Aplicações industriais envolvendo escoamentos multifásicos são inúmeras, sendo que, o aprimoramento de alguns desses processos pode resultar em um grande salto tecnológico com significativo impacto econômico. O estudo numérico dessas aplicações é imprescindível, pois fornece informações precisas e mais detalhadas do que a realização de testes experimentais. Um grande desafio é o estudo numérico de escoamentos viscoelásticos multifásicos envolvendo altas taxa de elasticidade, devido às instabilidades causadas por altas tensões elásticas, grandes deformações, e até mudanças topológicas na interface. Assim, a investigação numérica desse tipo de problema exige uma formulação precisa e robusta. No presente trabalho, um novo resolvedor de escoamentos bifásicos envolvendo fluidos complexos é apresentado, com particular interesse em escoamentos com altas taxas de elasticidade. A formulação proposta é baseada no método Volume-of-fluid (VOF) para representação da interface e no algoritmo Continuum Surface Force (CSF) para o balanço de forças na interface. A curvatura e advecção da interface são calculados via métodos geométricos para garantir a precisão dos resultados. Métodos de estabilização são utilizados quando números críticos de Weissenberg (Wi) são encontrados, devido ao famoso problema do alto número de Weissenberg (HWNP). O método da projeção, combinado com um método implícito para solução da equação da quantidade de movimento, são discretizados por um esquema de diferenças finitas em uma malha deslocada. Problemas de benchmarks foram resolvidos para acessar a precisão numérica da formulação em diferentes níveis de complexidade física, tal como representação e advecção da interface, influência das forças interfaciais, e características reológicas do fluido. A fim de demonstrar a capacidade do novo resolvedor, dois problemas bifásicos transientes, envolvendo fluidos viscoelásticos, foram resolvidos: o efeito de Weissenberg e o reômetro extensional (CaBER). O efeito de Weissenberg ou rod-climbing effect consiste em um bastão que gira dentro de um recipiente com fluido viscoelástico e, devido às forças elásticas, o fluido escala o bastão. Os resultados foram comparados com dados teóricos, numéricos e experimentais, encontrados na literatura para pequenas velocidades angulares. Além disso, resultados obtidos com altas velocidades angulares (alta elasticidade) são apresentados com o modelo Oldroyd-B, em que escaladas muito elevadas foram observadas. Valores críticos da velocidade angular foram identificados, e para valores acima foi observada a ocorrência de instabilidades elásticas, originadas pela combinação de tensões elásticas, curvatura interfacial, e escoamentos secundários. Até onde sabemos, numericamente, essas instabilidades nunca foram capturadas antes. O CaBER consiste no comportamento e colapso de um filamento de fluido viscoelástico, formado entre duas placas paralelas devido às forças capilares. Esse experimento envolve consideráveis dificuldades, dentre as quais podemos destacar a grande influência das forças capilares e a diferença de escalas de comprimento no escoamento. Em grande parte dos resultados encontrados na literatura, o CaBER é resolvido por modelos simplificados em uma dimensão. Resultados obtidos foram comparados com tais resultados da literatura e com soluções teóricas, apresentando admirável precisão. / Industrial applications involving multiphase flow are numerous. The improvement of some of these processes can result in a major technological leap with significant economic impact. The numerical study of these applications is essential because it provides accurate and more detailed information than conducting experiments. A challenge is the numerical study of high viscoelastic multiphase flows due to instabilities caused by the high elastic tension, large deformations and even topological changes in the interface. Thus the numerical investigation of this problem requires a robust formulation. In this study a new two-phase solver involving complex fluids is presented, with particular interest in the solution of highly elastic flows of viscoelastic fluids. The proposed formulation is based on the volume-of-fluid method (VOF) to interface representation and continuum surface force algorithm (CSF) for the balance of forces in the interface. The curvature and interface advection are calculated via geometric methods to ensure the accuracy of the results. Stabilization methods are used when critical Weissenberg numbers are found due to the famous high Weissenberg number problem (HWNP). The projection method combined with an implicit method for the solution of the momentum equation are discretized by a finite difference scheme in a staggered grid. Benchmark test problems are solved in order to access the numerical accuracy of different levels of physical complexities, such as the dynamic of the interface and the role of fluid rheology. In order to demonstrate the ability of the new resolver, two-phase transient problems involving viscoelastic fluids have been solved, theWeissenberg effect problem and the extensional rheometer (CaBER). The Weissenberg effect problem or rod-climbing effect consists of a rod that spins inside of a container with viscoelastic fluid and due to the elastic forces the fluid climbs the rod. The results were compared with numerical and experimental data from the literature for small angular velocities. Moreover results obtained for high angular velocities are presented using the Oldroyd-B model, which showed high climbing heights. Critical values of the angular speed have been identified. For values above a critical level were observed the occurrence of elastic instabilities caused by the combination of elastic tension, interfacial curvature and secondary flows. To our knowledge, numerically these instabilities were never captured before. The CaBER consists of the behavior and collapse of a viscoelastic fluid filament formed between two parallel plates due to capillary forces. This experiment involves considerable difficulties, among which we can highlight the great influence of the capillary forces and the difference of the length scales in the flow. In much of the results found in the literature, the CaBER is solved by simplified models. The results were compared with results reported in the literature and theoretical solutions, which showed remarkable accuracy.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-03-03T12:21:26Z No. of bitstreams: 1 alexandrebittencourtpigozzo.pdf: 866787 bytes, checksum: c6792b0cf7e2393b912ea7c1c8fdae2c (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-03-06T20:06:30Z (GMT) No. of bitstreams: 1 alexandrebittencourtpigozzo.pdf: 866787 bytes, checksum: c6792b0cf7e2393b912ea7c1c8fdae2c (MD5) / Made available in DSpace on 2017-03-06T20:06:30Z (GMT). No. of bitstreams: 1 alexandrebittencourtpigozzo.pdf: 866787 bytes, checksum: c6792b0cf7e2393b912ea7c1c8fdae2c (MD5) Previous issue date: 2011-02-28 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O sistema imunológico humano (SIH) é composto por uma rede complexa de células, tecidos e órgãos especializados em defender o organismo contra doenças. Para atingir tal objetivo, o SIH identifica e extermina uma ampla gama de agentes patogênicos externos, como vírus e bactérias, além de células do próprio organismo que podem estar se comportando de forma anormal, e que poderiam dar origem a tumores, caso não fossem eliminadas. O SIH é ainda responsável pelo processo de eliminação de células mortas e renovação de algumas estruturas do organismo. A compreensão do SIH é, portanto, essencial. Entretanto a sua complexidade e a interação entre seus muitos componentes, nos mais diversos níveis, torna a tarefa extremamente complexa. Alguns de seus aspectos, no entanto, podem ser melhor compreendidos se modelados computacionalmente, permitindo a pesquisadores da área realizar um grande volume de experimentos e testar um grande número de hipóteses em um curto período de tempo. A longo prazo, pode-se vislumbrar um quadro onde todo o SIH poderá ser simulado, permitindo aos cientistas desenvolverem e testarem vacinas e medicamentos contra várias doenças, bem como contra a rejeição de órgãos e tecidos transplantados, diminuindo o uso de animais experimentais. Neste contexto, o presente trabalho visa implementar e simular computacionalmente um modelo matemático do SIH, sendo o objetivo principal reproduzir a dinâmica de uma resposta imune ao lipopolissacarídeo (LPS) em um pequena seção de um tecido. O modelo matemático é composto de um sistema de equações diferenciais parciais (EDPs) que incorpora a dinâmica de alguns tipos de células e moléculas do SIH durante uma resposta imune ao LPS no tecido. / The Human Immune System (HIS) consists of a complex network of cells, tissues and organs. The HIS plays an crucial role in defending the body against diseases. To achieve this goal, the immune system identifies and kills a wide range of external pathogens such as viruses and bacteria, and the body's own cells which are behaving abnormally. If these cells were not eliminated, they could give rise to tumors. The HIS is also responsible for removing dead cells and replacing some of the structures of the body. The understanding of the HIS is therefore essential. However, its complexity and the intense interaction among several components, in various levels, make this task extremely complex. Some of its aspects, however, may be better understood if a computational model is used, which allows researchers to test a large number of hypotheses in a short period of time. In the future we can envision a computer program that can simulate the entire HIS. This computer program will allow scientists to develop and test new drugs against various diseases, as well as to treat organ or tissue transplant rejection, without requiring animals experiments. In this scenario, our work aims to implement and simulate a mathematical model of the HIS. Its main objective is to reproduce the dynamics of a immune response to lipopoly-saccharides (LPS) in a microscopic section of a tissue. The mathematical model is composed of a system of partial differential equations (PDEs) that defines the dynamics of some tissues and molecules of the HIS during the immune response to the LPS.

An easy-to-use spreadsheet version of a finite difference method for progressive landslide analysis has been developed. The finite difference method was originally developed by Dr. Stig Bernander, earlier adjunct professor at Luleå University of Technology and head of the Design Department of Skanska AB in Gothenburg, Sweden.. The so called Muskrat Falls Project consists in the ongoing construction of a hydroelectric power plant in Churchill River Valley, Labrador, Canada. The site hosting the project includes a land ridge which is supposed to be used as a natural dam and thus be submitted to important water pressures. Yet, previous landslides in the area have shown that a stability analysis is worth to be carried out in order to ensure the safety of the facility. Until now, investigations have only been carried out using the traditional limit equilibrium method and related elastic-plastic theory. For the sake of simplicity, this approach does not take into account deformations outside and inside the sliding body. However, because of the soil features in Churchill River Valley and particularly its ‘deformation softening’ behavior, there is increasing evidence that the conventional analysis is not relevant in this situation. Further, when analyzing the total stability of the ridge, only a horizontal failure surface has been used and not an inclined one, which is very optimistic and rather unrealistic.. In order to provide a more reliable study, a progressive failure analysis has been performed according to the finite difference method of Dr. Stig Bernander. The development of a spreadsheet adapted to this particular problem has allowed getting quickly and easily numerical results for several cases of study and assumptions. For assumed material properties and geometries of failure, the critical load-carrying capacity is below 1000 kN/m whereas a rise of the water level with 21 m will give an increased load of Nq  = 2420 kN/m. This is more than twice of the what the ridge may stand with the assumed properties. The investigation has led to the conclusion that the situation will be risky for many combinations of soil properties if the water level is raised as high as initially planned. The investigation also shows that more material tests are necessary and that stabilization work may be needed to eliminate the risk for a landslide.

L'oxydation sélective conduit à un appauvrissement du substrat qui contribue aux phénomènes de corrosion sous contrainte. Afin de prédire cet appauvrissement en élément oxydable, un modèle basé sur la diffusion dans le substrat et l'équilibre des flux au niveau de l'interface alliage/oxyde a été développé. La cinétique d'oxydation du matériau est utilisée comme donnée d'entrée du modèle et permet de piloter le déplacement de l'interface alliage/oxyde.Le modèle d'appauvrissement développé a été validé dans la cas de l'oxydation de l'alliage binaire Pt-Ni à 850 °C, en reproduisant la solution analytique du modèle de Wagner. L'utilisation de la méthode des différences finies a permis de lever les hypothèses d'une concentration à l'interface alliage/oxyde et d'un coefficient d'interdiffusion constants.L'appauvrissement initial en élément oxydable d'un alliage binaire (passivation, pré-oxydation) a peu d'influence sur l'évolution de l'appauvrissement de l'alliage lors de son oxydation à haute température. En revanche, lorsque le coefficient d'interdiffusion de l'alliage est plus grand en subsurface qu'en volume de cet alliage (écrouissage), la concentration en élément oxydable au niveau de l'interface alliage/oxyde décroit au cours de l'oxydation. Les profils d'appauvrissement présentent alors un point d'inflexion dû à une diffusion plus rapide au voisinage de l'interface.Enfin, le modèle a été appliqué à l'oxydation en milieu aqueux à une température de 290 °C pour étudier la déchromisation de l'alliage 690 en milieu primaire des REP. Ceci a permis de conforter la cinétique d'oxydation logarithmique directe proposée dans la littérature pour cet alliage. / High temperature selective oxidation of alloys usually results in substrate depletion. This phenomenon can be at the origin of stress corrosion cracking (SCC) initiation. To predict the depletion of the oxidizable element, a model based on diffusion in the substrate and fluxes balance at the oxide/alloy interface has been developed. The oxidation kinetics is used as input data of the model in order to drive the oxide/alloy interface displacement when the oxidizable element is "consumed" from the alloy.The depletion model presented in this work has been validated in the case of the oxidation at 850 °C of the Pt-Ni binary alloy by reproducing the Wagner's analytical solution. The two assumptions of a fixed concentration at the oxide/alloy interface, and of a diffusion coefficient homogeneous in the substrate and constant during oxidation, have been relaxed using finite difference method.An initial depletion of a binary alloy in oxidizable element (passivation, pre-oxidation) has a low impact on the substrate depletion evolution during high temperature oxidation. However, when the interdiffusion coefficient in the alloy is greater in subsurface than in the bulk (work-hardening), the oxidizable element concentration at the oxide/alloy interface decreases during the oxidation. Depletion profiles show an inflexion point due to faster diffusion close to the interface.Finally, the model has been applied to oxidation in aquaous media at a temperature of 290 °C to study Cr-depletion of alloy 690 in PWR primary water. The direct logarithmic oxidation kinetics proposed in the literature has been validated

Tato diplomová práce se zabývá tématem výměny tepla v zásobníku tepla typu ”packed bed”. Cílem je popsat přenos tepla v zásobníku tepla obsahující kamínky malých průměrů, skrz který proudí horký vzduch. Toto je modelováno v prostředí MATLAB. Na začátku je krátký úvod do problematiky zahrnující ukládání tepla a jeho možné využití. Dále je uveden krátký přehled o základech přenosu tepla, typech přenosu tepla a termofyzikální vlastnosti systému vzduch-kámen. Ve třetí kapitole je představen zásobník tepla typu ”packed bed” a rozličné modely a dané podmínky jsou vysvětleny. Další kapitola se zabývá s numerickými metodami, převážně s metodou konečných diferencí použitou v této práci. Pátá kapitola se zaměřuje na obecnou optimalizaci daného problému přenosu tepla. Populačně založený metaheuristický optimalizační algoritmus zvaný Genetický algoritmus je popsán. Sestavení modelu je ukázáno v šesté kapitole, stejně jako prezentace výsledků získaných z programu MATLAB. V poslední kapitole je pak diskutován závěr a doporučení.

This thesis outlines an iterative approach for determining the scattered wave for two dimensional multiple acoustic scattering problems using high order local absorbing boundary conditions and second order finite difference. We seek to approximate the total wave as it is scattered off of multiple arbitrarily shaped obstacles. This is done by decomposing the scattered wave into the superposition of single scattered waves. We then repeatedly solve the single scattering system for each obstacle, while updating the boundary conditions based off the incident wave and the scattered wave off the other obstacles. We solve each single scattering by enclosing the obstacle in a circular artificial boundary and generating a curvilinear coordinate system for the computational region between the obstacle and the artificial boundary. We impose an absorbing boundary condition, specifically Karp's Farfield Expansion ABC, on the artificial boundary. We use a finite difference method to discretize the governing equations and to discretize the absorbing boundary conditions. This will create a linear system whose solution will approximate the single scattered wave. The forcing vector of the linear system is determined from the total influence on the obstacle boundary from the incident wave and the scattered waves from the other obstacles. In each iteration, we solve the singular acoustic scattering problem for each obstacle by using the scattered wave approximations from the other obstacles obtained from the previous iteration. The iterations continue until the solutions converge. This iterative method scales well to multiple scattering configurations with many obstacles, and achieves errors on the order of 1E-5 in less than five minutes. This is due to using LU factorization to solve the linear systems, paired with parallelization. I will include numerical results which demonstrate the accuracy and advantages of this iterative technique.

[pt] Para avaliar projetos de investimento florestal, a Teoria de Opções Reais é utilizada com o propósito de incorporar questões relacionadas a incertezas e flexibilidades gerenciais. O objetivo desta dissertação é desenvolver uma modelagem para valoração de um projeto florestal, no qual a variação do estoque de árvores se aproxima do crescimento real de uma floresta, utilizando uma adaptação da equação logística. Desta forma, para um determinado nível de saturação, o estoque se estabiliza. Adicionalmente, o trabalho busca quantificar os benefícios econômicos de uma política ótima de produção a partir do corte de árvores. Para a análise proposta, os resultados são obtidos através do método de diferenças finitas explícitas. O problema apresenta três variáveis independentes - estoque, tempo e preço, sendo este modelado como um Movimento Geométrico Browniano - e duas variáveis dependentes - a taxa de corte e o valor da opção de investimento. É apresentada uma aplicação para uma floresta de eucalipto e os resultados são comparados considerando outras alternativas para a evolução do estoque de árvores, bem como para a decisão da quantidade a ser cortada. Para esta comparação, avalia-se o caso em que o estoque segue um modelo estocástico e o caso em que a taxa de corte é fixa. Os resultados mostram que é vantajoso adotar uma política ótima de corte, corroborando resultados obtidos em trabalhos anteriores de opções reais na área florestal. Além disso, o maior valor da opção é obtido quando o estoque é modelado pela equação logística para o crescimento. / [en] In order to incorporate uncertainty and managerial flexibilities in forestry investment projects, financial literature uses the real options approach. The aim of this work is to develop a model for valuation of a forestry project, in which the inventory growth of trees follows a logistic equation based in the estimated real growth of a forest. Thus, for a given level of saturation, the inventory stabilizes. In addition, this dissertation aims to quantify the economic benefits of an optimal production policy from cutting trees. For the proposal analysis, the results are obtained by the finite difference method in the explicit form. The problem has three independent variables – inventory, time and price, which is modeled as a Geometric Brownian Motion – and two dependent variables – the cutting rate and the value of the investment option. An application for an eucalyptus forest is presented and the results are compared considering other alternatives for the evolution of the inventory and for the decision on the cutting amount. For this purpose, two different assumptions are made, considering a stochastic model for the inventory and a fixed shear rate. The results show that it is advantageous to adopt a optimal cutting policy, confirming results obtained in previous studies of real options in forestry. Moreover, the greatest option value is obtained when the inventory is modeled by logistic equation for growth.

Portfolio selection has always been a fundamental challenge in the field of finance and captured the attention of researchers in the financial area. Merton's portfolio problem is an optimization problem in finance and aims to maximize an investor's portfolio. This thesis studies Merton's Optimal Investment-Consumption Problem under the Jourdain--Sbai stochastic volatility model and seeks to maximize the expected discounted utility of consumption and terminal wealth. The results of our study can be split into three main parts. First, we derived the Hamilton--Jacobi--Bellman equation related to our stochastic optimal control problem.  Second, we simulated the optimal controls, which are the weight of the risky asset and consumption. This has been done for all the three models within the scope of the Jourdain--Sbai model: Quadratic Gaussian, Stein & Stein, and Scott's model. Finally, we developed the system of equations after applying the Crank-Nicolson numerical scheme when solving our HJB partial differential equation.

Obtaining the modal parameters of a deflected and rolling tire represents a challenge due to the complex vibration characteristics that cause the tire's symmetry distortion and the natural frequencies' bifurcation phenomena. The modal parameters are usually extracted using a detailed finite element model. The main issue with full modal models (FEA, for example) is the inability to integrate the tire modal model with the vehicle models to tune the suspension system for optimal ride comfort. An in-plane rigid–elastic-coupled tire model was used to examine the 200 DOF finite difference method (FDM) modal analysis accuracy under non-ground contact and non-rotating conditions. The discrete in-plane rigid–elastic-coupled tire model was modified to include the contact patch restriction, centrifugal force, Doppler, and Coriolis effects, covering a range of 0-300 Hz. As a result, the influence of the contact patch and the rotating tire conditions on the natural frequencies and modes were obtained through modal analysis. The in-plane rigid–elastic-coupled modal model with varying conditions was created that connects any two DOFs around the tire's tread or sidewall as inputs or outputs. The vertical movement of the wheel was incorporated into the in-plane rigid–elastic-coupled tire modal model to extract the transfer function (TF) that connects road irregularities as an input to the wheel's vertical movement as an output. The TF was utilized in a quasi-static manner to obtain the tire's enveloping characteristics rolling over short wavelength obstacles as a direct function of vertical wheel displacement under varying contact patch length constraints. The tire modal model was implemented with the quarter car model to obtain the vehicle response rolling over short wavelength obstacles. Finally, a sensitivity analysis was performed to examine the influence of tire parameters and pretension forces on natural frequencies. / Doctor of Philosophy / The goal of vehicle manufacturers is to predict the vehicle's behavior under various driving conditions using mathematical models and simulation. Automotive companies rely heavily on computational simulation tools instead of real-time tests to shorten the product development cycle and reduce costs. However, the interaction between the tire and the road is one of the most critical aspects to consider when evaluating automobile stability and performance. The tires are responsible for generating the forces and moments that drive and maneuver the vehicle. Tires are complex products due to their intricate design, and their characteristics are affected by many factors such as vertical load, inflation pressure, speed, and a road with an uneven surface profile. Consequently, this project aims to describe the influence of various driving circumstances and load conditions on tire properties, as well as to develop a model that can represent the vertical tire and vehicle behavior while traveling over a cleat under different vehicle loads.

本文的主要內容為評價JPMorgan Chase & Co.（美國摩根大通銀行）及UBS（瑞士銀行）所發行的兩檔結構型票券，共同的特色是票券為保本型且不付息，報酬條款中附有雙重界限觸及失效選擇權，其價值對於標的資產的波動程度相當敏感。一旦標的資產價格觸及任一界限，具有額外收益的選擇權將失效，投資人僅能拿回原始投資本金，相當於損失了原本可能獲得的無風險利息。 　　針對雙重界限觸及失效選擇權，我們使用顯式、隱式以及Crank-Nicolson三種有限差分法來進行評價，並比較蒙地卡羅模擬和封閉解的結果，藉以了解各種方法的準確性及效率。接著我們求算避險參數Greeks，分析發行商所面臨的風險。同時根據市場未來的情況，分析投資人的預期收益，進而了解這種商品在市場上廣為流通的原因，以及此類新奇結構型商品對於風險的重分配方式，如何締造買方賣方雙贏的局面。