In modern society, cancer has become one of the most terrifying diseases because of its high and increasing death rate. The disease's deep impact demands extensive research to detect and eradicate it in all its forms. Breast cancer is one of the most common forms of cancer, and approximately one in nine women in the Western world will develop it over the course of their lives. Screening programmes have been shown to reduce the mortality rate, but they introduce an enormous amount of information that must be processed by radiologists on a daily basis. Computer Aided Diagnosis (CAD) systems aim to assist clinicians in their decision-making process, by acting as a second opinion and helping improve the detection and classification ratios by spotting very difficult and subtle cases. Although the field of cancer detection is rapidly developing and crosses over imaging modalities, X-ray mammography remains the principal tool to detect the first signs of breast cancer in population screening. The advantages and disadvantages of other imaging modalities for breast cancer detection are discussed along with the improvements and difficulties encountered in screening programmes. Remarkable achievements to date in breast CAD are equally presented. This thesis introduces original results for the detection of features from mammographic image analysis to improve the effectiveness of early cancer screening programmes. The detection of early signs of breast cancer is vital in managing such a fast developing disease with poor survival rates. Some of the earliest signs of cancer in the breast are the clusters of microcalcifications. The proposed method is based on image filtering comprising partial differential equations (PDE) for image enhancement. Subsequently, microcalcifications are segmented using characteristics of the human visual system, based on the superior qualities of the human eye to depict localised changes of intensity and appearance in an image. Parameters are set according to the image characteristics, which makes the method fully automated. The detection of breast masses in temporal mammographic pairs is also investigated as part of the development of a complete breast cancer detection tool. The design of this latter algorithm is based on the detection sequence used by radiologists in clinical routine. To support the classification of masses into benign or malignant, novel tumour features are introduced. Image normalisation is another key concept discussed in this thesis along with its benefits for cancer detection.

La thèse constitue une juxtaposition de plusieurs contributions originales à lélaboration et lanalyse de modèles numériques capables de décrire une vaste gamme découlements à surface libre ainsi que les phénomènes de transport associés. Deux axes principaux sous-tendent les recherches entreprises. Il sagit, dune part, dune contribution à létude de modèles visant à reproduire adéquatement les interactions du fluide avec divers constituants transportés, tels que de lair entraîné, un polluant ou des sédiments. Cette phase du travail inclut également la caractérisation et la prédiction du comportement de lécoulement en présence dune topographie mobile ou érodable, y compris dans le cas dun barrage en remblai subissant une surverse. Dautre part, partant du constat quune modélisation fidèle des processus de transport, notamment hydrosédimentaires, passe inévitablement par un raffinement du calcul hydrodynamique proprement dit, une partie des travaux effectués dans le cadre de cette thèse est spécifiquement orientée vers un enrichissement de la connaissance des champs hydrodynamiques au sein du modèle.

Diffusion Tensor MRI can be used to depict the anisotropy of tissue. Translation of this technique to moving objects such as the beating heart has recently become feasible, but remains a challenging task, often leading to high noise levels and limited accuracy. Ultimately, knowledge of the 3D fibre architecture of the myocardium invivo should allow for a better understanding of the cardiac function both in healthy and pathological situations. The main goal of the work presented in this thesis is to overcome the difficulties that such technology presents, by introducing a combination of image processing and analysis approaches. In particular, the characteristic ellipsoidal shape of the left ventricular chamber is used to introduce a shape-based prolate spheroidal coordinate frame that allows for comprehensive, robust and dedicated analysis of diffusion tensor data within the myocardial wall. It is shown that the description of this information is more compact in this coordinate frame. Furthermore, it is demonstrated that the acquisition limitations can be overcome by introducing an approximation scheme based on this coordinate frame. These techniques are tested on ex-vivo datasets to assess their fidelity and sensitivity. Finally, these techniques are applied in-vivo on a group of healthy volunteers, where 2D DTI slices of the LV were acquired at end diastole and end systole, using cardiac dedicated diffusion MR acquisition. Results demonstrate the advantages of using curvilinear coordinates both for the analysis and the approximation of cardiac DTI information. Resulting in-vivo fibre architectures were found to agree with previously reported studies on ex-vivo specimens. The outcome of this work can open the door for clinical applications and cardiac electrophysiology modelling, and improve the understanding of the left ventricular structure and dynamics.

L’objectif de cette thèse est de développer une méthode Galerkine discontinue d’ordre élevé capable de prendre en considération des simulations réalistes liées à la nanophotonique. Au cours des dernières décennies, l’évolution des techniques de lithographie a permis la création de structure géométriques de tailles nanométriques, révélant ainsi une large gamme de phénomènes nouveaux nés de l’interaction lumière-matière à ces échelles. Ces effets apparaissent généralement pour des objets de taille égale ou (très) inférieure à la longueur d’onde du champ incident. Ce travail repose sur le développement et l’implémentation de modèles de dispersion appropriés (principalement pour les métaux), ainsi que sur un large éventail de méthodes computationnelles classiques. Deux développements méthodologiques majeurs sont présentés et étudiés en détails: (i) les éléments courbes, et (ii) l’ordre d’approximation local. Ces études sont accompagnées de plusieurs cas-tests réalistes tirés de la nanophotonique. / The goal of this thesis is to develop a discontinuous Galerkin time-domain method to be able to handle realistic nanophotonics computations. During the last decades, the evolution of lithography techniques allowed the creation of geometrical structures at the nanometer scale, thus unveiling a variety of new phenomena arising from light-matter interactions at such levels. These effects usually occur when the device is of comparable size or (much) smaller than the wavelength of the incident field. This work relies on the development and implementation of appropriate models for dispersive materials (mostly metals), as well as on a large panel of classical computational techniques. Two major methodological developments are presented and studied in details: (i) curvilinear elements, and (ii) local order of approximation. This work is complemented with several physical studies of real-life nanophotonics applications.

The master's thesis deals with Navier-Stokes equations in curvilinear coordinates and their solution for quasi-potential flow. The emphasis is on detailed description of curvilinear space and its expression using Bézier curves, Bézier surfaces and Bézier bodies. Further, fundamental concepts of hydromechanics are defined, including potential and quasi-potential flow. Cauchy equations are derived as a result of the law of momentum conservation and continuity equation is derived as a result of principle of mass conservation. Navier-Stokes equations are then derived as a special case of Cauchy equations using Cauchy stress tensor of Newtonian compressible fluid. Further transformation into curvilinear coordinates is accomplished through differential operators in curvilinear coordinates and by using curvature vector of space curve. In the last section we use results from previous chapters to solve boundary value problem of quasi-potential flow, which was solved by finite difference method using Matlab environment.

This thesis deals with a new approach to the design of impeller, blade and spiral of centrifugal pump. The mathematic model of flow inside meridional section of impeller and spiral is based on the instruments of differential geometry applied to Bezier surfaces. This formerly introduced theory is more deeply developed in this thesis and the conclusions are applied to the design of centrifugal pump parts working with fluid. The main thesis output is the mathematic model and on its principles created software determined for the design of impeller, blade and spiral. The received results are exportable into one of the commonly used 3D modeling programs.

Les estuaires sont des zones à l’interface terre-mer au coeur de la question du devenir des apports continentaux drainés par les grands bassins versants. L’objet de cette étude est focalisé sur l’estuaire de la Loire et ses zones adjacentes (i.e. baie de Bourgneuf et le Mor-Bras) situés dans le nord-est du Golfe de Gascogne. C’est un environnement soumis à l’influence significative de la marée qui se propage en amont de l’embouchure à plus de 100 km, de forçages météorologiques de moyennes latitudes donc hautement variables qui induisent en particulier des débits fluviaux pouvant varier d’un facteur dix. Cette variabilité est étudiée à l’aide d’un modèle numérique et des outils de description de la circulation qui permettent de mieux cerner les temps de séjours et de transits des eaux continentales dans l’estuaire et vers les baies riveraines. L’approche s’appuie sur un modèle en grille structurée mais dont la malléabilité pour décrire la complexité du domaine à simuler est donnée par le caractère non orthogonal des mailles employées pour la discrétisation. Le choix d’un système de coordonnées optimale (covariantes ou contravariantes) est discuté puis implémenté dans le code MARS-3D. Ce nouvel outil est qualifié et validé sur des cas-test puis implémenté en conditions réelles sur un domaine à la géométrie particulièrement accidentée. Les simulations reproduisent très finement la dynamique du grand panache de la Loire et confirment sa très grande variabilité spatiale et temporelle que décrivent partiellement des observations à haute fréquence et ponctuelles ; elles permettent de décrire les chemins privilégiés des masses d’eau à travers les sections de références choisies. / Estuaries are key areas in between land and ocean which play a major role in the spreading ofcontinental runoff drained by large watershed. This study focused on the Loire Estuary and its adjacentbays (i.e. Bourgneuf bay and Mor-Braz sea) all located in the north-east side of the bay of Biscay. It isinfluenced by the large tidal wave that propagates upstream the mouth on more than a 100 km, by highlymid-latitude meteorological forcing that may not only induced High variability in the circulation driversbut also on the river runoffs that may vary from 1 to 10 from early spring to late summer. This Highvariability is studied thanks to numerical simulation and tools dedicated to describe the circulation withsynthetic index such as transit time and mean age of water. The approach lies on a numerical modeldiscretized on a structure grid which constraints have been relaxed to better fit the fractal coastal lineusing non orthogonal grid cells. The optimal coordinate framework (co or contra-variant) have beendiscussed, and implemented within a pre-existing code (i.e. MARS-3D). This tools was validated withtest cases and implemented on a domain with a particular complex geometry. The numerical simulationscatch very accurately the dynamic of this large plume at least as it is described by available in situobservations. This numerical solution allowed to exhibit the main path of water masses through the areaand from place to place and their variability according to the main forcings.

In this thesis we look at acoustic wave propagation under water. We look in particular at waves generated by a point source and what happens with the propagation when we model the bottom as flat or as curvilinear. We assume the source to be working at a certain frequency and therefore we model this problem by solving the Helmholtz equation. Since Helmholtz equation has some unwanted numerical properties we are interested in finding new numerical methods that could accelerate the solver. In this thesis we use the Waveholtz iteration, which solves Helmholtz equation by connecting it to the time-dependent wave equation. We use finite differences and the SBP-SAT method to approximate the spatial problem numerically and for modelling the sea bottom we use curvilinear coordinates.  To compare the Waveholtz iteration we also solve Helmholtz equation with a naive solver. The naive solver consists of approximating the equation with finite differences and then solving the linear system of equation by some iterative solver, which for our tests will be GMRES. The results show that the Waveholtz iteration converges in less iterations than our naive solver. It also shows that the number of iterations stays unchanged when changing our discretization, which otherwise is a big problem for our naive solver. This allows us to increase the accuracy of our numerical solution without changing the computation time too much.  We show that the number of iterations increases according to theory for an increasing frequency, and that for open problems we even see a smaller increase. For certain resonant frequencies in Helmholtz equation we do not expect the Waveholtz iteration to converge. In the neighbourhood of these frequencies the convergence becomes slow and we need many iterations for a solution of a certain accuracy. By reformulating the Waveholtz iteration as a Krylov solution we can see that resonances in Helmholtz equation have a smaller impact of the convergence. / I detta examensarbete undersöker vi akustisk vågutbredning i vatten. Vi kollar specifikt på vågor som genereras av en punktkälla och vad som sker när vi modellerar botten som plan eller som kurvlinjär. Då vi antar att punktkällan arbetar vid en bestämd frekvens, kommer vi modellera det fysikaliska problemet genom att lösa Helmholtz ekvation. Helmholtz ekvation har dock några numeriska egenskaper som är oönskade, och därför finns ett intresse av att hitta nya numeriska metoder som löser ekvationen. I detta examensarbete undersöker vi Waveholtz iteration, som löser Helmholtz ekvation genom att koppla den till den tidsberoende vågekvationen. Vi använder finita differenser och SBP-SAT metoden för att approximera det rumsliga problemet numeriskt. För att ge en detaljerad beskrivning av botten använder vi kurvlinjära koordinater. För att jämföra Waveholtz iterationen med något löser vi även Helmholtz med hjälp av en naiv lösare. Den naiva lösaren består av att approximera problemet med finita differenser och sedan lösa det linjära systemet rakt av med en iterativ lösare (vilket för våra fall kommer vara GMRES). Resultatet visar att Waveholtz iteration konvergerar på ett lägre antal iterationer än vår naiva lösare. Det visar även att antalet iterationer inte förändras när vi ändrar diskretisering, vilket annars är ett problem för vår naiva lösare. Detta innebär att vi kan få en högre noggrannhet utan att förlänga beräkningstiden alltför mycket.  Vi visar även att antalet iterationer ökar som förväntat med en ökad frekvens, samt att för öppna problem så ökar antalet iteration mindre än enligt teorin. Vid vissa resonanta frekvenser i Helmholtz ekvation förväntar vi oss att Waveholtz iteration inte kommer konvergerar. I närheten av dessa frekvenser blir konvergensen långsam och vi behöver många iterationer för att lösa problemet. Genom att formulera Waveholtz iteration som en Krylov lösning kommer resonanser i Helmholtz ekvation ge en mindre negativ effekt på konvergensen än om den är formulerad som en fixpunkts iteration.

Space weather is the field within the space sciences that studies how the Earths magnetosphere is influenced by the Sun. The Sun is constantly emitting dangerous radiation and plasma which in some cases can affect or damage the systems on Earth. Scientists have an interest in studying this interaction and therefore visualizations of space weather data are useful. OpenSpace is an interactive software that visualizes the entire known universe with real-time data. OpenSpace supports a range of different visualization methods and techniques, for this work, the relevant visualization tools are field lines and cut planes. GAMERA is a simulation model that simulates a wide range of situations where plasma is subjected to the influence of magnetic fields, the simulations are based on curvilinear grids. This project focuses on implementing data from GAMERA into OpenSpace. OpenSpace already supports a variety of different simulation models, although none that uses curvilinear grids for the data. The curvilinear grid can adapt to the specific shape and geometry of the data, allowing for more accurate data representation. The project aims to create a pipeline for reading data files from simulation runs and visualize it as field lines and cut planes. The files used in this project contain data suitable for volumes and field lines. The method was to first develop a reader to extract and manage desired data from HDF5 files in which the simulation data is stored. The data used to visualize field lines is rendered with an already existing component in OpenSpace. Secondly, a slice operation was developed to extract cut planes from the files containing data for volume visualization, these are then visualized with the help of a component for rendering cut planes which was developed during this work. The work led to a pipeline that reads and manages simulation data from GAMERA and the data is successfully visualized. However, there is room for improvement in color rendering, robustness and level of user interaction during runtime. / <p>Examensarbetet är utfört vid Institutionen för teknik och naturvetenskap (ITN) vid Tekniska fakulteten, Linköpings universitet</p>

Throughout time man has discovered that the human form, in all its harmonious proportion, can be used as a guide, gauge and tool to design and build structures. However, the human figure has not been the only organic form used to create architecture. Many animals create dwellings that synchronize with not only their own unique physical characteristics and survival instincts, but with their aesthetic preferences as well. It is logical that a design should respond to its surroundings, program and most importantly, its inhabitants. This thesis design is for two specific occupants: the cat and the human. They are both meant to inhabit the building wholly and simultaneously. The way each of them experiences and uses the space, however, differs greatly. For a building to survive it needs many of the same things as living creatures: sunlight, air and movement, to name a few. It also needs to function like a living creature. It must breathe, sleep, respond to the changing seasons, and adapt over time. This thesis is an investigation of how both human and cat can dwell in a building of harmonious proportion, scale, light, and material. / Master of Architecture