Birkhoffian Systems in Infinite Dimensional Manifolds

We generalize the theory of Kobayashi and Oliva (On the Birkhoff Approach to Classical Mechanics. Resenhas do Instituto de Matematica e Estatistica da Universidade de Sao Paulo, 2003) to infinite dimensional Banach manifolds with a view towards applications in partial differential equations.

Modeling and simulation of the anode in direct ethanol fuels cells

Mathematical modeling has been extensively applied to the study and development of fuel cells. In this work, the objective is to characterize a mechanistic model for the anode of a direct ethanol fuel cell and perform appropriate simulations. The software Comsol Multiphysics (R) (and the Chemical Engineering Module) was used in this work. The software Comsol Multiphysics (R) is an interactive environment for modeling scientific and engineering applications using partial differential equations (PDEs). Based on the finite element method, it provides speed and accuracy for several applications. The mechanistic model developed here can supply details of the physical system, such as the concentration profiles of the components within the anode and the coverage of the adsorbed species on the electrode surface. Also, the anode overpotential-current relationship can be obtained. To validate the anode model presented in this paper, experimental data obtained with a single fuel cell operating with an ethanol solution at the anode were used. (C) 2008 Elsevier B.V. All rights reserved.

Análise dinâmica de vigas assimétricas em curva com parede fina e aberta submetidas a ação de carga móveis

Fundamentalmente, o presente trabalho faz uma análise elástica linear de pontes ou vigas curvas assimétricas de seção transversal aberta e de parede fina, com propriedades físicas, geométricas e raio de curvatura constantes ao longo do eixo baricêntrico. Para tanto, utilizaram-se as equações diferenciais de VLASOV considerando o acoplamento entre as deformações nas direções vertical, transversal, axial de torcão nal. Na solução do sistema de quatro equações com derivadas parciais foi utilizado um apropriado método numérico de integração (Diferenças Finitas Centrais). A análise divide-se, basicamente, em dois tipos: análise DINÂMICA e ESTATICA. Ambas são utilizadas também na determinação do coeficiente de impacto (C.M.D.). A primeira refere-se tanto na determinação das características dinâmicas básicas (frequências naturais e respectivos modos de vibração), como também na determinação da resposta dinâmica da viga, em tensões e deformações, para cargas móveis arbitrárias. Vigas com qualquer combinação das condições de contorno, incluindo bordos rotulados e engastados nas três direções de flexão e na torção, são consideradas. 0s resultados da análise teórica, obtidos pela aplicação de programas computacionais implementados em microcomputador (análise estática) e no computador B-6700 (análise dinâmica), são comparados tanto com os da bibliografia técnica como também com resultados experimentais, apresentando boa correlação.

Welfare costs of inflation: the case for interest-bearing money and empirical estimates for Brazil

We provide in this paper a closed fonn for the Welfare Cost of Inflation which we prove to be closer than Bailey's expression to the correct solution of the corresponding non-separable differential equation. Next. we extend this approach to ao economy with interest-bearing money, once again presenting a better appoximation than the one given by Bailey's approach. Fmally, empirical estimates for Brazil are presented.

Avaliação de projetos na presença de volatilidade: estudo de caso de empresas no setor de telecomunicações

Quando as empresas decidem se devem ou não investir em determinado projeto de investimentos a longo prazo (horizonte de 5 a 10 anos), algumas metodologias alternativas ao Fluxo de Caixa Descontado (FCD) podem se tornar úteis tanto para confirmar a viabilidade do negócio como para indicar o melhor momento para iniciar o Empreendimento. As análises que levam em conta a incerteza dos fluxos de caixa futuros e flexibilidade na data de início do projeto podem ser construídos com a abordagem estocástica, usando metodologias como a solução de equações diferenciais que descrevem o movimento browniano. Sob determinadas condições, as oportunidades de investimentos em projetos podem ser tratados como se fossem opções reais de compra, sem data de vencimento, como no modelo proposto por McDonald-Siegel (1986), para a tomada de decisões e momento ótimo para o investimento. Este trabalho analisa a viabilidade de investimentos no mercado de telecomunicações usando modelos não determinísticos, onde a variável mais relevante é a dispersão dos retornos, ou seja, que a variância representa o risco associado a determinado empreendimento.

WeIfare costs of inflation the case for interest-bearing money and empiricaI Estimates for Brazil

We provide in this paper a closed fonn for the Welfare Cost of Inflation which we prove to be closer than Bailey's expression to the correct solution of the corresponding non-separable differential equation. Next, we extend this approach to an economy with interest-bearing money, once again presenting a better appoximation than the one given by Bailey's approach. Finally, empirical estimates for Brazil are presented.

Affine processes, arbitrage-Free Term structures of legendre polynomials,and option pricing

Multivariate Affine term structure models have been increasingly used for pricing derivatives in fixed income markets. In these models, uncertainty of the term structure is driven by a state vector, while the short rate is an affine function of this vector. The model is characterized by a specific form for the stochastic differential equation (SDE) for the evolution of the state vector. This SDE presents restrictions on its drift term which rule out arbitrages in the market. In this paper we solve the following inverse problem: Suppose the term structure of interest rates is modeled by a linear combination of Legendre polynomials with random coefficients. Is there any SDE for these coefficients which rules out arbitrages? This problem is of particular empirical interest because the Legendre model is an example of factor model with clear interpretation for each factor, in which regards movements of the term structure. Moreover, the Affine structure of the Legendre model implies knowledge of its conditional characteristic function. From the econometric perspective, we propose arbitrage-free Legendre models to describe the evolution of the term structure. From the pricing perspective, we follow Duffie et al. (2000) in exploring Legendre conditional characteristic functions to obtain a computational tractable method to price fixed income derivatives. Closing the article, the empirical section presents precise evidence on the reward of implementing arbitrage-free parametric term structure models: The ability of obtaining a good approximation for the state vector by simply using cross sectional data.

Modelagem dinâmica e simulação computacional de poços de petróleo verticais e direcionais com elevação por bombeio mecânico

LINS, Filipe C. A. et al. Modelagem dinâmica e simulação computacional de poços de petróleo verticais e direcionais com elevação por bombeio mecânico. In: CONGRESSO BRASILEIRO DE PESQUISA E DESENVOLVIMENTO EM PETRÓLEO E GÁS, 5. 2009, Fortaleza, CE. Anais... Fortaleza: CBPDPetro, 2009.

Simulador computacional para poços de petróleo com método de elevação artificial por bombeio mecânico

This work proposes a computer simulator for sucker rod pumped vertical wells. The simulator is able to represent the dynamic behavior of the systems and the computation of several important parameters, allowing the easy visualization of several pertinent phenomena. The use of the simulator allows the execution of several tests at lower costs and shorter times, than real wells experiments. The simulation uses a model based on the dynamic behavior of the rod string. This dynamic model is represented by a second order partial differencial equation. Through this model, several common field situations can be verified. Moreover, the simulation includes 3D animations, facilitating the physical understanding of the process, due to a better visual interpretation of the phenomena. Another important characteristic is the emulation of the main sensors used in sucker rod pumping automation. The emulation of the sensors is implemented through a microcontrolled interface between the simulator and the industrial controllers. By means of this interface, the controllers interpret the simulator as a real well. A "fault module" was included in the simulator. This module incorporates the six more important faults found in sucker rod pumping. Therefore, the analysis and verification of these problems through the simulator, allows the user to identify such situations that otherwise could be observed only in the field. The simulation of these faults receives a different treatment due to the different boundary conditions imposed to the numeric solution of the problem. Possible applications of the simulator are: the design and analysis of wells, training of technicians and engineers, execution of tests in controllers and supervisory systems, and validation of control algorithms

Controle inteligente de sistemas eletroidráulicos utilizando redes neurais artificiais

This work describes the development of a nonlinear control strategy for an electro-hydraulic actuated system. The system to be controlled is represented by a third order ordinary differential equation subject to a dead-zone input. The control strategy is based on a nonlinear control scheme, combined with an artificial intelligence algorithm, namely, the method of feedback linearization and an artificial neural network. It is shown that, when such a hard nonlinearity and modeling inaccuracies are considered, the nonlinear technique alone is not enough to ensure a good performance of the controller. Therefore, a compensation strategy based on artificial neural networks, which have been notoriously used in systems that require the simulation of the process of human inference, is used. The multilayer perceptron network and the radial basis functions network as well are adopted and mathematically implemented within the control law. On this basis, the compensation ability considering both networks is compared. Furthermore, the application of new intelligent control strategies for nonlinear and uncertain mechanical systems are proposed, showing that the combination of a nonlinear control methodology and artificial neural networks improves the overall control system performance. Numerical results are presented to demonstrate the efficacy of the proposed control system

Avaliacao de dados de secagem de suspensoes de polpas de frutas em leito de jorro com alimentacao intermitente

The objective of this work was the development and improvement of the mathematical models based on mass and heat balances, representing the drying transient process fruit pulp in spouted bed dryer with intermittent feeding. Mass and energy balance for drying, represented by a system of differential equations, were developed in Fortran language and adapted to the condition of intermittent feeding and mass accumulation. Were used the DASSL routine (Differential Algebraic System Solver) for solving the differential equation system and used a heuristic optimization algorithm in parameter estimation, the Particle Swarm algorithm. From the experimental data food drying, the differential models were used to determine the quantity of water and the drying air temperature at the exit of a spouted bed and accumulated mass of powder in the dryer. The models were validated using the experimental data of drying whose operating conditions, air temperature, flow rate and time intermittency, varied within the limits studied. In reviewing the results predicted, it was found that these models represent the experimental data of the kinetics of production and accumulation of powder and humidity and air temperature at the outlet of the dryer

Evolução top-hat hidrodinâmica em campos de velocidades peculiares primordiais

We investigate the cosmology of the vacuum energy decaying into cold dark matter according to thermodynamics description of Alcaniz & Lima. We apply this model to analyze the evolution of primordial density perturbations in the matter that gave rise to the first generation of structures bounded by gravity in the Universe, called Population III Objects. The analysis of the dynamics of those systems will involve the calculation of a differential equation system governing the evolution of perturbations to the case of two coupled fluids (dark matter and baryonic matter), modeled with a Top-Hat profile based in the perturbation of the hydrodynamics equations, an efficient analytical tool to study the properties of dark energy models such as the behavior of the linear growth factor and the linear growth index, physical quantities closely related to the fields of peculiar velocities at any time, for different models of dark energy. The properties and the dynamics of current Universe are analyzed through the exact analytical form of the linear growth factor of density fluctuations, taking into account the influence of several physical cooling mechanisms acting on the density fluctuations of the baryonic component of matter during the evolution of the clouds of matter, studied from the primordial hydrogen recombination. This study is naturally extended to more general models of dark energy with constant equation of state parameter in a flat Universe

Métodos numéricos para resolução de equações diferenciais ordinárias lineares baseados em interpolação por spline

In this work we have elaborated a spline-based method of solution of inicial value problems involving ordinary differential equations, with emphasis on linear equations. The method can be seen as an alternative for the traditional solvers such as Runge-Kutta, and avoids root calculations in the linear time invariant case. The method is then applied on a central problem of control theory, namely, the step response problem for linear EDOs with possibly varying coefficients, where root calculations do not apply. We have implemented an efficient algorithm which uses exclusively matrix-vector operations. The working interval (till the settling time) was determined through a calculation of the least stable mode using a modified power method. Several variants of the method have been compared by simulation. For general linear problems with fine grid, the proposed method compares favorably with the Euler method. In the time invariant case, where the alternative is root calculation, we have indications that the proposed method is competitive for equations of sifficiently high order.

Scattering and bound states of spinless particles in a mixed vector-scalar smooth step potential

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Colombeau's theory and shock wave solutions for systems of PDEs

In this article we study the existence of shock wave solutions for systems of partial differential equations of hydrodynamics with viscosity in one space dimension in the context of Colombeau's theory of generalized functions. This study uses the equality in the strict sense and the association of generalized functions (that is the weak equality). The shock wave solutions are given in terms of generalized functions that have the classical Heaviside step function as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function that have to satisfy part of the equations in the strict sense and part of the equations in the sense of association.