Le contexte de ma thèse rentre dans le cadre du projet IMD3D, supporté par le FUI. L'objectif de ce projet consiste à proposer une méthode automatisée permettant la décoration d'objets 3D quelconques. La solution choisie consiste à positionner un film imprimé dans le moule, ce film sera déformé par la fermeture du moule puis par injection. Ma thèse porte sur la génération de décoration. Les données dont nous disposons en entrée sont un maillage et une ou plusieurs images. Nous souhaitons d'abord obtenir le plaquage de cette image sur le maillage, de telle sorte que le rendu visuel soit équivalent à l'image initiale. Pour cela, nous avons décidé de choisir un point de vue par image et de le favoriser. Nous paramétrions alors le maillage par le biais d'une projection orthogonale ou perspective définie par ce point de vue. Nous réalisons alors la transformée inverse de déformation du maillage. L'utilisation d'une application conforme pour la déformation inverse permet de coller au mieux à la physique du problème. Nous visualisons donc le résultat à imprimer sur le film. Il reste alors à générer la texture permettant de décorer l'objet injecté par le procédé. Il suffit de parcourir bilinéairement l'intérieur des mailles et simultanément la partie de l'image correspondante, de manière à remplir les pixels de l'image. Ceci permet d'obtenir finalement la texture finale qui sera imprimée sur le film. Mais, lors des premiers essais effectués par les industriels avec une mire colorée, un effet de décoloration a été relevé. Nous avons donc pris en compte ce changement de couleur pour modifier l'image et obtenir le résultat visuel escompte, même au niveau du rendu des couleurs / This work takes part in a global industrial project called IMD3D, which is supported by FUI and aims at decorating 3D plastic objects using Insert Molding technology with an automated process. Our goal is to compute the decoration of 3D virtual objects, using data coming from polymer film characterization and mechanical simulation. My thesis deals with the generation of decoration. Firstly, we want to map the texture onto the mesh, so that the visual rendering would be equivalent to the initial picture. In order to do so, we decided to choose a viewpoint per texture and to favor it. Thus, a specific view-dependent parameterization is defined. Thus, the first goal which is to define the texture mapping with visual constraints is reached. After this step, the inverse distortion of the mesh is performed. The use of a conformal map for this inverse transform allows to respect the physics issues. Therefore we get a planar mesh representing the initial mesh of simulation whose associated textures have also been modified by this transform. The result to be printed on the film can be viewed. Finally, the texture enabling the decoration of the object injected by the process can be generated. This texture combines information from several mapped images. The inner part of the mesh and in the same time the part of the corresponding texture shall be followed in a bilinear way in order to fill the pixel of the generated picture. But during the first tests performed by industries with a colors pattern, a discoloration effect was detected. As a consequence, we thought to take into account this color change to modify the picture and to obtain the expected visual rendering

Um desafio constante no projeto aerodinâmico de uma superfície é obter a forma geométrica que permite, baseado em uma determinada medida de mérito, o melhor desempenho possível. No contexto de projeto de aeronaves de transporte, o desempenho ótimo em cruzeiro é a principal meta do projetista. Nesse cenário, o uso da Dinâmica do Fluidos Computacional como não só uma ferramenta de análise mas também de síntese torna-se uma forma atrativa para melhorar o projeto de aeronaves que é uma atividade dispendiosa em termos de tempo e recursos financeiros. O método adotado para projeto aerodinâmico é baseado na teoria de controle ótimo. Essa abordagem para o problema de otimização aerodinâmica foi inicialmente proposta por Jameson (1997) e é chamada de método adjunto. Esse método apresenta uma grande diminuição de custo computacional se comparado com a abordagem de diferenças finitas para a otimização baseada em gradiente. Essa dissertação apresenta o método adjunto contínuo aplicado às equações de Euler. Tal método está inserido no contexto de um ciclo de projeto inverso aerodinâmico. Nesse ciclo, tanto o código computacional de solução das equações do escoamento quanto o código de solução das equações adjuntas foram desenvolvidos ao longo desse trabalho. Além disso, foi adotada uma metodologia de redução do gradiente da função de mérito em relação às variáveis de projeto. O algorítmo utilizado para a busca do mínimo da função de mérito é o steepest descent. Os binômios de Bernstein foram escolhidos para representar a geometria do aerofólio de acordo com a parametrização proposta por Kulfan e Bussoletti (2006). Apresenta-se um estudo dessa parametrização mostrando suas características relevantes para a otimização aerodinâmica. Os resultados apresentados estão divididos em dois grupos: validação do ciclo de projeto inverso e aplicações práticas. O primeiro grupo consiste em exercícios de projeto inverso nos quais são estabelecidas distribuições de pressão desejadas obtidas a partir de geometrias conhecidas, desta forma garante-se que tais distribuições são realizáveis. No segundo grupo, porém, as distribuições desejadas são propostas pelo projetista baseado em sua experiência e, portanto, não sendo garantida a realizabilidade dessas distribuições. Em ambos os grupos, incluem-se resultados nos regimes de escoamento transônico e subsônico incompressível. / A constant endeavor in aerodynamic design is to find the shape that yields optimum performance, according to some context-dependent measure of merit. In particular for transport aircrafts, an optimum cruise performance is usually the designers main goal. In this scenario the use of the Computational Fluid Dynamics (CFD) technique as not only an analysis tool but as a design tool becomes an attractive aid to the time and financial resource consuming activity that is aircraft design. The method adopted for aerodynamic design is based on optimal control theory. This approach to the design problem was first proposed by Jameson (1997) and it is called adjoint method. It shows a great computational cost advantage over the finite difference approach to gradient-based optimization. This dissertation presents an Euler adjoint method implemented in context of an inverse aerodynamic design loop. In this loop both the flow solver and the adjoint solver were developed during the course of this work and their formulation are presented. Further on, a gradient reduction methodology is used to obtain the gradient of the cost function with respect to the design variables. The method chosen to drive the cost function to its minimum is the steepest descent. Bernstein binomials were chosen to represent the airfoil geometry as proposed by Kulfan and Bussoletti (2006). A study of such geometric representation method is carried on showing its relevant properties for aerodynamic optimization. Results are presented in two groups: inverse design loop validation and practical application. The first group consists of inverse design exercises in which the target pressure distribution is from a known geometry, this way such distribution is guaranteed to be realizable. On the second group however, the target distribution is proposed based on the designers knowledge and its not necessarily realizable. In both groups the results include transonic and subsonic incompressible conditions.

Este trabalho apresenta uma formulação do Método dos Elementos Discretos (MED) utilizando uma abordagem vetorial para o tratamento das rotações. As rotações são calculadas com a parametrização de Rodrigues. As principais contribuições do trabalho são: o cálculo dos deslocamentos tangentes utilizando o vetor das rotações incrementais da parametrização de Rodrigues; e, a integração do movimento de rotação utilizando o método leapfrog com as expressões da parametrização das rotações de Rodrigues. A formulação é apresentada para partículas esféricas e superelipsóides. O cálculo do deslocamento tangente, que é utilizado para o cálculo das forças de atrito, é feito a partir da velocidade angular da partícula. Em geral, o deslocamento tangente é calculado a partir da velocidade linear instantânea do ponto de contato. Aqui, o deslocamento do ponto de contato é dado pelo movimento da partícula, tanto de translação quanto de rotação. Apesar da abordagem por meio de rotações, é mostrado este cálculo pode ser feito sem o uso de tensores de segunda ordem. O movimento da partícula é descrito por uma abordagem incremental. É apresentada uma formulação do método de integração leapfrog com a utilização da expressão das rotações sucessivas da parametrização de Rodrigues. A detecção do contato entre superelipsóides é feita por um método do tipo \"vetor normal comum\", resolvido como um problema de minimização. Os resultados mostram que a parametrização de Rodrigues pode ser utilizada com método dos elementos discretos tanto para a execução da rotação quanto para o cálculo de grandezas que envolvem este tipo de movimento como o deslocamento tangente. / This work presents a formulation for Discrete Element Method (DEM) adopting a vector ap-proach to solve rotations. Herein, rotations are solved using Rodrigues parameterization. The main contributions of this work are: tangential displacements using the incremental rotation vector from Rodrigues parameterization, and integration of the rotation movement using leap-frog method and Rodrigues rotation tensor. The formulations are presented to spheres and superelliptical particles. Tangential displacements, which are used to get friction forces, are calculated through angular velocity. In most of DEM implementations, tangential displacements are calculated through the instantaneous linear velocity of the contact point. Instead, here the displacement of the contact point is given through the rotation of the particle. It is showed that the vector of in-cremental rotations can be calculated through the angular velocity. Particle movement is described using an updated Lagrangian approach. Leapfrog method is formulated in such a way to use the Rodrigues expression for successive rotations. Contact detection between superellipsoids is solved using a technic called \"common normal approach\", and it is solved as a minimization problem. The results show that the Rodrigues parameterization can be applied to discrete element method to both execute rotations and to evaluate physical quantities that are related to this kind of movement as tangential displacement.

Améliorer la représentation de la couche limite stable constitue un des grands challenges de la prévision numérique du temps et du climat. Sa représentation est clé pour la prévision du brouillard, du gel des surfaces, des inversions de température, du jet de basse couche et des épisodes de pollution. De plus, à l'échelle climatique, la hausse de la température moyenne globale de l'air en surface impacte davantage les régions polaires : améliorer la représentation de la couche limite stable est un enjeu important pour réduire les incertitudes autour des projections climatiques. Depuis une quinzaine d'années, les exercices d'intercomparaison de modèles GABLS ont montré que le mélange turbulent dans la couche limite stable est généralement surestimé par les modèles de prévision du temps. En effet, de nombreux modèles intensifient artificiellement l'activité de leur schéma de turbulence afin d'éviter une décroissance inévitable du mélange lorsque la stabilité dépasse un seuil critique en terme de nombre de Richardson gradient. Ce problème numérique et théorique n'est pas en accord avec de nombreuses observations et simulations à haute résolution qui montrent une activité turbulente séparée en deux régimes : un régime faiblement stable dans lequel l'atmosphère est turbulente de manière continue et intense, et un régime très stable dans lequel la turbulence est très intermittente, anisotrope et faible en intensité. Ces travaux de thèse s'articulent autour de deux parties dont l'objectif principal est d'améliorer la paramétrisation de la turbulence dans le modèle atmosphérique de recherche Méso-NH développé conjointement par Météo-France et le Laboratoire d'Aérologie, et dans le modèle opérationnel AROME. Cette étude utilise une méthodologie communément employée dans le développement de paramétrisations qui consiste à comparer des simulations à très haute résolution qui résolvent les structures turbulentes les plus énergétiques (LES) à des simulations uni-colonnes d'un modèle méso-échelle. Plusieurs simulations 3D couvrant différents régimes de stabilité de l'atmosphère sont réalisées avec Méso-NH. Les limites du modèle LES en stratification stable sont documentées. Une première partie répond à la problématique de la surestimation du mélange dans le régime faiblement stable. Une expression originale pour la longueur de mélange est formulée. La longueur de mélange est un paramètre clé pour les schémas de turbulence associés à une équation pronostique pour l'énergie cinétique turbulente. Cette longueur de mélange non-locale combine un terme de cisaillement vertical du vent horizontal à une formulation existante qui repose sur la flottabilité. Le nouveau schéma est évalué dans des simulations 1D par rapport aux LES d'une part ; et dans le modèle opérationnel AROME par rapport aux observations de l'ensemble du réseau opérationnel de Météo-France d'autre part. Une deuxième partie apporte des éléments d'évaluation d'un schéma combinant deux équations pronostiques pour les énergies cinétiques et potentielles turbulentes. En condition stable, le flux de chaleur négatif contribue à la production d'énergie potentielle turbulente. L'interaction entre les deux équations d'évolution permet, via une meilleure prise en compte de l'anisotropie et d'un terme à contre gradient dans le flux de chaleur, de limiter la destruction de l'énergie turbulente dans les modèles. Dans les cas simulés, cette nouvelle formulation ne montre pas un meilleur comportement par rapport à un schéma à une équation pour l'énergie cinétique turbulente car le mécanisme d'auto-préservation n'est pas dominant par rapport au terme de dissipation. Il conviendra d'améliorer la paramétrisation du terme de dissipation dans le régime très stable. / The modeling of the stable atmospheric boundary layer is one of the current challenge faced by weather and climate models. The stable boundary layer is a key for the prediction of fog, surface frost, temperature inversion, low-level jet and pollution peaks. Furthermore, polar regions, where stable boundary layer predominates, are one of the region with the largest temperature rise : the stable boundary layer modeling is crucial for the reduction of the spread of climate predictions. Since more than 15 years, the GABLS models intercomparison exercices have shown that turbulent mixing in the stable boundary layer is overestimated by numerical weather prediction models. Numerous models artificially strengthen the activity of their turbulence scheme to avoid a laminarization of the flow at a critical value of the gradient Richardson number. The existence of this threshold is only a theoretical and a numerical issues. Numerous observations and high-resolution numerical simulations do not support this concept and show two different regimes : the weakly stable boundary layer that is continuously and strongly turbulent; and the very stable boundary layer globally intermittent with a highly anisotropic and very weak turbulence. This thesis aims at improving the turbulence scheme within the atmospheric research model Méso-NH developped by Météo-France and the Laboratoire d'Aérologie, and the operational weather forecast model AROME. We use a traditional methodology based on the comparison of high-resolution simulations that dynamically resolve the most energetic turbulent eddies (Large-Eddy Simulations) to single-column simulations. Several LES covering the weakly and the very stable boundary layer were performed with Méso-NH. The limits of applicability of LES in stratified conditions are documented. The first part of the study deals with the overmixing in the weakly stable boundary layer. We propose a new diagnostic formulation for the mixing length which is a key parameter for turbulence schemes based on a prognostic equation for the turbulent kinetic energy. The new formulation adds a local vertical wind shear term to a non-local buoyancy-based mixing length currently used in Méso-NH and in the French operational model AROME. The new scheme is evaluated first in single-column simulations with Méso-NH and compared to LES, and then in the AROME model with respect to observations collected from the operational network of Météo-France. The second part presents a theoretical and numerical evaluation of a turbulence scheme based on two prognostic equations for the turbulent kinetic and potentiel energies. In stratified conditions, the heat flux contributes to the production of turbulent potential energy. The laminarization of the flow is then limited by a reduction of the destruction of the turbulent kinetic energy by a better representation of the anisotropy and a counter-gradient term in the heat flux. On the simulated cases, this new formulation behaves similarly than the scheme with one equation for the turbulent kinetic energy because the self-preservation mechanism is not dominant compared to the dissipation term. Further research should improve the turbulent kinetic energy dissipation closure in the very stable regime.

O cálculo da área de poligonais geodésicas é um desafio matemático instigante. Como calcular a área de uma poligonal sobre o elipsóide, se seus lados não possuem parametrização conhecida? Alguns trabalhos já foram desenvolvidos no intuito de solucionar este problema, empregando, em sua maioria, sistemas projetivos equivalentes ou aproximações sobre esferas autálicas. Tais métodos aproximam a superfície de referência elipsoidal por outras de mais fácil tratamento matemático, porém apresentam limitação de emprego, pois uma única superfície não poderia ser empregada para todo o planeta, sem comprometer os cálculos realizados sobre ela. No Código de Processo Civil, Livro IV, Título I, Capítulo VIII, Seção III artigo 971 diz, em seu parágrafo único, que não havendo impugnação, o juiz determinará a divisão geodésica do imóvel. Além deste, existe ainda a Lei 10.267/2001, que regula a obrigatoriedade, para efetivação de registro, dos vértices definidores dos limites dos imóveis rurais terem suas coordenadas georreferenciadas ao Sistema Geodésico Brasileiro (SGB), sendo que áreas de imóveis menores que quatro módulos fiscais terão garantida isenção de custos financeiros.Este trabalho visa fornecer uma metodologia de cálculo de áreas para poligonais geodésicas, ou loxodrômicas, diretamente sobre o elipsóide, bem como fornecer um programa que execute as rotinas elaboradas nesta dissertação. Como a maioria dos levantamentos geodésicos é realizada usando rastreadores GPS, a carga dos dados é pautada em coordenadas (X, Y, Z), empregando o Sistema Geodésico WGS-84, fornecendo a área geodésica sem a necessidade de um produto tipo SIG. Para alcançar o objetivo deste trabalho, foi desenvolvida parametrização diferente da abordagem clássica da Geodésia geométrica, para transformar as coordenadas (X, Y, Z) em geodésicas. / The area calculation of geodetic polygonal is a compelling mathematical challenge. How could one calculate the area of a polygon over the ellipsoid, if the sides do not have known parameterization? Some works have already been developed in order to solve this problem, employing mostly equivalent projective systems or authalic spheres approaches. Such methods near the ellipsoidal reference surface by other of easier mathematical treatment, but have limited employment, for a single surface cannot be used for the entire planet, without compromising the calculations over it. In the Code of Civil Procedure, Book IV, Title I, Chapter VIII, Section III, Article 971 says, in its sole paragraph, that "if there is no objection, the judge shall determine the division of the geodesic property. Besides this, there is the Law 10.267/2001, which regulates the requirement for effective registration, that the vertices defining the boundaries of the farms should have their geo-referenced coordinates to Brazilian Geodetic System (BGS), and areas of buildings less than four modules have guaranteed tax-free financial costs. This paper aims to provide a methodology of area calculation for traverses delimited by geodetic lines, or rhumb lines, directly on the ellipsoid, and provide a program that executes routines developed on this work. Since most geodetic surveys are developed using GPS equipment, the data input is based on (X, Y, Z) coordinates, using WGS-84 datum, providing the geodetic area without needing a GIS product. In order to achieve the paper objective, it was developed a different parameterization from the classical geometric Geodesy approach, to transform (X, Y, Z) coordinates into geodetic ones.

Une étude de sensibilité aux échelles kilométriques et hectométriques de simulations idéalisées de convection profonde montre qu’une résolution horizontale minimale de 1 km est nécessaire pour commencer à bien représenter les structures convectives et qu'il faut améliorer la turbulence dans les nuages convectifs. Une simulation LES (50 m de résolution) d'un nuage convectif profond permet d’obtenir les flux turbulents de référence, dégradés ensuite à différentes résolutions (2, 1 et 0.5 km), et d'évaluer ainsi la paramétrisation actuelle de la turbulence au sein des nuages convectifs. Les défauts mis en évidence sont une énergie cinétique turbulente insuffisante, liée à une sous-estimation de la production thermique notamment dans des zones à contre-gradient, et des vitesses verticales trop fortes. Une paramétrisation alternative de certains flux turbulents, basée sur des gradients horizontaux, montre une meilleure partition entre mouvements résolus et sous-maille à 1 km de résolution. / The purpose of adaptive observation (AO) strategies is to design optimal observation networks in a prognostic way to provide guidance on how to deploy future observations. The overarching objective is to improve forecast skill. Most techniques focus on adding observations. Some AO techniques account for the dynamical aspects of the atmosphere using the adjoint model and for the data assimilation system (DAS), which is usually either a 3D or 4D-Var (ie. solved by the minimization of a cost function). But these techniques rely on a single (linearisation) trajectory. One issue is to estimate how the uncertainty related to the trajectory aects the eciency of one technique in particular : the KFS. An ensemble-based approach is used to assess the sensitivity to the trajectory within this deterministic approach (ie. with the adjoint model). Experiments in a toy model show that the trajectory uncertainties can lead to signicantly diering deployments of observations when using a deterministic AO method (with adjoint model and VDAS). This is especially true when we lack knowledge on the VDAS component. During this work a new tool for observation targeting called Variance Reduction Field (VRF) has been developed. This technique computes the expected variance reduction of a forecast Score function that quanties forecast quality. The increase of forecast quality that is a reduction of variance of that function is linked to the location of an assimilated test probe. Each model grid point is tested as a potential location. The VRF has been implemented in a Lorenz 96 model using two approaches. The rst one is based on a deterministic simulation. The second approach consists of using an ensemble data assimilation and prediction system. The ensemble approach can be easily implemented when we already have an assimilation ensemble and a forecast ensemble. It does not need the use of the adjoint model. The implementation in real NWP system of the VRF has not been conducted during this work. However a preliminary study has been done to implement the VRF within OOPS (2013 version). After a description of the different components of OOPS, the elements required for the implementation of the VRF are described.

<p>New methods for global shape description of three-dimensional digital objects are presented. The shape of an object is first represented by a digital surface where the faces are either triangles or quadrilaterals. Techniques for computing a high-quality parameterization of the surface are developed and this parameterization is used to approximate the shape of the object. Spherical harmonics are used as basis functions for approximations of the coordinate functions. Information about the global shape is then captured by the coefficients in the spherical harmonics expansions.</p><p>For a starshaped object it is shown how a parameterization can be computed by a projection from its surface onto the unit sphere. An algorithm for computing the position at which the centre of the sphere should be placed, is presented. This algorithm is suited for digital voxel objects. Most of the work is concerned with digital objects whose surfaces are homeomorphic to the sphere. The standard method for computing parameterizations of such surfaces is shown to fail on many objects. This is due to the large distortions of the geometric properties of the surface that often occur with this method. Algorithms to handle this problem are suggested. Non-linear optimization methods are used to find a mapping between a surface and the sphere that minimizes geometric distortion and is useful as a parameterization of the surface. </p><p>The methods can be applied, for example, in medical imaging for shape recognition, detection of shape deformations and shape comparisons of three-dimensional objects.</p>

Due to its relevance for global climate, the realistic representation of the Atlantic meridional overturning circulation (AMOC) in ocean models is a key task.<br> In recent years, two paradigms have evolved around what are its driving mechanisms: diapycnal mixing and Southern Ocean winds. This work aims at clarifying what sets the strength of the Atlantic overturning components in an ocean general circulation model and discusses the role of spatially inhomogeneous mixing, numerical diffusion and winds. Furthermore, the relation of the AMOC with a key quantity, the meridional pressure difference is analyzed. <br><br> Due to the application of a very low diffusive tracer advection scheme, a realistic Atlantic overturning circulation can be obtained that is purely wind driven.<br> On top of the winddriven circulation, changes of density gradients are caused by increasing the parameterized eddy diffusion in the North Atlantic and Southern Ocean. The linear relation between the maximum of the Atlantic overturning and the meridional pressure difference found in previous studies is confirmed and it is shown to be due to one significant pressure gradient between the average pressure over high latitude deep water formation regions and a relatively uniform pressure between 30°N and 30°S, which can directly be related to a zonal flow through geostrophy. Under constant Southern Ocean windstress forcing, a South Atlantic outflow in the range of 6-16 Sv is obtained for a large variety of experiments. Overall, the circulation is winddriven but its strength not uniquely determined by the Southern Ocean windstress. <br><br> The scaling of the Atlantic overturning components is linear with the background vertical diffusivity, not confirming the 2/3 power law for one-hemisphere models without wind forcing. The pycnocline depth is constant in the coarse resolution model with large vertical grid extends. It suggests the ocean model operates like the Stommel box model with a linear relation of the pressure difference and fixed vertical scale for the volume transport. However, this seems only valid for vertical diffusivities smaller 0.4 cm²/s, when the dominant upwelling within the Atlantic occurs along the boundaries. For larger vertical diffusivities, a significant amount of interior upwelling occurs. It is further shown that any localized vertical mixing in the deep to bottom ocean cannot drive an Atlantic overturning. However, enhanced boundary mixing at thermocline depths is potentially important. <br><br> The numerical diffusion is shown to have a large impact on the representation of the Atlantic overturning in the model. While the horizontal numerical diffusion tends to destabilize the Atlantic overturning the verital numerical diffusion denotes an amplifying mechanism. / Wegen ihrer Bedeutung für das globale Klima ist die realistische Darstellung des Atlantischen meridionalen overturnings in Ozeanmodellen eine zentrale Aufgabe.<br> In den letzten Jahren haben sich zwei verschiedene Hypothesen darüber entwickelt, was diese Zirkulation antreibt: diapyknische Vermischung und Winde im südlichen Ozean.<br> Die vorliegende Arbeit zielt darauf aufzuklären, welche Rolle eine räumlich inhomogene Verteilung der Vermischung, die numerische Diffusion und Winde beim Bestimmen der Stärke des Atlantischen overturnings spielen. Ausserdem wird die Beziehung des Atlantischen overturnings zu meridionalen Druckgradienten untersucht. <br><br> Durch Anwenden eines sehr gering diffusiven Tracer-Advektionsschemas kann eine realistische Zirkulation erzeugt werden, die rein von den Winden im südlichen Ozean getrieben wird. Ausgehend von der windgetriebenen Zirkulation werden Änderungen der Dichtegradienten durch Verstärkung der parametrisierten Eddy Diffusion im Nordatlantik und südlichen Ozean hervorgerufen. Dadurch wird das Bild einer vom Wind bestimmten Zirkulation in der letztendlich Druckgradienten nicht ausschlaggebend sein würden, modifiziert. Das lineare Verhältnis zwischen dem Maximum des Atlantischen overturnings und dem meridionalen Druckgradienten wird bestätigt und erklärt. Diese Linearität ist auf einen signifikanten Druckgradienten zwischen den Tiefenwasserbildungsgebieten und einem zwischen 30°N and 30°S homogenen Druck zurückzuführen. Der Volumentransport bei 30°S variiert über eine Bandbreite von 10 Sv für verschiedene Experimente unter konstantem Wind über dem südlichen Ozean. Zusammenfassend ist die Zirkulation zwar windgetrieben aber ihre Stärke nicht allein vom Wind bestimmt. <br><br> Die Skalierung des Atlantischen overturnings ist linear mit vertikaler Vermischung, was die Skalierung mit einem Exponenten von 2/3 in ein-hemisphärischen Modellen ohne Wind-Antrieb nicht bestätigt. Die Tiefe der Pyknokline bleibt mit der groben vertikalen Auflösung konstant. Die Ergebnisse deuten darauf hin, dass das Ozeanmodell sich wie das Stommel-Box Modell verhält mit einer linearen Beziehung zum meridionalen Druckgradienten und einer festen vertikalen Skala für den Volumentransport. Das scheint jedoch nur für Diffusivitäten kleiner als 0.4 cm²/s zu gelten, wenn das Aufsteigen im Atlantischen Ozean bevorzugt an den Ozeanrändern statt findet. <br><br> In Bezug auf den Antrieb des Atlantischen overturnings wird gezeigt, dass vertikale Vermischung in der Nähe des Ozeanbodens keinen Einfluss hat. Verstärkte vertikale Vermischung an den Ozeanrändern in der Tiefe der Thermokline jedoch ist potentiell wichtig. <br><br> Die numerische Diffusion hat einen grossen Einfluss auf das Atlantische overturning im Modell. Während die horizontale numerische Diffusion das overturning eher zu destabilisieren tendiert, bewirkt die vertikale numerische Diffusion einen Verstärkungsmechanismus.

New methods for global shape description of three-dimensional digital objects are presented. The shape of an object is first represented by a digital surface where the faces are either triangles or quadrilaterals. Techniques for computing a high-quality parameterization of the surface are developed and this parameterization is used to approximate the shape of the object. Spherical harmonics are used as basis functions for approximations of the coordinate functions. Information about the global shape is then captured by the coefficients in the spherical harmonics expansions. For a starshaped object it is shown how a parameterization can be computed by a projection from its surface onto the unit sphere. An algorithm for computing the position at which the centre of the sphere should be placed, is presented. This algorithm is suited for digital voxel objects. Most of the work is concerned with digital objects whose surfaces are homeomorphic to the sphere. The standard method for computing parameterizations of such surfaces is shown to fail on many objects. This is due to the large distortions of the geometric properties of the surface that often occur with this method. Algorithms to handle this problem are suggested. Non-linear optimization methods are used to find a mapping between a surface and the sphere that minimizes geometric distortion and is useful as a parameterization of the surface. The methods can be applied, for example, in medical imaging for shape recognition, detection of shape deformations and shape comparisons of three-dimensional objects.

Multi-ribbed serpentine belt is the core of the automotive accessory drive system, which distributes the engine power to other auxiliary systems of the car. Development of a belt life model is of a significant importance to the accessory drive system manufacturers, in order to prevent any premature failures of these belts. However, any numerical analysis on the belt life is heavily dependent on gaining an understanding of stress distribution in the belts under the operational loading conditions. The presented work demonstrates a new systematic approach for determining the hyperelastic material parameters of rubber with specific application in Finite Element Analysis (FEA) of serpentine accessory drive belts. This new approach can be used as a stand-alone tool by manufacturers to determine the stress distribution in the belt under operational conditions; the results of which can be applied to assess the life of accessory drive belts, in a relatively short time.