Dissertations / Theses on the topic 'Numerical results and simulation for M'

The chemical master equation, formulated on the Markov assumption of underlying chemical kinetics, offers an accurate stochastic description of general chemical reaction systems on the mesoscopic scale. The chemical master equation is especially useful when formulating mathematical models of gene regulatory networks and protein-protein interaction networks, where the numbers of molecules of most species are around tens or hundreds. However, solving the master equation directly suffers from the so called "curse of dimensionality" issue. This thesis first tries to study the numerical properties of the master equation using existing numerical methods and parallel machines. Next, approximation algorithms, namely the adaptive aggregation method and the radial basis function collocation method, are proposed as new paths to resolve the "curse of dimensionality". Several numerical results are presented to illustrate the promises and potential problems of these new algorithms. Comparisons with other numerical methods like Monte Carlo methods are also included. Development and analysis of the linear Shepard algorithm and its variants, all of which could be used for high dimensional scattered data interpolation problems, are also included here, as a candidate to help solve the master equation by building surrogate models in high dimensions.<br>Ph. D.

Made available in DSpace on 2014-12-17T14:58:12Z (GMT). No. of bitstreams: 1 ElsonANM.pdf: 918866 bytes, checksum: 54ffb16de332a5a9c76c3afd577bcea1 (MD5) Previous issue date: 2005-09-16<br>Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico<br>The study of aerodynamic loading variations has many engineering applications, including helicopter rotor blades, wind turbines and turbo machinery. This work uses a Vortex Method to make a lagrangian description of the a twodimensional airfoil/ incident wake vortex interaction. The flow is incompressible, newtonian, homogeneus and the Reynolds Number is 5x105 .The airfoil is a NACA 0018 placed a angle of attack of the 0? and 5?simulates with the Painel Method with a constant density vorticity panels and a generation poit is near the painel. The protector layer is created does not permit vortex inside the body. The vortex Lamb convection is realized with the Euler Method (first order) and Adans-Bashforth (second order). The Random Walk Method is used to simulate the diffusion. The circular wake has 366 vortex all over positive or negative vorticity located at different heights with respect to the airfoil chord. The Lift was calculated based in the algorithm created by Ricci (2002). This simulation uses a ready algorithm vatidated with single body does not have a incident wake. The results are compared with a experimental work The comparasion concludes that the experimental results has a good agrement with this papper<br>Este estudo simula numericamente, atrav?s do M?todo de V?rtices, a intera??o entre uma nuvem de circula??o incidente e um aerof?lio NACA 0018 posicionado com ?ngulos de ataque de 0? e 5?. O n?mero de Reynolds utilizado ? de 5x105 e o escoamento ? considerado incompress?vel. Devido a complexidade do fen?meno de geometria tridimensional, apenas uma se??o do aerof?lio ? simulada transformando o trabalho em bidimensional. Utiliza-se o M?todo dos Pain?is com vorticidades distribu?das para simular o corpo e o ponto de gera??o de vorticidade ? deslocado da superf?cie do painel. Uma camada protetora ? criada para evitar a entrada de v?rtices no corpo. A convec??o dos v?rtices de Lamb presentes ? realizada atrav?s dos esquemas de Euler (1?ordem) e de Adams-Bashforth (2?ordem). A difus?o utiliza o M?todo do Avan?o Rand?mico. As cargas de sustenta??o s?o calculadas atrav?s de um algoritmo desenvolvido por Ricci (2002). A nuvem utilizada tem 366 v?rtices com circula??o de +0.001375692 ou -0.001375692 formando um c?rculo de raio 0,2. A simula??o utilizou um algoritmo existente que foi modificado para o problema em quest?o. Validado atrav?s da simula??o do perfil sem a presen?a da nuvem. Os resultados encontrados mostram uma boa concord?ncia com os encontrados em trabalhos experimentais

Dans cette thèse, nous nous sommes principalement intéressés à l’étude théorique et numérique de quelques équations qui décrivent la dynamique des densités des dislocations. Les dislocations sont des défauts microscopiques qui se déplacent dans les matériaux sous l’effet des contraintes extérieures. Dans un premier travail, nous démontrons un résultat d’existence globale en temps des solutions discontinues pour un système hyperbolique diagonal qui n’est pas nécessairement strictement hyperbolique, dans un espace unidimensionnel. Ainsi dans un deuxième travail, nous élargissons notre portée en démontrant un résultat similaire pour un système d’équations de type eikonal non-linéaire qui est en fait une généralisation du système hyperbolique déjà étudié. En effet, nous prouvons aussi l’existence et l’unicité d’une solution continue pour le système eikonal. Ensuite, nous nous sommes intéressés à l’analyse numérique de ce système en proposant un schéma aux différences finies, par lequel nous montrons la convergence vers le problème continu et nous consolidons nos résultats avec quelques simulations numériques. Dans une autre direction, nous nous sommes intéressés à la théorie de contraction différentielle pour les équations d’évolutions. Après avoir introduit une nouvelle distance, nous construisons une nouvelle famille des solutions contractantes positives pour l’équation d’évolution p-Laplace<br>In this thesis, we are mainly interested in the theoretical and numerical study of certain equations that describe the dynamics of dislocation densities. Dislocations are microscopic defects in materials, which move under the effect of an external stress. As a first work, we prove a global in time existence result of a discontinuous solution to a diagonal hyperbolic system, which is not necessarily strictly hyperbolic, in one space dimension. Then in another work, we broaden our scope by proving a similar result to a non-linear eikonal system, which is in fact a generalization of the hyperbolic system studied first. We also prove the existence and uniqueness of a continuous solution to the eikonal system. After that, we study this system numerically in a third work through proposing a finite difference scheme approximating it, of which we prove the convergence to the continuous problem, strengthening our outcomes with some numerical simulations. On a different direction, we were enthused by the theory of differential contraction to evolutionary equations. By introducing a new distance, we create a new family of contracting positive solutions to the evolutionary p-Laplacian equation

Les méthodes de type quasi-Monte Carlo sont des versions déterministes des méthodes de Monte Carlo. Les nombres aléatoires sont remplacés par des nombres déterministes qui forment des ensembles ou des suites à faible discrepance, ayant une meilleure distribution uniforme. L'erreur d'une méthode quasi-Monte Carlo dépend de la discrepance de la suite utilisée, la discrepance étant une mesure de la déviation par rapport à la distribution uniforme. Dans un premier temps nous nous intéressons à la résolution par des méthodes quasi-Monte Carlo d'équations différentielles pour lesquelles il y a peu de régularité en temps. Ces méthodes consistent à formuler le problème avec un terme intégral pour effectuer ensuite une quadrature quasi-Monte Carlo. Ensuite des méthodes particulaires quasi-Monte Carlo sont proposées pour résoudre les équations cinétiques suivantes : l'équation de Boltzmann linéaire et le modèle de Kac. Enfin, nous nous intéressons à la résolution de l'équation de la diffusion à l'aide de méthodes particulaires utilisant des marches quasi-aléatoires. Ces méthodes comportent trois étapes : un schéma d'Euler en temps, une approximation particulaire et une quadrature quasi-Monte Carlo à l'aide de réseaux-$(0,m,s)$. A chaque pas de temps les particules sont réparties par paquets dans le cas des problèmes multi-dimensionnels ou triées si le problème est uni-dimensionnel. Ceci permet de démontrer la convergence. Les tests numériques montrent pour les méthodes de type quasi-Monte Carlo de meilleurs résultats que ceux fournis par les méthodes de type Monte Carlo.

Dans ce travail de thèse, on s'intéresse é l'emploi de techniques de traitement de signal de systèmes de communication MIMO (Multiple Input Multiple Output) pour des applications aux réseaux de capteurs sans fil. Les contraintes énergétiques de cette classe de réseau font appel à des topologies particulières et le réseau peut être perçu comme étant un ensemble de grappes de nœuds capteurs. Ceci ouvre la porte à des techniques avancées de communication de type MIMO. Dans un premier temps, les différents aspects caractérisant les réseaux de capteurs sans fil sont introduits. Puis, les efforts engagés pour optimiser la conservation de l'énergie dans ces réseaux sont résumés. Les concepts de base de systèmes MIMOs sont abordés dans le deuxième chapitre et l'exploration par voie numérique de différentes pistes de la technologie MIMO sont exposées. Nous nous intéressons à des techniques de diversité de polarisation dans le cadre de milieux de communication riches en diffuseurs. Par la suite, des méthodes de type beamforming sont proposées pour la localisation dans les réseaux de capteurs sans fil. Le nouvel algorithme de localisation est présenté et les performances sont évaluées. Nous identifions la configuration pour la communication inter-grappes qui permet pour les meilleurs compromis entre énergie et efficacité spectrale dans les réseaux de capteurs sans fil. Finalement, nous envisageons la technique de sélection de nœuds capteurs afin de réduire la consommation de l'énergie dans le réseau de capteur sans fil<br>The aim of this work is to study from a signal processing point of view the use of MIMO (Multiple Input Multiple Output) communication systems for algorithms dedicated to wireless sensor networks. We investigate energy-constrained wireless sensor networks and we focus on cluster topology of the network. This topology permits for the use of MIMO communication system model. First, we review different aspects that characterize the wireless sensor network. Then, we introduce the existing strategies for energy conservation in the network. The basic concepts of MIMO systems are presented in the second chapter and numerical results are provided for evaluating the performances of MIMO techniques. Of particular interest, polarization diversity over rich scattering environment is studied. Thereafter, beamforming approach is proposed for the development of an original localization algorithm in wireless sensor network. The novel algorithm is described and performances are evaluated by simulation. We determine the optimal system configuration between a pair of clusters that permits for the highest capacity to energy ratio in the fourth chapter. The final chapter is devoted to sensor nodes selection in wireless sensor network. The aim of using such technique is to make energy conservation in the network

<p>Cracking in continuous casting has always been one of the main problems of steel mills. Many cracks that occur during solidification are difficult to observe from outside the industrial mold. In order to better understand the formation of this defect, compared with the large-scale simulation used in the entire industrial process, microsimulation is also essential. A comprehensive study of using phase field method to simulate microstructure evolution has been conducted. A variety of two-dimensional models based on phase-filed method has been developed in order to simulate dendrites growth in continuous casting process. The basic concepts of phase-field method are presented. Among those models, Kobayashi model was first introduced to describe the morphology of pure material solidification, in this article, which are pure water and pure iron. In order to get closer to the actual situation of continuous casting, a multi-component model was introduced to solve the problem. To go a step further, by introducing a series of temperature parameters and modifications to a series of terms, the binary alloy directional solidification model was used to simulate the process of dendrite growth in continuous casting. Furthermore, the detailed derivation of the binary alloy solidification model and how to apply the model in open source software will also be introduced in this article. The effects of physical parameters such as anisotropic strength, temperature gradient and cooling rate on the growth and evolution of the dendrite interface were quantitatively analyzed. Finally, potential improvement of this model, optimization to primary cooling section in continuous casting process and various applications of the simulation were discussed.</p>

As a comparative study, the global performance of two cases for a floating harbor system are researched by numerical analysis and compared with results from experiments: one is a two-body case such that a floating quay is placed next to a fixed quay, a normal harbor, and the other is a three-body case such that a container ship is posed in the middle of the floating quay and the fixed quay. The numerical modeling is built based on the experimental cases. Mooring system used in the experiments is simplified to sets of linear springs, and gaps between adjacent bodies are remarkably narrow as 1.3m~1.6m with reference to large scales of the floating structures; a water plane of the fixed quay is 480m×160m, and the ship is 15000 TEU (twenty-foot equivalent unit) class. With the experiment-based models, numerical analysis is implemented on two domains: frequency domain using a three dimensional constant panel method, WAMIT, and time domain using a coupled dynamic analysis program of moored floating structures, CHARM3D/HARP. Following general processes of the two main tools, additional two calibrations are implemented if necessary: revision of external stiffness and estimation of damping coefficients. The revision of the external stiffness is conducted to match natural frequency of the simulation with that of the experiment; to find out natural frequencies RAO comparison is used. The next, estimation of damping coefficients is carried out on time domain to match the responses of the simulation with those of the experiment. After optimization of the numerical analysis, a set of experimental results from regular wave tests is compared with RAO on frequency domain, and results from an irregular wave test of the experiment are compared with response histories of simulation on time domain. In addition, fender forces are compared between the simulation and experiment. Based on response histories relative motions of the floating quay and container ship are compared. And the floating harbor system, the three-body case, is compared with a conventional harbor system, a fixed quay on the portside of the container ship, in terms of motions of the container ship. As an additional simulation, the three-body case is investigated on an operating sea state condition. From the present research, the experimental results are well matched with the numerical results obtained from the simulation tools optimized to the experiments. In addition, the floating harbor system show more stable motions of the container ship than the conventional harbor system, and the floating harbor system in the operating sea state condition have motions even smaller enough to operate in term of relative motions between the floating quay and the container ship.

No<br>The influence of loose plant leaves on the acoustic absorption of a porous substrate is experimentally and numerically studied. Such systems are typical in vegetative walls, where the substrate has strong acoustical absorbing properties. Both experiments in an impedance tube and theoretical predictions show that when a leaf is placed in front of such a porous substrate, its absorption characteristics markedly change (for normal incident sound). Typically, there is an unaffected change in the low frequency absorption coefficient (below 250 Hz), an increase in the middle frequency absorption coefficient (500-2000 Hz) and a decrease in the absorption at higher frequencies. The influence of leaves becomes most pronounced when the substrate has a low mass density. A combination of the Biot's elastic frame porous model, viscous damping in the leaf boundary layers and plate vibration theory is implemented via a finite-difference time-domain model, which is able to predict accurately the absorption spectrum of a leaf above a porous substrate system. The change in the absorption spectrum caused by the leaf vibration can be modeled reasonably well assuming the leaf and porous substrate properties are uniform.

碩士<br>國立臺灣科技大學<br>機械工程系<br>105<br>In this study, the Particle Image Velocimetry (P.I.V.) measurements of a finite length cylinder with a 1D cap at its tip are used to analyze the velocity data in its wake region. Two-dimensional PIV measurement results on two different observation planes, X-Y plane and Y-Z plane, are analyzed with Reynolds numbers (ReD) as 250、560 and 1080. The average and instantaneous Y velocity data are analyzed at nine observation points, which are located away from the cylinder tip (X/D = 0) and the cylinder axial (Y/D = 0) short、middle and long distances respectively. In the near wake region (Y/D = -1), three observation points are observed, the observation point (-1.5, -1, 0) near the cylinder tip has the most significant non-dimensional average velocity difference between two different observation planes, and the other two observation points are similar between them. In the transition region (Y/D = -3), three observation points are observed, the non-dimensional average velocity difference between two different observation planes is around 0.05 ~ 0.45, and the Y-Z plane has a greater velocity than that on the X-Y plane. In the far field wake region (Y/D = -5), three observation points are observed, the non-dimensional average velocity between two different observation planes is similar, and the velocity of the observation point (-1.5, -5, 0) near the cylinder tip is close to the freestream velocity. Two observation points (-1.5, -3, 0) and (-1.5, -5, 0) among nine observation points, the instantaneous velocity data distributions have significant deviations from the normal distribution on two different observation planes; the X-Y plane has more than 45% of the instantaneous velocity data concentrated in [μ-σ, μ], and the Y-Z plane instantaneous velocity data are mostly distributed in two specific ranges, more than 60% of the instantaneous velocity data concentrated in [μ-σ, μ]. In the X-Y plane, experimental average velocity results near the cylinder tip and during Y/D = 0 ~ -3, show that there is an obvious X-direction velocity component and Y-direction velocity component is opposite to the freestream velocity; numerical simulation average velocity results during Y/D = 0 ~ -2, show that X-direction velocity component and Y-direction velocity component have a periodic change in space. In the Y-Z plane, experimental average velocity results at X/D = -1.5, show that Y-direction velocity component is reduced in the range of Y/D = 0 ~ -6 as ReD = 250; Y/D = 0 ~ -3.5 as ReD = 560 and Y/D = 0 ~ -3 as ReD = 1080. The influence extent of Y-direction velocity component near the cylinder tip decreases as the Reynolds number (ReD) increases. At X/D = -5.5 and -10.5, Y-direction velocity component is reduced in the range of Y/D = 0 ~ -10 and Z-direction velocity component has one to three pairs of vortices in the middle and far distances away from the cylinder tip. Numerical simulation average velocity results at X/D = -1.5, show that Y-direction velocity component is reduced in the range of Y/D = 0 ~ -5 as ReD = 250; Y/D = 0 ~ -5.5 as ReD = 560 and Y/D = 0 ~ -8 as ReD = 1080 near the cylinder tip. At X/D = -5.5 and -10.5, Y-direction velocity component is reduced in the range of Y/D = 0 ~ -7 as ReD = 250; Y/D = 0 ~ -8 as ReD = 560 and Y/D = 0 ~ -10 as ReD = 1080. The influence extent of Y-direction velocity component in the near、middle and far distances away from the cylinder tip increases as the Reynolds number (ReD) increases, Z-direction velocity component has only a pair of vortices in the near、middle and far distances away from the cylinder tip.

碩士<br>國立中央大學<br>大氣物理研究所<br>100<br>Pearl River Delta (PRD) is located in southern China near the coastline. It is one the most populated regions in China with more than 50 million people living in this area. Through the last two decades, PRD region has experienced the unprecedented land-use and land-cover changes as a result of rapid economic development and urban expansion. Its possible impact on regional air quality and climate change is a major concern of the national government as well as the global community. In this study, Weather Research and Forecasting (WRF) meteorological model is performed using the updated land use data for a high ozone event (October 24 to 26, 2007). In addition, the land use data is re-classified and updated using the 500-m resolution Moderate Resolution Imaging Spectroradiometer (MODIS) satellite products. The simulation using the updated land use data improves the wind speed, temperature and wind direction. Analysis of the wind field simulation result demonstrated that the see-breeze flow direction is opposite to the prevailing wind (1300 to 1800 LST) that forms a stagnant wind condition near the Macao and Pearl River Estuary region. The sustained sunlight combined with stagnant wind condition favors the accumulation of the air pollutants. The trajectory analysis showed that the ozone concentration is transported from Shen-Zhen and Dong-Guan industrial area in the Guang-Dong province.

Dissertação de Mestrado Integrado em Engenharia Mecânica apresentada à Faculdade de Ciências e Tecnologia<br>A maioria dos componentes mecânicos está sujeita a cargas cíclicas em serviço. Esses componentes podem falhar em serviço devido ao fenómeno de fadiga. Sendo assim, o dimensionamento à fadiga é processo fundamental na vida útil destes equipamentos. O estudo deste tipo de falha é feito, classicamente, recorrendo a curvas da/dN – ΔK, que permitem prever a vida útil do componente. No entanto, a utilização de um parâmetro linear elástico, ΔK, na caracterização de um fenómeno não linear e irreversível como é a deformação plástica, apesar dos bons resultados já obtidos, apresenta algumas limitações. Essas limitações levam à procura de parâmetros capazes de prever a vida útil destes elementos. Posto isto, o objetivo principal desta dissertação é a validação do modelo numérico desenvolvido pelo grupo de investigação comparando as previsões com os resutlados experimentais obtidos por Luís Borrego para dois materiais de base: as ligas de alumínio 6082-T6 e 7050-T6. Utilizando-se o programa de elementos finitos DD3IMP, as simulações foram efetuadas para provetes do tipo MT e a propagação de fenda é controlada pelo valor de deformação plástica acumulada na extremidade da fenda. Assim sendo, foram realizadas 34 simulações numéricas e posterior tratamento de dados para verificar a autenticidade dos resultados. Primeiramente, foram efetuados testes para as duas ligas de alumínio com carregamento em amplitude constante, para três razões de tensão diferentes, R, e quatros valores de comprimento de fenda inicial, a0. Posteriormente, apenas para a liga de alumínio 6082-T6 realizaram-se simulações numéricas com carregamento em sobrecarga, para dois valores de razão de tensão, dois valores de ΔK e alguns valores de sobrecarga, OLR Por fim procedeu-se a análise de fecho de fenda com o cálculo da percentagem de ciclo de carga em que a fenda permaneceu fechada, U*, na última propagação da fenda para cada simulação de carregamento em amplitude constante.A comparação com os resultados experimentais permite a validação do modelo numérico de elementos finitos. De uma forma geral, os resultados obtidos através do modelo revelaram-se muito assertivos. As curvas numéricas descrevem de forma excelente o comportamento esperado para os dois tipos de carregamentos e apresentam-se muito próximas das curvas experimentais. Os efeitos da razão de tensão, R, do ΔKBL e do OLR são retratados pelos resultados numéricos tal e qual como esperado e apresentado pelos resultados experimentais. Em suma, os resultados numéricos obtidos transmitirão reconhecimento e credibilidade às simulações numéricas, muitas vezes questionadas pelos revisores.<br>Most mechanical components undergo cyclical loading in service. These components can fail in service due to fatigue. Therefore, fatigue dimensioning is a fundamental process in the useful life of these equipments. The study of this type of failure is classically done using curves da/dN – ΔK, which allows predicting the useful life of the component. However, the use of an elastic linear parameter, ΔK, in the characterization of a non-linear and irreversible phenomenon such as plastic strain, despite the good results already obtained, has some limitations. These limitations lead to the search for parameters capable of predicting the useful life of these elements.That said, the main goal of this dissertation is the validation of the numerical model developed by the research group comparing the results obtained with the experimental ones obtained by Luís Borrego for two base materials: the 6082-T6 and 7050-T6 aluminum alloys. Using the finite element program DD3IMP, simulations were carried out for MT type specimens and the crack propagation is controlled by the plastic strain value at the end of the crack. Therefore, 34 numerical simulations were carried out and subsequent data processing to verify the authenticity of the results. First, tests were carried out for the two aluminum alloys with constant amplitude loading, for three different stress ratios, R, and four values of initial crack length, a0. Subsequently, numerical simulations were only carried out for the 6082-T6 aluminum alloy with overload loading, for two values of voltage ratio, two values of ΔK and some values of overload, OLR. Finally, a crack closure analysis was performed with the calculation of the percentage of load cycle in which a crack remained closed, U *, in the last crack propagation for each constant amplitude loading simulation.Finally, the comparison with the experimental results allows the validation of the finite element numerical model. In general, the results obtained through the model proved to be very assertive. The numerical curves excellently describe the expected behaviour for the two types of loads and are very close to the experimental curves. The effects of stress ratio, R, ΔKBL and OLR are portrayed by the numerical results as expected and presented by the experimental results. In short, the numerical results obtained will convey recognition and credibility to numerical simulations, often questioned by reviewers.

Dissertação de Mestrado Integrado em Engenharia Mecânica apresentada à Faculdade de Ciências e Tecnologia<br>A maioria dos componentes mecânicos está sujeita a cargas cíclicas em serviço. Esses componentes podem falhar em serviço devido ao fenómeno de fadiga. Sendo assim, o dimensionamento à fadiga é processo fundamental na vida útil destes equipamentos. O estudo deste tipo de falha é feito, classicamente, recorrendo a curvas da/dN – ΔK, que permitem prever a vida útil do componente. No entanto, a utilização de um parâmetro linear elástico, ΔK, na caracterização de um fenómeno não linear e irreversível como é a deformação plástica, apesar dos bons resultados já obtidos, apresenta algumas limitações. Essas limitações levam à procura de parâmetros capazes de prever a vida útil destes elementos. Posto isto, o objetivo principal desta dissertação é a validação do modelo numérico desenvolvido pelo grupo de investigação comparando as previsões com os resutlados experimentais obtidos por Luís Borrego para dois materiais de base: as ligas de alumínio 6082-T6 e 7050-T6. Utilizando-se o programa de elementos finitos DD3IMP, as simulações foram efetuadas para provetes do tipo MT e a propagação de fenda é controlada pelo valor de deformação plástica acumulada na extremidade da fenda. Assim sendo, foram realizadas 34 simulações numéricas e posterior tratamento de dados para verificar a autenticidade dos resultados. Primeiramente, foram efetuados testes para as duas ligas de alumínio com carregamento em amplitude constante, para três razões de tensão diferentes, R, e quatros valores de comprimento de fenda inicial, a0. Posteriormente, apenas para a liga de alumínio 6082-T6 realizaram-se simulações numéricas com carregamento em sobrecarga, para dois valores de razão de tensão, dois valores de ΔK e alguns valores de sobrecarga, OLR Por fim procedeu-se a análise de fecho de fenda com o cálculo da percentagem de ciclo de carga em que a fenda permaneceu fechada, U*, na última propagação da fenda para cada simulação de carregamento em amplitude constante.A comparação com os resultados experimentais permite a validação do modelo numérico de elementos finitos. De uma forma geral, os resultados obtidos através do modelo revelaram-se muito assertivos. As curvas numéricas descrevem de forma excelente o comportamento esperado para os dois tipos de carregamentos e apresentam-se muito próximas das curvas experimentais. Os efeitos da razão de tensão, R, do ΔKBL e do OLR são retratados pelos resultados numéricos tal e qual como esperado e apresentado pelos resultados experimentais. Em suma, os resultados numéricos obtidos transmitirão reconhecimento e credibilidade às simulações numéricas, muitas vezes questionadas pelos revisores.<br>Most mechanical components undergo cyclical loading in service. These components can fail in service due to fatigue. Therefore, fatigue dimensioning is a fundamental process in the useful life of these equipments. The study of this type of failure is classically done using curves da/dN – ΔK, which allows predicting the useful life of the component. However, the use of an elastic linear parameter, ΔK, in the characterization of a non-linear and irreversible phenomenon such as plastic strain, despite the good results already obtained, has some limitations. These limitations lead to the search for parameters capable of predicting the useful life of these elements.That said, the main goal of this dissertation is the validation of the numerical model developed by the research group comparing the results obtained with the experimental ones obtained by Luís Borrego for two base materials: the 6082-T6 and 7050-T6 aluminum alloys. Using the finite element program DD3IMP, simulations were carried out for MT type specimens and the crack propagation is controlled by the plastic strain value at the end of the crack. Therefore, 34 numerical simulations were carried out and subsequent data processing to verify the authenticity of the results. First, tests were carried out for the two aluminum alloys with constant amplitude loading, for three different stress ratios, R, and four values of initial crack length, a0. Subsequently, numerical simulations were only carried out for the 6082-T6 aluminum alloy with overload loading, for two values of voltage ratio, two values of ΔK and some values of overload, OLR. Finally, a crack closure analysis was performed with the calculation of the percentage of load cycle in which a crack remained closed, U *, in the last crack propagation for each constant amplitude loading simulation.Finally, the comparison with the experimental results allows the validation of the finite element numerical model. In general, the results obtained through the model proved to be very assertive. The numerical curves excellently describe the expected behaviour for the two types of loads and are very close to the experimental curves. The effects of stress ratio, R, ΔKBL and OLR are portrayed by the numerical results as expected and presented by the experimental results. In short, the numerical results obtained will convey recognition and credibility to numerical simulations, often questioned by reviewers.

By means of numerical simulations, the thesis aims at improvements in the understanding of light propagation in dielectric optical waveguides, with emphasis on nonreciprocal integrated magnetooptic devices. The results include: Proposal, implementation, and assessment of the WMM mode solver (Wave Matching Method) For waveguides with piecewise constant, rectangular permittivity profiles, the calculation of guided modes can be based on a local expansion into factorizing harmonic or exponential trial functions. A least squares expression for the mismatch in the continuity conditions at dielectric boundaries connects the fields on neighbouring regions. Minimization of this error allows to compute propagation constants and mode fields. The procedure has been implemented both for semivectorial and fully vectorial mode analysis. The piecewise defined trial fields are well suited to deal with field discontinuities or discontinuous derivatives. Numerical assessment shows excellent agreement with accepted previous results from other methods. The WMM turns out to be effective especially for structures described by only a few rectangles. It yields semianalytical mode field representations which are not restricted to a computational window. The fields are therefore perfectly suited for further processing, e.g. in the framework of various kinds of perturbation theory. Perturbational geometry tolerancing procedure Shifting the location of a dielectric boundary in the cross section of a waveguide with piecewise constant refractive index profile results in a permittivity perturbation in a layer along the discontinuity line. On the basis of these thin layer perturbations, perturbational expressions for the derivatives of the propagation constants with respect to geometry parameters are discussed. The approach provides direct access to wavelength dependences. Comparison with rigorously calculated data shows that the accuracy is sufficient to yield reasonable tolerance estimates for realistic integrated optical devices, at almost no extra computational cost. This perturbational approach allows to establish and to quantify guidelines for geometry tolerant devices. Numerical assessment of nonreciprocal wave propagation The coefficients of coupled mode theory for the magnetooptic permittivity contribution allow a classification of the influences of gyrotropy on guided wave propagation. For mirror symmetric waveguides, one identifies the dominant effects of TE phase shift, TM phase shift, and TE/TM polarization conversion, for polar, equatorial, and longitudinal magnetooptic configurations, respectively. Layered equatorial magnetooptic profiles lead to the well known phase shifters for TM modes. Analogously, sliced asymmetric polar magnetooptic profiles yield phase shifts for TE polarized modes. Simulations of rib waveguides with a magnetooptic domain lattice predict effects of the same order of magnitude as the phase shift for TM modes. Phase matching as a condition for complete polarization conversion in longitudinally magnetized waveguides can be realized with selected geometries of raised strip waveguides or embedded square waveguides. Based on coupled mode theory for hybrid fundamental modes, the analysis of the performance of such devices in an isolator setting includes birefringence, optical absorption, and an explicit perturbational evaluation of fabrication tolerances. A magnetooptic waveguide which is magnetized at a tilted angle may perform as a unidirectional polarization converter. The term specifies a device that converts TE to TM light for one direction of propagation, while it maintains the polarization for the opposite direction. A double layer setup with two magnetooptic films of opposite Faraday rotation is proposed and simulated. Designs of three waveguide couplers for applications as isolators/circulators and polarization splitters Three-guide couplers with multimode central waveguides allow for a remote coupling between the outer waveguides. While the power transfer is a truly multimode interference process, one can identify two different regimes where either two or three supermodes dominate the coupling behaviour. Numerical simulations show reasonable agreement between the main coupling features in planar an three dimensional devices. The specific form of the relevant modes suggests the design of integrated optical isolators and circulators. Both planar and three dimensional concepts are investigated. A radiatively coupled waveguide polarization splitter should be designed such that the entire dynamic range of the coupling length variations is exploited. This is easily possible with a three dimensional raised strip configuration. Combination of two magnetooptic unidirectional polarization converters and two radiatively coupled waveguide based polarization splitters leads to a concept for a polarization independent integrated four port circulator device. The simulation predicts a total length of about three millimeters.