Made available in DSpace on 2014-06-11T19:24:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-06-18Bitstream added on 2014-06-13T18:47:47Z : No. of bitstreams: 1 correia_jm_me_rcla.pdf: 4924512 bytes, checksum: c773abdfa8e36c6a93d48c33494b327d (MD5) / Universidade Estadual Paulista (UNESP) / O objetivo desta dissertação é sugerir duas formas de apresentação do estudo da equação geral de uma quádrica. Uma delas, quando seu público alvo é formado por alunos ingressantes (do primeiro ano de um curso da Área de Ciências Exatas e da Terra) e a outra quando seu público alvo tem noções de Álgebra Linear / In this work we present two ways to study the general equation of a quadric. One of them when the public is formed by beginners students and the other one when the public is formed by students with notions of Linear Algebra

This investigation focuses on the production, strength properties, and marketability of a new ultra stiff wood composite. The basis of the examination is to compare strength properties such as, Modulus of Rupture, Modulus of Elasticity, Work to Max Load, and Density with currently available products. The final analysis of the ultra stiff product suggested that this product would compete favorably in today’s market due to the strength properties of the product. Although the current hot-pressing method is not economical for mass production, other ways of pressing can be utilized. It is noted in this research that the wood moisture content can influence MOE, MOR, and density properties. By manipulating and controlling the press cycle and the moisture content, a competitive product was produced.

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Problemas provenientes de química atmosférica, possuem uma característica especial denominada stiffness, indicando que as soluções dos sistemas de equações diferenciais ordinárias envolvidos variam em diferentes ordens de grandeza. Isso faz com que métodos numéricos adequados devam ser aplicados no intuito de obter soluções numéricas convergentes e estáveis. Os métodos mais eficazes para tratar este tipo de problema são os métodos implícitos, pois possuem uma região de estabilidade ilimitada que permite grandes variações no tamanho do passo, mantendo o erro de discretização dentro de uma dada tolerância. Mais precisamente, estes métodos possuem a propriedade de A-estabilidade ou A(alpha)-estabilidade. Neste trabalho, comparamos dois métodos numéricos com estas características: o método de Rosenbrock e a fórmula de diferenciação regressiva (métodos BDF). O primeiro é usado no módulo de Química do modelo CCATT-BRAMS do Centro de Previsão de Tempo e Estudos Climáticos (CPTEC), sendo incluído na previsão numérica de regiões com intensas fontes de poluição. Este é um método de passo simples implícito com um controle de passo adaptativo. Aqui empregamos também o segundo, um método de passo múltiplo que dispõe de uma fórmula que permite variação no tamanho do passo e na ordem, empregando o pacote LSODE. Os resultados de nossas comparações indicam que os métodos BDF podem se constituir em interessante alternativa para uso no CCATT-BRAMS. / Problems from atmospheric chemistry have a special characteristic denominated stiffness, indicating that the solutions of the involved ordinary differential equations systems vary in different scales. This means that appropriate methods should be applied in order to get convergent and stable numerical solutions. The most powerful methods to treat problems like this are implicit schemes, since they have unlimited stabity regions, allowing large variations in step size, keeping the discretization error within a given tolerance. More precisely, these methods have the A-stability or A(alpha)-stability properties. In this work, we compared two numerical methods with those characteristics: the Rosenbrock method and the backward differentiation formula (BDF). The first one is employed in the Chemistry package within CCATT-BRAMS local weather model of CPTEC (Center for Weather Forecasts and Climate Studies), which is mainly used for the numerical forecasting of regions with intense pollution. This is a implicit one-step method with an adaptative stepsize control. We compare it with the second method, a multistep method with a formula that allows variations in step size and order, with the help of the LSODE package. The results of our comparisons indicate that BDF methods are an interesting alternative to be used within CCATT-BRAMS.

Problemas provenientes de química atmosférica, possuem uma característica especial denominada stiffness, indicando que as soluções dos sistemas de equações diferenciais ordinárias envolvidos variam em diferentes ordens de grandeza. Isso faz com que métodos numéricos adequados devam ser aplicados no intuito de obter soluções numéricas convergentes e estáveis. Os métodos mais eficazes para tratar este tipo de problema são os métodos implícitos, pois possuem uma região de estabilidade ilimitada que permite grandes variações no tamanho do passo, mantendo o erro de discretização dentro de uma dada tolerância. Mais precisamente, estes métodos possuem a propriedade de A-estabilidade ou A(alpha)-estabilidade. Neste trabalho, comparamos dois métodos numéricos com estas características: o método de Rosenbrock e a fórmula de diferenciação regressiva (métodos BDF). O primeiro é usado no módulo de Química do modelo CCATT-BRAMS do Centro de Previsão de Tempo e Estudos Climáticos (CPTEC), sendo incluído na previsão numérica de regiões com intensas fontes de poluição. Este é um método de passo simples implícito com um controle de passo adaptativo. Aqui empregamos também o segundo, um método de passo múltiplo que dispõe de uma fórmula que permite variação no tamanho do passo e na ordem, empregando o pacote LSODE. Os resultados de nossas comparações indicam que os métodos BDF podem se constituir em interessante alternativa para uso no CCATT-BRAMS. / Problems from atmospheric chemistry have a special characteristic denominated stiffness, indicating that the solutions of the involved ordinary differential equations systems vary in different scales. This means that appropriate methods should be applied in order to get convergent and stable numerical solutions. The most powerful methods to treat problems like this are implicit schemes, since they have unlimited stabity regions, allowing large variations in step size, keeping the discretization error within a given tolerance. More precisely, these methods have the A-stability or A(alpha)-stability properties. In this work, we compared two numerical methods with those characteristics: the Rosenbrock method and the backward differentiation formula (BDF). The first one is employed in the Chemistry package within CCATT-BRAMS local weather model of CPTEC (Center for Weather Forecasts and Climate Studies), which is mainly used for the numerical forecasting of regions with intense pollution. This is a implicit one-step method with an adaptative stepsize control. We compare it with the second method, a multistep method with a formula that allows variations in step size and order, with the help of the LSODE package. The results of our comparisons indicate that BDF methods are an interesting alternative to be used within CCATT-BRAMS.

This thesis presents new numerical methods for solving differential equations with periodicity. Spectral methods for solving linear and nonlinear ODEs, linear ODE eigenvalue problems and linear time-dependent PDEs on a periodic interval are reviewed, and a novel approach for computing multiplication matrices is presented. Choreographies, periodic solutions of the n-body problem that share a common orbit, are computed for the first time to high accuracy using an algorithm based on approximation by trigonometric polynomials and optimization techniques with exact gradient and exact Hessian matrix. New choreographies in spaces of constant curvature are found. Exponential integrators for solving periodic semilinear stiff PDEs in 1D, 2D and 3D periodic domains are reviewed, and 30 exponential integrators are compared on 11 PDEs. It is shown that the complicated fifth-, sixth- and seventh-order methods do not really outperform one of the simplest exponential integrators, the fourth-order ETDRK4 scheme of Cox and Matthews. Finally, algorithms for solving semilinear stiff PDEs on the sphere with spectral accuracy in space and fourth-order accuracy in time are proposed. These are based on a new variant of the double Fourier sphere method in coefficient space and standard implicit-explicit time-stepping schemes. A comparison is made against exponential integrators and it is found that implicit-explicit schemes perform better. The algorithms described in each chapter of this thesis have been implemented in MATLAB and made available as part of Chebfun.

Three- and four-derivative k-step Hermite-Birkhoff-Obrechkoff (HBO) methods are constructed for solving stiff systems of first-order differential equations of the form y'= f(t,y), y(t0) = y0. These methods use higher derivatives of the solution y as in Obrechkoff methods. We compute their regions of absolute stability and show the three- and four-derivative HBO are A( 𝜶)-stable with 𝜶 > 71 ° and 𝜶 > 78 ° respectively. We conduct numerical tests and show that our new methods are more efficient than several existing well-known methods.

Orientador: Messias Meneguette Júnior / Banca: Gilcilene Sanchez de Paulo / Banca: Erwin Doescher / Resumo: As equações diferenciais parciais hiperbólicas tem recebido uma atenção especial nos últimos anos devido sua grande aplicabilidade em diversas áreas da ciência e pelas dificuldades numéricas que elas impõem. O presente projeto leva em conta a importância do termo fonte e as implicações que isto representa na solução numérica das equações hiperbólicas, em especial nas leis de conservação. Todo o trabalho é focado no caso bidimensional das leis de conservação hiperbólicas, considerando termos fonte stiff. Este tipo de termo fonte impõe diferença de escala de propagação das ondas e das escalas advindas do próprio termo fonte. A equação hiperbólica com termo fonte deve ser tratada de forma especial. Utilizando os métodos mais recomendados na prática, resolvemos tal equação separando-a em duas ou mais partes, e depois acoplamos as partes na solução final. Os métodos utilizados em cada parte separada tem grande influência na solução... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The hyperbolic partial differential equations has had special attention in recent years due to their wide application in various areas of science and the numerical difficulties they impose. This project takes into account the importance of the font term and the implications this represents in the numerical solution of hyperbolic equations, especially in conservation laws. All work is focused on the case of two-dimensional hyperbolic conservation laws, considering the font terms stiff. This type of font term imposes difference in scale propagation of waves and those scales that comes from the font term. The hyperbolic equation with font term should be treated in a special way. Using the methods recommended in practice, we solve this equation by separating it into two or more parts, and then put the parties together in the final solution. The methods used... (Complete abstract click electronic access below) / Mestre

Bridges with external post-tensioned tendons are considered to be more durable than bridges with internal tendons (tendons within the webs and flanges), because external tendons are easier to inspect. In addition, in the event that extensive corrosion damage is detected, it is possible to replace an external tendon. However, an appropriate inspection for detecting damage needs to be determined for external tendons. This investigation focuses on the vibration technique, which uses the dynamic properties of the external tendon to infer the effective prestress force. Four large-scale external tendons, designed to simulate one section of an external tendon between two deviators in a post-tensioned bridge, were tested. In the study, damage to the tendons was induced in a quantifiable fashion at a specific location and the tensile force was measured directly. In addition, free-vibration tests were conducted periodically. This provided a direct means of measuring the sensitivity of measured natural frequencies and measured tensile force to local damage. The measured data were correlated with an approximation of the stiff string vibration model. In addition to the laboratory specimens, field testing was conducted on a bridge with external post-tensioned tendons. The findings from the study show that a loss in tensile force was not linear with a loss in the cross-sectional area of the strand, which results from stress redistribution within the tendon. Also, the natural frequencies were much less sensitive to the level of induced damage than the tensile force. While the measured data from the laboratory data compared very well with the analytical model, the field measurements exhibited a much greater deviation from the model. Due to several factors, the difference between the laboratory specimens and the bridge tendons are believed to be caused by larger levels of inherent error in the model. The findings from the investigation support the notion that vibration testing is most appropriately used in comparing relative differences between peer tendons. / text

Accurately predicting surface ground motions is critical for many earthquake engineering applications. Equivalent-linear (EQL) site response analysis is a numerical technique used to compute surface ground motions from input motions at bedrock using the site-specific dynamic soil properties. The purpose of this study was to investigate the accuracy of EQL site response analysis for stiff soil sites by comparing computed and observed transfer functions and response spectral amplification. The Kiban Kyoshin network (KiK-net) in Japan is a seismograph network consisting of downhole array sites with strong-motion accelerometers located at the ground surface and at depth. Recorded motions and shear wave velocity profiles are available for most sites. Observed transfer functions and response spectral amplification were computed for 930 individual seismic recordings at 11 stiff soil KiK-net sites. Computed transfer functions and response spectral amplification were calculated from EQL site response analysis by specifying the KiK-net base sensor motion as the input motion. Sites were characterized using the measured shear wave velocity profiles and nonlinear soil properties estimated from empirical models. Computed and observed transfer functions and response spectral amplification were compared at different levels of strain for each site. The average difference between the observed and computed response spectral amplification across the 11 sites were compared at different levels of strain. Overall, there is reasonable agreement between the computed and observed transfer functions and response spectral amplification. There is agreement between the computed and observed site periods, but with over-prediction of the computed response at the observed site periods. Higher modes often computed by the theoretical model were not always observed by the recordings. There is very good agreement between the computed and observed transfer functions and response spectral amplification for periods larger than the site periods. There is less agreement between the computed and observed transfer functions and response spectral amplification for periods less than the site periods. There is mostly over-prediction of the response spectral amplification at these periods, although some under-prediction also occurred. Across all 11 sites the predicted spectral amplification is within +/-20% at shear strains less than 0.01%. At shear strains between approximately 0.01 and 0.03%, the spectral amplification is over-predicted for these sites, in some instances by as little as 5% and in other instances by a factor of 2 or more. / text