Solution techniques for transport problems involving steep concentration gradients: application to noncatalytic fluid solid reactions

Some efficient solution techniques for solving models of noncatalytic gas-solid and fluid-solid reactions are presented. These models include those with non-constant diffusivities for which the formulation reduces to that of a convection-diffusion problem. A singular perturbation problem results for such models in the presence of a large Thiele modulus, for which the classical numerical methods can present difficulties. For the convection-diffusion like case, the time-dependent partial differential equations are transformed by a semi-discrete Petrov-Galerkin finite element method into a system of ordinary differential equations of the initial-value type that can be readily solved. In the presence of a constant diffusivity, in slab geometry the convection-like terms are absent, and the combination of a fitted mesh finite difference method with a predictor-corrector method is used to solve the problem. Both the methods are found to converge, and general reaction rate forms can be treated. These methods are simple and highly efficient for arbitrary particle geometry and parameters, including a large Thiele modulus. (C) 2001 Elsevier Science Ltd. All rights reserved.

The effects of time delays in adaptive phase measurements

It is not possible to make measurements of the phase of an optical mode using linear optics without introducing an extra phase uncertainty. This extra phase variance is quite large for heterodyne measurements, however it is possible to reduce it to the theoretical limit of log (n) over bar (4 (n) over bar (2)) using adaptive measurements. These measurements are quite sensitive to experimental inaccuracies, especially time delays and inefficient detectors. Here it is shown that the minimum introduced phase variance when there is a time delay of tau is tau/(8 (n) over bar). This result is verified numerically, showing that the phase variance introduced approaches this limit for most of the adaptive schemes using the best final phase estimate. The main exception is the adaptive mark II scheme with simplified feedback, which is extremely sensitive to time delays. The extra phase variance due to time delays is considered for the mark I case with simplified feedback, verifying the tau /2 result obtained by Wiseman and Killip both by a more rigorous analytic technique and numerically.

Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.

A variable stepsize implementation for stochastic differential equations

Stochastic differential equations (SDEs) arise from physical systems where the parameters describing the system can only be estimated or are subject to noise. Much work has been done recently on developing higher order Runge-Kutta methods for solving SDEs numerically. Fixed stepsize implementations of numerical methods have limitations when, for example, the SDE being solved is stiff as this forces the stepsize to be very small. This paper presents a completely general variable stepsize implementation of an embedded Runge Kutta pair for solving SDEs numerically; in this implementation, there is no restriction on the value used for the stepsize, and it is demonstrated that the integration remains on the correct Brownian path.

A four-stage index 2 Diagonally Implicit Runge-Kutta method

High index Differential Algebraic Equations (DAEs) force standard numerical methods to lower order. Implicit Runge-Kutta methods such as RADAU5 handle high index problems but their fully implicit structure creates significant overhead costs for large problems. Singly Diagonally Implicit Runge-Kutta (SDIRK) methods offer lower costs for integration. This paper derives a four-stage, index 2 Explicit Singly Diagonally Implicit Runge-Kutta (ESDIRK) method. By introducing an explicit first stage, the method achieves second order stage calculations. After deriving and solving appropriate order conditions., numerical examples are used to test the proposed method using fixed and variable step size implementations. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.

Compara����o de desempenho entre a formula����o direta do M��todo dos Elementos de Contorno com Fun����es Radiais e o M��todo dos Elementos Finitos em problemas de Poisson e Helmholtz

O presente trabalho objetiva avaliar o desempenho do MECID (M��todo dos Elementos de Contorno com Interpola����o Direta) para resolver o termo integral referente �� in��rcia na Equa����o de Helmholtz e, deste modo, permitir a modelagem do Problema de Autovalor assim como calcular as frequ��ncias naturais, comparando-o com os resultados obtidos pelo MEF (M��todo dos Elementos Finitos), gerado pela Formula����o Cl��ssica de Galerkin. Em primeira inst��ncia, ser��o abordados alguns problemas governados pela equa����o de Poisson, possibilitando iniciar a compara����o de desempenho entre os m��todos num��ricos aqui abordados. Os problemas resolvidos se aplicam em diferentes e importantes ��reas da engenharia, como na transmiss��o de calor, no eletromagnetismo e em problemas el��sticos particulares. Em termos num��ricos, sabe-se das dificuldades existentes na aproxima����o precisa de distribui����es mais complexas de cargas, fontes ou sorvedouros no interior do dom��nio para qualquer t��cnica de contorno. No entanto, este trabalho mostra que, apesar de tais dificuldades, o desempenho do M��todo dos Elementos de Contorno �� superior, tanto no c��lculo da vari��vel b��sica, quanto na sua derivada. Para tanto, s��o resolvidos problemas bidimensionais referentes a membranas el��sticas, esfor��os em barras devido ao peso pr��prio e problemas de determina����o de frequ��ncias naturais em problemas ac��sticos em dom��nios fechados, dentre outros apresentados, utilizando malhas com diferentes graus de refinamento, al��m de elementos lineares com fun����es de bases radiais para o MECID e fun����es base de interpola����o polinomial de grau (um) para o MEF. S��o geradas curvas de desempenho atrav��s do c��lculo do erro m��dio percentual para cada malha, demonstrando a converg��ncia e a precis��o de cada m��todo. Os resultados tamb��m s��o comparados com as solu����es anal��ticas, quando dispon��veis, para cada exemplo resolvido neste trabalho.

Dense motion field estimation from myocardial boundary displacements

Minimally invasive cardiovascular interventions guided by multiple imaging modalities are rapidly gaining clinical acceptance for the treatment of several cardiovascular diseases. These images are typically fused with richly detailed pre-operative scans through registration techniques, enhancing the intra-operative clinical data and easing the image-guided procedures. Nonetheless, rigid models have been used to align the different modalities, not taking into account the anatomical variations of the cardiac muscle throughout the cardiac cycle. In the current study, we present a novel strategy to compensate the beat-to-beat physiological adaptation of the myocardium. Hereto, we intend to prove that a complete myocardial motion field can be quickly recovered from the displacement field at the myocardial boundaries, therefore being an efficient strategy to locally deform the cardiac muscle. We address this hypothesis by comparing three different strategies to recover a dense myocardial motion field from a sparse one, namely, a diffusion-based approach, thin-plate splines, and multiquadric radial basis functions. Two experimental setups were used to validate the proposed strategy. First, an in silico validation was carried out on synthetic motion fields obtained from two realistic simulated ultrasound sequences. Then, 45 mid-ventricular 2D sequences of cine magnetic resonance imaging were processed to further evaluate the different approaches. The results showed that accurate boundary tracking combined with dense myocardial recovery via interpolation/ diffusion is a potentially viable solution to speed up dense myocardial motion field estimation and, consequently, to deform/compensate the myocardial wall throughout the cardiac cycle. Copyright �� 2015 John Wiley & Sons, Ltd.

Active and passive behaviors of soft tissues: Pelvic floor muscles

: A new active-contraction visco-elastic numerical model of the pelvic floor (skeletal) muscle is presented. Our model includes all elements that represent the muscle constitutive behavior, contraction and relaxation. In contrast with the previous models, the activation function can be null. The complete equations are shown and exactly linearized. Small verification and validation tests are performed and the pelvis is modeled using the data from the intra-abdominal pressure tests

Desenfumagem em edif��cios: parque de estacionamento coberto (retail - Oeiras parque)

Os parques de estacionamento surgiram da necessidade de disponibiliza����o de espa��o de parqueamento de ve��culos que fazem parte do quotidiano do Homem, no entanto devido ao facto de poderem ser confinados ou subterr��neos requerem a instala����o de ventila����o for��ada (ventiladores axiais e ventiladores de impulso). Este trabalho tem como objectivo a an��lise, utilizando m��todos de simula����o num��rica da ventila����o for��ada criada pelos ventiladores de impulso e pelos ventiladores axiais instalados num parque de estacionamento subterr��neo. V��o ser comparadas v��rias simula����es com situa����es diferentes em termos de condi����es de fronteira, obstru����es ao escoamento, etc., por forma a tirar conclus��es sobre o comportamento do parque numa situa����o de emerg��ncia, ou seja, num inc��ndio. Este comportamento vai ter em conta a efici��ncia de evacua����o dos gases libertados, as temperaturas no parque que permitem verificar onde est��o localizados os gases mais quentes e os campos de velocidade do ar que permitem uma visualiza����o do escoamento e at�� certo ponto a turbul��ncia do mesmo. No final pretende-se concluir por meio de compara����o com outros documentos consultados, a ���confiabilidade��� do software usado (FDS-Fire Dynamics Simulator) e adicionalmente tirar conclus��es sobre o projecto do parque, nomeadamente sobre a necessidade de introdu����o de altera����es.

Coletores de distribui����o e sua otimiza����o hidr��ulica, aplicados a uma instala����o de produ����o de ��gua arrefecida em sistemas de AVAC ( F��rum Picoas)

Trabalho Final de Mestrado para obten����o do grau de Mestre em Engenharia Mec��nica

Avalia����o experimental do comportamento din��mico de um edif��cio do s��culo XIX: aplica����o �� calibra����o de modelos num��ricos

Trabalho de Disserta����o de natureza cient��fica para obten����o do grau de Mestre em Engenharia Civil na ��rea de Especializa����o em Estruturas

Instrumenta����o e monitoriza����o na avalia����o do comportamento de maci��os e estruturas envolventes: caso de po��os em meio urbano

Atualmente, a escava����o de po��os em locais densamente ocupados requer medidas severas para reduzir riscos e poss��veis influ��ncias quer na pr��pria obra quer em estruturas pr��ximas. Neste campo, a instrumenta����o geot��cnica e a sua monitoriza����o tem um papel determinante na execu����o de obras geot��cnicas, sendo que neste trabalho �� dado um especial realce �� instrumenta����o utilizada, ��s atividades de observa����o geot��cnica, bem como �� an��lise e interpreta����o das leituras para o controlo de movimentos induzidos no terreno pelas escava����es. Este acompanhamento �� baseado num plano de instrumenta����o, sendo descrito de uma forma transversal a import��ncia do projeto e em particular das fases do processo de investiga����o geot��cnica. O acompanhamento da execu����o dos po��os para a futura Esta����o da Reboleira, permitiu validar as solu����es de projeto para um determinado m��todo construtivo, determinadas atrav��s de m��todos num��ricos e semi-emp��ricos, e abordados neste trabalho. A monitoriza����o sistem��tica desde o in��cio das escava����es at�� ao revestimento secund��rio, permitiu tecer aprecia����es sobre os valores obtidos, apresentando-se alguns registos. Todas estas a����es visam controlar e antecipar riscos de acidentes provocados pela execu����o de escava����es, pelo que nesta tese �� tamb��m real��ada a import��ncia da seguran��a e higiene no trabalho na preven����o dos riscos profissionais, independentemente da sua origem.

Node adaptation for global collocation with radial basis functions using direct multisearch for multiobjective optimization

Meshless methods are used for their capability of producing excellent solutions without requiring a mesh, avoiding mesh related problems encountered in other numerical methods, such as finite elements. However, node placement is still an open question, specially in strong form collocation meshless methods. The number of used nodes can have a big influence on matrix size and therefore produce ill-conditioned matrices. In order to optimize node position and number, a direct multisearch technique for multiobjective optimization is used to optimize node distribution in the global collocation method using radial basis functions. The optimization method is applied to the bending of isotropic simply supported plates. Using as a starting condition a uniformly distributed grid, results show that the method is capable of reducing the number of nodes in the grid without compromising the accuracy of the solution. (C) 2013 Elsevier Ltd. All rights reserved.

Estudo de falha em placas laminadas usando m��todos anal��ticos e num��ricos

Trabalho Final de Mestrado para obten����o do grau de Mestre em Engenharia de Manuten����o

The use of the boundary element method in the analysis of single lap joints

The most common techniques for stress analysis/strength prediction of adhesive joints involve analytical or numerical methods such as the Finite Element Method (FEM). However, the Boundary Element Method (BEM) is an alternative numerical technique that has been successfully applied for the solution of a wide variety of engineering problems. This work evaluates the applicability of the boundary elem ent code BEASY as a design tool to analyze adhesive joints. The linearity of peak shear and peel stresses with the applied displacement is studied and compared between BEASY and the analytical model of Frostig et al., considering a bonded single-lap joint under tensile loading. The BEM results are also compared with FEM in terms of stress distributions. To evaluate the mesh convergence of BEASY, the influence of the mesh refinement on peak shear and peel stress distributions is assessed. Joint stress predictions are carried out numerically in BEASY and ABAQUS��, and analytically by the models of Volkersen, Goland, and Reissner and Frostig et al. The failure loads for each model are compared with experimental results. The preparation, processing, and mesh creation times are compared for all models. BEASY results presented a good agreement with the conventional methods.