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.

In this thesis work, a 3D Synthetic Human Face Modelling Software is implemented using C++ and OpenGL. B&eacute / zier surfaces, B-spline surfaces, Nonuniform Rational B-spline surfaces, Hierarchical B-Spline surfaces and T-spline surfaces are evaluated as options for the surface description method. T-spline surfaces are chosen since they are found to be superior considering the requirements of the work. In the modelling process, a modular approach is followed. Firstly, high detailed facial regions (i.e. nose, eyes, mouth) are modelled, then these models are unified in a complete face model employing the merging capabilities of T-splines. Local and global features of the face model are parameterized in order to have the ability to create and edit various face models. To enhance the visual quality of the model, a region-variable rendering scheme is employed. In doing this, a new file format to define T-Spline surfaces is proposed. To reduce the computational and memory cost of the software, a simplified version of the T-Spline surface description method is proposed and used.

The most popular and fundamental portfolio optimization problem is Markowitz&#039 / s one period mean-variance portfolio selection problem. However, it is criticized because of its one period static nature. Further, the estimation of the stock price expected return is a particularly hard problem. For this purpose, there are a lot of studies solving the mean-variance portfolio optimization problem in continuous time. To solve the estimation problem of the stock price expected return, in 1992, Black and Litterman proposed the Bayesian asset allocation method in discrete time. Later on, Lindberg has introduced a new way of parameterizing the price dynamics in the standard Black-Scholes and solved the continuous time mean-variance portfolio optimization problem. In this thesis, firstly we take up the Lindberg&#039 / s approach, we generalize the results to a jump-diffusion market setting and we correct the proof of the main result. Further, we demonstrate the implications of the Lindberg parameterization for the stock price drift vector in different market settings, we analyze the dependence of the optimal portfolio from jump and diffusion risk, and we indicate how to use the method. Secondly, we present the Lagrangian function approach of Korn and Trautmann and we derive some new results for this approach, in particular explicit representations for the optimal portfolio process. In addition, we present the L2-projection approach of Schweizer for the continuous time mean-variance portfolio optimization problem and derive the optimal portfolio and the optimal wealth processes for this approach. While, deriving these results as the underlying model, the market parameterization of Lindberg is chosen. Lastly, we compare these three different optimization frameworks in detail and their attractive and not so attractive features are highlighted by numerical examples.

Anthropogenic atmospheric aerosols (suspended particulate matter) can modify the radiative balance (and climate) of the Earth by altering the properties and global distribution of clouds. Current climate models however cannot adequately account for many important aspects of these aerosol-cloud interactions, ultimately leading to a large uncertainty in the estimation of the magnitude of the effect of aerosols on climate. This thesis focuses on the development of physically-based descriptions of aerosol-cloud processes in climate models that help to address some of such predictive uncertainty. It includes the formulation of a new analytical parameterization for the formation of ice clouds, and the inclusion of the effects of mixing and kinetic limitations in existing liquid cloud parameterizations. The parameterizations are analytical solutions to the cloud ice and water particle nucleation problem, developed within a framework that considers the mass and energy balances associated with the freezing and droplet activation of aerosol particles. The new frameworks explicitly account for the impact of cloud formation dynamics, the aerosol size and composition, and the dominant freezing mechanism (homogeneous vs. heterogeneous) on the ice crystal and droplet concentration and size distribution. Application of the new parameterizations is demonstrated in the NASA Global Modeling Initiative atmospheric and chemical and transport model to study the effect of aerosol emissions on the global distribution of ice crystal concentration, and, the effect of entrainment during cloud droplet activation on the global cloud radiative properties. The ice cloud formation framework is also used within a parcel ensemble model to understand the microphysical structure of cirrus clouds at very low temperature. The frameworks developed in this work provide an efficient, yet rigorous, representation of cloud formation processes from precursor aerosol. They are suitable for the study of the effect of anthropogenic aerosol emissions on cloud formation, and can contribute to the improvement of the predictive ability of atmospheric models and to the understanding of the impact of human activities on climate.

Orientador: Dilson Amâncio Alves / Banca: Anna Diva Plasencia Lotufo / Banca: Edmárcio Antonio Belati / Resumo: Este trabalho apresenta o método de Newton desacoplado para o fluxo de carga continuado. O método foi melhorado por uma técnica de parametrização geométrica possibilitando assim o traçado completo das curvas P-V, e o cálculo do ponto de máximo carregamento de sistemas elétricos de potência, sem os problemas de mau condicionamento. O objetivo é o de apresentar de forma didática os passos envolvidos no processo de melhoria do método de Newton Desacoplado a partir da observação das trajetórias de solução do fluxo de carga. A técnica de parametrização geométrica que consiste na adição de uma equação de reta que passa por um ponto no plano formado pelas variáveis: tensão nodal de uma barra k qualquer e o fator de carregamento eliminam os problemas de singularidades das matrizes envolvidas no processo e ampliam o grupo das variáveis de tensão que podem ser usadas como parâmetro da continuação. Os resultados obtidos com a nova metodologia para o sistema teste do IEEE (14, 30, 57, 118 e 300 barras) e também para os sistemas reais de grande porte, o 638 barras do sistema Sul-Sudeste brasileiro e do sistema de 904 barras do sudoeste Americano, mostram que as características do método convencional são melhoradas na região do ponto de máximo carregamento e que a região de convergência ao redor da singularidade é sensivelmente aumentada. São apresentados vários testes com a finalidade de prover um completo entendimento do funcionamento do método proposto e também avaliar seu desempenho / Abstract: This work presents the decoupled Newton method for continuation power flow. The method was improved by using a geometric parameterization technique that allows the complete tracing of P-V curves, and the computation of maximum loading point of a power system, without ill-conditioning problems. The goal is to present in a clear and didactic way the steps involved in the development of the improved decoupled Newton method obtained from the observation of the geometrical behavior of power flow solutions. The geometric parameterization technique that consists of the addition of a line equation, which passes through a point in the plane determined by the bus voltage magnitude and loading factor variables, can eliminate the ill-conditioning problems of matrices used by the method and can enlarge the set of voltage variables that can be used as continuation parameter to P-V curve tracing. The method is applied to the IEEE systems (14, 30, 57, 118 and 300 buses) and two large real systems: the south-southeast Brazilian system (638 buses) and the 904-bus southwestern American system. The results show that the best characteristics of the conventional decoupled Newton's method are improved in the vicinity of the maximum loading point and therefore the region of convergence around it is enlarged. Several tests are presented with the purpose of providing a complete understanding of the behavior of the proposed method and also to evaluate its performance / Mestre

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.

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.

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.

Forests in the southern United States with diverse forest ownership entities are facing threats associated with climate change and natural disturbances. This study represented the relationship between climate and species dominance, predicted future species distribution probability under a changing climate, and projected forest dynamics under ownership-based management regimes. Correlative statistics and mechanistic modeling approaches are implemented. Temporal scale includes the recent past 40 years and the future 60 years; spatial scale downscaled from southern United States to the coastal region of the northern Gulf of Mexico. In the southern United States, dominance of four major pine species experienced shifts from 1970 to 2000; quantile regression models built on the relationships among pine dominance and climatic variables can be used to predict future southern pine dominance. Furthermore, multiple climate envelope models (CEMs) were constructed for nineteen native and one invasive tree species (Chinese tallow, Triadica sebifera) to predict species establishment probabilities (SEPs) on the various land types from 2010 to 2070. CEMs achieved both predictive consistency and ecological conformity in estimating SEPs. Chinese tallow was predicted to have the highest invasionability in longleaf/slash pine and oak/gum/cypress forests during the next 60 years. Forest dynamics, in the coastal region, was projected by linking CEMs and forest landscape model (LANDIS) to evaluate ownership-based management regimes under climate change and natural disturbances. The dominance of forest species will diminish due to climate change and natural disturbances at both spatial scales—in the coastal region and non-industrial private forest (NIPF). No management on NIPF land was predicted to substantially increase the ratio of occupancy area between pines and oaks, but moderate and intensive management regimes were not significantly different. Pines are expected to be more resistant than oaks by maintaining stable age structures, which matched the forest inventory records. Overall, this study projected a future of southern forests on climate-species relationship, invasion risks, and forest community dynamics under multiple scenarios in the United States. Such knowledge could assist forest managers and landowners in foreseeing the future and making effective management prescriptions to mitigate potential threats.

The Swedish Armed Forces setup of the Weather Research and Forecasting Model (WRF) has problems to forecast low clouds in stably stratified conditions when the ground is covered by snow. The aim of this thesis is to understand what causes this deficit. Simulations during January and February 2018 are here compared with observations from Sodankylä in northern Finland. It is revealed that neither type of planetary boundary layer parameterization chosen nor vertical or horizontal interpolation are responsible for the deficiency. Instead, our experiments show that, to first order, poor initialization of Stratocumulus (Sc) clouds from the host model, Atmospheric Model High Resolution (HRES), of the Integrated Forecast System (IFS) is the missing link. In situations when Sc clouds are missing in the IFS analysis, although they exist in reality, we use information from vertical soundings from Sodankylä. In the initialization process we used the fact that liquid potential temperature is constant in a well-mixed cloud. Initializing cloud water and cloud ice from IFS HRES and from soundings with different methods improves the model performance and the formation of very low artificial clouds at the first model level is prohibited.