodological point of view, as we illustrate by its use for assessing the topological behavior of images under rigid transformations