Dissertations / Theses on the topic 'Inverted Residual'

The present study is concerned with the development of an inverse analysis of the depth-sensing indentation test based on a multi-objective function (MOF) optimisation model. The input data of this model are the load-displacement (P-h) curve extracted from the indentation instrument and the surface topography of the residual imprint left by the indenter after the removal of the load measured via atomic force microscopy (AFM). A Swift’s power law material model was considered to represent the indented material and thus, the output of the optimisation are the Young’s modulus (E), yield stress (σy) and strain-hardening exponent (n). The optimisation problem was designed to minimise the error between both the experimental and predicted P-h curves, i.e. the first objective, and pile-up profiles, i.e. the second objective, with the aim of addressing the non-uniqueness of the inverse analysis of indentation. A 3D FE model of the depth-sensing indentation test has been developed in ABAQUS in order to generate the predicted data from a set of trial material properties, i.e. E, σy and n. The generation of FE input files (pre-processor) and extraction of FE output files (post-processor) have been automated through MATLAB and Python subroutines. The optimisation problem was solved by the trust-region reflective algorithm available in the MATLAB Optimization ToolboxTM and thus, concisely, the model minimised the experimental and predicted data by modifying iteratively the material properties, starting from the initial guess properties specified by the user, until convergence was reached. Upon convergence, the material properties were said to describe the elastic-plastic behaviour of the indented material. A comprehensive experimental programme was carried out in order to investigate the load dependency of the indentation response of three different materials, including a steel (CrMoV), a titanium alloy (Ti-6Al-4V) and a high-purity copper (C110). The study of the topography of the residual imprints provided a better understanding of the effects of the microstructural arrangement on the plastic displacement of material beneath the indenter. The extent of piling-up was observed to be very sensitive to the difference in material properties from grain to grain and the crystallographic plane of the indented grain. Furthermore, it was concluded that the structural arrangement of the indented material may also contribute to the asymmetry observed in the pile-up profiles, in particular in materials with large grains relative to the projected area of the indenter, e.g. C110. This piece of work therefore, is suggested as a guideline for the use of height measurements of the residual imprint in the characterisation of the plastic behaviour of materials. The multi-objective function optimisation model is proved to be a step forward to the characterisation of the near-surface properties as, in contrast to the P-h curve, the residual imprint is strongly linked to the plastic behaviour of the indented material. Therefore, the physics governing the indentation problem were better represented. Therefore, the optimised P-h curve provided a very good fit to the corresponding experimental curve, to within an error of less than 2.4% and 8.4% the maximum (hmax) and residual (hr) depth, respectively, for all three materials, CrMoV steel, C110 copper and Ti-6Al-4V. Furthermore, a deviation of less than 12.4% was achieved between the area of indentation provided by the FE model and AFM instrument. Additionally, the value of maximum peak height (hpeak) was predicted with a maximum error of 11% in relation with the experimental pile-up profiles. Therefore, it was concluded that the optimised solution provided a very good representation of the complex mechanical response to indentation such that the volume of plastically displaced material as predicted by the optimised FE model was observed notably in accordance with experimental measurements. Furthermore, the complementary information provided by the second objective function allowed the model to distinguish between different materials showing identical indentation response – referred to in the literature as ‘mystical’ materials. In addition, a key outcome of this investigation suggested that stress-strain curves generated by mechanical tests performed at different scales, exhibit similar behaviour with only the magnitude of the stress increasing or decreasing depending upon the scale. Part of this thesis is dedicated to the application of the proposed inverse analysis for the characterisation of three phases located across the joint of a like-to-like inertia friction weld of SCMV steel, including martensite in the tempered, quenched and over-tempered condition. This study, characterised the generation of residual stresses into two stages: the thermal strain dominated initial cooling period that accounts for the majority of the residual stresses, and the phase transformation strain dominated final cooling period. In addition, it was concluded that at the onset of transformation from austenite to martensite, the volumetric changes experienced in the lattice relax up to 70% of the predicted tensile hoop stress found in the vicinity of the weld line near the inner surface and that the interaction of soft regions of austenite and hard regions of heat unaffected martensite accounts for up to 17% of the peak tensile stress. The indentation response of the set of optimised properties that represent each of the phases, was in very good agreement with the corresponding P-h curve and residual pile-up profile extracted from the indentation instrument and AFM, respectively. The capability of the inverse analysis to build the stress-strain relationship in the elastic-plastic regime using the optimised mechanical properties of the parent metal has been validated using experimental data extracted from the compressive test of an axisymmetric sample of tempered martensite [1]. The inclusion of the softer over-tempered martensite phase allowed the FE prediction to determine the proportion of the heat affected zone (HAZ) comprised by each phase in better agreement with the experimental weld-trial. Based on the interpretation of the microhardness test performed across the weld, the harder region formed due to the quenching process extends approximately 54% the length of the HAZ, whereas the rest 46% is comprised by the softer over-tempered martensitic phase. According to the FE prediction, the heat affected zone was composed by a proportion of 57% quenched martensite and 43% over-tempered martensite. Moreover, the distance from the weld line to the region where martensite fully tempered was observed to extend 79 and 71% the length of the HAZ, as determined by the FE model and experimental measurements, respectively. The presence of a softer region, OTM, between two harder regions, namely QM and TM, relaxed 7 to 11%, 1 to 6% and 12.8 to 15.3% the peak values of stress in the radial, axial and hoop directions respectively. A key observation from the results of the FE prediction was that the peak hoop residual stress is located at the boundary of the quenched and over-tempered martensite, and not at the edge of the heat affected zone. This observation was in agreement with the residual stress measurements published by Moat et al. [2].

The thesis deals with solving the time dependent inverse heat conduction and heat transfer problem of the quenching process of a rotary solid cylinder by multiple impinging water jets. The development of such investigation consists of two parts that complement each other. As is the case of any scientific experiment, first of all, an initial hypothesis will be set to be demonstrated theoretically. The numerical validation is carried out with a series of artificial cooling curve data and sensitivity analyses in the inverse solution. Then, a series of recorded temperature data were implemented into the inverse solution to predict the surface heat transfer during the quenching process.The numerical study consists of the solution of a two-dimensional linear time dependent inverse heat conduction problem based on the Generalized Minimal Residual Method (GMRES). The inverse solution method is based on the solution of an iterative problem, validated by a set of artificial temperature data. Such solution allows the prediction of the surface temperature and heat flux distribution in the quenching process, making use of recorded internal temperatures of the specimen. In order to solve the problem, the Matlab and Comsol Multiphysics programs were used. The GMRES algorithm was written as Matlab code, while the computational domain was defined in Comsol Multiphysics. Moreover, both programs collaborated in the solution of the inverse problem. Once the problem was solved, a sensitivity analysis was carried out in order to study the dependence of the numerical result on various parameters and optimize the inverse solution setup for application of recorded experimental data.The validated inverse solution setup examined by the sensitivity analyses was used on a set of experimental data, allowing the demonstration of the initially proposed hypothesis. This sensitivity analyses were performed consecutively for different key parameters regarding the numerical definition of the problem. The values for the parameters were considered optimal when minimum values for the error of the predicted surface temperature were recorded. In this case, the analyzed parameters were the m-value, mesh cell size, effect of noise, initial quenching temperature and quenching cooling rate. The connection between the experimental and numerical studies is obvious, as the first oneprovides the latter with input data of the inner temperature data of the specimen for the solving of the inverse problem, as is the case of the practical application of the code developed in the present thesis, and the inverse solution is essential in order to predict thesurface temperature and heat flux that are key information in studying quenching systems.

The first essay compares six common models, linear, quadratic, Cobb-Douglas, translog, logarithmic, and transcendental, to estimate wheat yield and area functions for Saudi Arabia. Data cover 1990-2016 for all the variables that affect wheat supply. After testing the models using Box-Cox, multicollinearity, and autocorrelation tests, we decide that the Cobb-Douglas models provide the best fit for both yield and area. We find the price elasticity of wheat is inelastic. Yield price elasticities are more inelastic than area elasticities. The impact of government policy number 335 has a larger effect on area than yield. The cultivated area of wheat, the one-year lag of yield, and the number of machines per hectare are the most influential factors affecting wheat yield. The primary factors influencing the area models are a one-year lag of both cultivated area and yield, as well as the number of machines per hectare. The second essay estimates the residual demand elasticity that rice exporters face in Saudi Arabia. The inverse residual demand methods, as proposed by Reed and Saghaian 2004, are used for rice exporters to Saudi Arabia during the period 1993-2014. Estimation results of the elasticities of the residual demand indicate that Australia, India, and Pakistan enjoy market power, while Egypt faces a perfectly elastic demand curve. We find Thailand and the US had positive inverse residual demand which means they also have no market power. The last essay is about the virtual water trade in Saudi Arabia. Using the concept of virtual water introduced by Allan 1994 and developed by Hoekstra and Hung (2002), we estimate virtual water trade for 20 crops of Saudi Arabia during 2000-2016. Our result shows the average virtual water trade was 12.5 billion m3/year. Saudi has net virtual water imports, with the most significant virtual water imports coming from cereals & alfalfa and vegetables; and there is net virtual water export of fruit. Saudi virtual water trade reduces pressure on water resources by 52%. Distance plays a role in Saudi virtual water export; we found that more than 90% of exports go to neighboring countries, including 45% to GCC countries. More than 30% of virtual water imports come from Europe. A Gravity model is used to investigate whether water scarcity variables influence trade. We compare the OLS, Fixed effects, Random effects, and PPML estimators to get the best model. The AIC, and tests for multicollinearity, and heteroskedasticity assist in determining estimation procedures and the final models. We cluster the errors by distance to improve the specific country effect variables such as economic mass variables. For the cereals and alfalfa group, we find that water-related variables influence virtual water imports of cereals, millet, sorghum, corn, barley, and sesame. Therefore, we suggest that a basic gravity model be applied to the other crops. In the vegetable group, we find that related water variables impact virtual water trade for all crops except marrow. Dates are the only fruit crop that are not influenced by the water-related variables.

Le contexte industriel actuel impose l’optimisation des ressources de production, notamment des matières premières et de l’énergie consommée. Cet engagement ne répond pas seulement aux critères de compétitivité liés aux coûts de production mais aussi à l’impact environnemental du processus global de fabrication. Pour répondre à ce problème, il est nécessaire de disposer de modèles pour définir des stratégies d'optimisation efficientes tout au long du processus complet de mise en forme d'une pièce mécanique.La plupart des lois de comportement habituellement utilisées pour modéliser le comportement des matériaux métalliques dans les procédés de transformation, sont caractérisées par un comportement isotrope. Ces modèles sont efficaces pour prédire le comportement d’un procédé sous chargement proportionnel, mais par définition ne peuvent pas prendre en compte l’anisotropie développée durant l’écrouissage. Cette caractéristique ne permet pas de prendre en compte les effets de l’interaction entre les différents procédés constitutifs du processus. Ce travail explore les lois de comportement phénoménologiques capables de modéliser ce phénomène afin d’obtenir un modèle précis du processus global. Sachant que la modélisation de chaque procédé nécessite un solveur et des mises en œuvre particulières, une méthodologie de travail ainsi que les outils numériques nécessaires pour gérer les variables d’état du processus ont été développés. Cette méthodologie permet un suivi des valeurs de variables d’écrouissage tout au long de la simulation du processus.Ce travail explore également des l'estimation du profil des contraintes résiduelles obtenu par des méthodes de mesure destructives afin en confrontant les résultats de simulations avec des données expérimentales. Une nouvelle méthodologie basée sur l’analyse inverse est développée et mise en œuvre. La nouvelle méthode est comparée avec les résultats obtenus avec deux méthodes destructives de référence. Les résultats obtenus dans cette application montrent une diminution à la fois de l'erreur et du niveau d'incertitude
The current industrial context requires the optimization of production resources, particularly raw materials and energy consumption. This commitment does not only meet the criteria of competitiveness related to production costs but also to the environmental impact of the overall manufacturing process. To solve this problem, is required a mode to define optimization strategies through a complete forming process during a mechanical part manufacturing.Most behavior laws used for metals, dedicated to perform simulations of forming and machining processes are characterized by an isotropic behavior. These models are effective in predicting the behavior under proportional loading, but by definition cannot consider the anisotropy developed during work hardening. This limitation makes it impossible to take to consider the interaction effects between the different stages of the manufacturing process. This work goes through the phenomenological behavior laws capable of modeling this phenomenon, in order to obtain an accurate model of the overall process. Knowing that the modeling of each process stage requires a solver and specific definitions, a methodology as well as numerical tools necessary to manage the hardening variables along the process have been developed. This methodology allows a traceability of the values of hardening variables throughout the simulation of the process, dividing the global simulation, admitting the use of different solvers or software.This work explores the profile estimation obtained with destructive residual stresses measurement methods in order to compare simulation results with experiments. A new methodology using inverse analysis is developed and implemented. From numerical generated data, the new method is applied and compared with two destructive reference methods. The results in this application show, a decrease in both the error and the uncertainty level

Nas últimas décadas, teorias têm sido formuladas para interpretar o comportamento de solos não saturados e estas têm se mostrado coerentes com resultados experimentais. Paralelamente, várias técnicas de campo e de laboratório têm sido desenvolvidas. No entanto, a determinação experimental dos parâmetros dos solos não saturados é cara, morosa, exige equipamentos especiais e técnicos experientes. Como resultado, essas teorias têm aplicação limitada a pesquisas acadêmicas e são pouco utilizados na prática da engenharia. Para superar este problema, vários pesquisadores propuseram equações para representar matematicamente o comportamento de solos não saturados. Estas proposições são baseadas em índices físicos, caracterização do solo, em ensaios convencionais ou simplesmente em ajustes de curvas. A relação entre a umidade e a sucção matricial, convencionalmente denominada curva característica de sucção do solo (SWCC) é também uma ferramenta útil na previsão do comportamento de engenharia de solos não saturados. Existem muitas equações para representar matematicamente a SWCC. Algumas são baseadas no pressuposto de que sua forma está diretamente relacionada com a distribuição dos poros e, portanto, com a granulometria. Nestas proposições, os parâmetros são calibrados pelo ajuste da curva de dados experimentais. Outros métodos supõem que a curva pode ser estimada diretamente a partir de propriedades físicas dos solos. Estas propostas são simples e conveniente para a utilização prática, mas são substancialmente incorretas, uma vez que ignoram a influência do teor de umidade, nível de tensões, estrutura do solo e mineralogia. Como resultado, a maioria tem sucesso limitado, dependendo do tipo de solo. Algumas tentativas têm sido feitas para prever a variação da resistência ao cisalhamento com relação a sucção matricial. Estes procedimentos usam, como uma ferramenta, direta ou indiretamente, a SWCC em conjunto com os parâmetros efetivos de resistência c e . Este trabalho discute a aplicabilidade de três equações para previsão da SWCC (Gardner, 1958; van Genuchten, 1980; Fredlund; Xing, 1994) para vinte e quatro amostras de solos residuais brasileiros. A adequação do uso da curva característica normalizada, proposta por Camapum de Carvalho e Leroueil (2004), também foi investigada. Os parâmetros dos modelos foram determinados por ajuste de curva, utilizando técnicas de problema inverso; dois métodos foram usados: algoritmo genético (AG) e Levenberq-Marquardt. Vários parâmetros que influênciam o comportamento da SWCC são discutidos. A relação entre a sucção matricial e resistência ao cisalhamento foi avaliada através de ajuste de curva utilizando as equações propostas por Öberg (1995); Sällfors (1997), Vanapalli et al., (1996), Vilar (2007); Futai (2002); oito resultados experimentais foram analisados. Os vários parâmetros que influênciam a forma da SWCC e a parcela não saturadas da resistência ao cisalhamento são discutidos.
In the last decades, theories have been formulated to interpret the behavior of unsaturated soils and found to be consistent with the experimental response. Besides, several techniques for field and laboratory testing have been developed, as well. However, the experimental determination of unsaturated soil parameters is costly, time-consuming, requires particular test equipments and experienced technicians. As a result, these theories application are limited to academic researches and are barely used in engineering practice. To overcome this issue, several researchers proposed equations to mathematically represent the experimental behavior unsaturated soils. These propositions are based on physical indexes, soil characterization, and current laboratory tests or simply curve fitting. The relationship of soil-water content and matric suction, conventionally referred to as the soil-water characteristic curve (SWCC) is also useful tool in the prediction of the engineering behavior of unsaturated soils. There are many equations to mathematically represent SWCC. Some are based on the assumption that its shape is directly related to the pore distribution, and, therefore, the grain size distribution. In these propositions the parameters are calibrated by curve adjustment of the experimental data. Others assume that the curve can be directly estimated from physical properties of soils. These proposals are simple and convenient for practical use, but are substantially incorrect since they disregard the influence of moisture content, stress level, soil structure and mineralogy. As a result, most of them have limited success depending on soil types. Some attempts have also been made to predict the variation of the shear strength with respect to matric suction. These procedures use SWCC as a tool either directly or indirectly along with the saturated strength parameters c and . This work discusses the applicability of three SWCC equations (Gardner, 1958; van Genuchten, 1980; and Fredlund and Xing, 1994) for twenty four residual soils from Brazil. The suitability of the normalized soil-water characteristic curve, proposed by Camapum de Carvalho and Leroueil (2004), was also investigated. Models parameters were determined by curve fitting, using inverse problem techniques; two optimization methods were used: Genetic Algorithm (GA) and Levenberq-Marquardt method. Several parameters that influence the SWCC behavior are discussed, as well. The relationship between matric suction and shear strength was evaluated by curve fitting using the equations proposed by Öberg and Sällfors (1995, 1997), Vanapalli et al., (1996), Vilar (2007) and Futai (2002); eight experimental results were analyzed. Several parameters that influence the SWCC behavior and the unsaturated shear strength are discussed, as well.

Dans les dernières décennies, les progrès des techniques expérimentales ont permis une augmentation considérable du nombre de séquences d'ADN et de protéines connues. Cela a incité au développement de méthodes statistiques variées visant à tirer parti de cette quantité massive de données. Les méthodes dites co-évolutives en font partie, utilisant des idées de physique statistique pour construire un modèle global de la variabilité des séquences de protéines. Ces méthodes se sont montrées très efficaces pour extraire des informations pertinentes des seules séquences, comme des contacts structurels ou les effets mutationnels. Alors que les modèles co-évolutifs sont pour l'instant utilisés comme outils prédictifs, leur succès plaide pour une meilleure compréhension de leur fonctionnement. Dans cette thèse, nous proposons des élaborations sur les méthodes déjà existantes tout en questionnant leur fonctionnement. Nous étudions premièrement sur la capacité de l'Analyse en Couplages Directs (DCA) à reproduire les motifs statistiques rencontrés dans les séquences des familles de protéines. La possibilité d'inclure d'autres types d'information comme des effets mutationnels dans cette méthode est présentée, suivie de corrections potentielles des biais phylogénétiques présents dans les données utilisées. Finalement, des considérations sur les limites des modèles co-évolutifs actuels sont développées, de même que des suggestions pour les surmonter
In the last decades, progress in experimental techniques have given rise to a vast increase in the number of known DNA and protein sequences. This has prompted the development of various statistical methods in order to make sense of this massive amount of data. Among those are pairwise co-evolutionary methods, using ideas coming from statistical physics to construct a global model for protein sequence variability. These methods have proven to be very effective at extracting relevant information from sequences, such as structural contacts or effects of mutations. While co-evolutionary models are for the moment used as predictive tools, their success calls for a better understanding of they functioning. In this thesis, we propose developments on existing methods while also asking the question of how and why they work. We first focus on the ability of the so-called Direct Coupling Analysis (DCA) to reproduce statistical patterns found in sequences in a protein family. We then discuss the possibility to include other types of information such as mutational effects in this method, and then potential corrections for the phylogenetic biases present in available data. Finally, considerations about limitations of current co-evolutionary models are presented, along with suggestions on how to overcome them

In response to serious environmental and economic concerns, the design and production of aircrafts have been changing profoundly over the past decades with the nose-to-tail switch from metallic materials to lightweight composite materials such as carbon fibre reinforced plastic (CFRP). In this context, the present doctoral research work aimed to contribute to the development of a CFRP booster casing, a real innovation in the field initiated and conducted by Safran Aero Boosters. More specifically, this thesis addresses the matter of joining metal/CFRP hybrid structures, which are prone to possibly detrimental residual stresses.The issue is treated with an approach combining experimental characterisation and finite element (FE) simulations. The multi-layered system’s state of damage was systematically examined on hundreds of micrographs, and the outcome of this study is presented under the form of a statistical analysis. Further, the defects’ 3D morphology is investigated by incremental polishing. A number of thermal and mechanical properties are measured by diverse physical tests on part of the constituent materials, i.e. the aerospace grade RTM6 epoxy resin, the structural Redux 322 epoxy film adhesive, and AISI 316L stainless steel. They are used as input data in a FE model of the multilayer that is developed and progressively refined to obtain detailed residual stress fields after thermal loading. These results are compared to experimental data acquired by X-ray diffraction stress analysis and with the curvature-based Stoney formula. Cohesive elements are placed at specific locations within the FE model to allow simulating progressive damage. Peel tests, mode I, mode II and mixed mode I/II fracture tests are thus performed in view of measuring the joint toughness. The results of these tests are discussed and the presence of residual stress in the fracture specimens is highlighted. Key information for the calibration of the cohesive law is finally identified via inverse FE analysis of the mode I test, this being a significant step in the process of building a damage predictive FE model of the multi-layered system.
Doctorat en Sciences de l'ingénieur et technologie
info:eu-repo/semantics/nonPublished

碩士
逢甲大學
資訊工程研究所
85
This thesis extends and modifies Classified Vector Quantization (CVQ) to solve the problem of inverse halftoning from error-diffused images. The process consists of two phases: the encoding phase and decoding phase. The encoding process needs a codebook for the encoder which transforms a halftoned image to a set of codewords. The decoding process also requires a different codebook for the decoder which reconstructs a gray- scale image from a set of codewords. According the relationships between these two codebooks, we modified the traditional generalized Lloyd Algorithm to fit our purpose. On the other hand, we also developed a process for inverse halftoning of error-diffused color image. Compared with other available techniques, our approach has the better quality for reconstructed image. Using CVQ, the reconstructed gray-scale image and color image can be stored in compressed form and no further compression maybe required. This is contrast to the existing algorithms which reconstruct a halftoned image in an uncompressed form. The bit-rate is about 0.52 bits per pixel for encoding a reconstructed gray-scale image, and about 0.96 bits per pixel for encoding a reconstructed color image. The main contribution of this thesis is it opens an area of application on signal reconstruction for VQ.

博士
國立臺灣大學
應用力學研究所
88
A theory for inverting residual stresses based on an acoustoelasticity theory referring to the initial state is established. A general incremental constitutive relation of residually stressed medium is first derived from basic continuum theories of material constitution together with an assumption that the superimposed deformation caused by ultrasonic waves is infinitesimal and elastic. Equations illustrating acoustoelastic effects induced by ultrasonic waves are then followed. In the theory, a globally optimal inversion of residual stresses based on quasi-transverse and quasi-longitudinal body waves, rather than the traditional pure-transverse acoustoelastic birefringence, is studied and proposed. From the results of sensitivity analysis, error analysis encountered with phase velocity measurements, and numerical simulation, the globally optimal inversion of residual stresses is more robust withstanding the random errors from phase velocity measurements than previous approaches. The relative errors of the difference of residual stresses with Thompson, Lee & Smith approach [11] and the absolute of residual stresses with Man & Lu approach [13] are 2 and 6 times of present inverting procedures, respectively. No assumption on the origin of residual stresses is needed, nor the assumption on the existence of ‘natural state’ of the materials. It then eludes the notorious difficulties of ‘natural state’ and ‘texture separation’ automatically. The traditional sextic formulation is extended to the cases of prestressed medium. The dispersion equation is a nonlinear integral equation of surface wave speeds. Numerical integration and recursive iteration are needed to retrieve the surface wave speeds. The inversion of residual stresses is affected tremendously by the numerical precision of the integration. A new sextic formulation is also proposed. A dispersion equation is obtained and expressed in a form of polynomial with surface wave speeds as variables, which relates incident angles of saggital plane, surface wave speed, elastic moduli of initial state, and residual stress. In this new sextic formulation the surface wave speeds are simply the roots of a twelve-degrees polynomial, at most. It can be benefit to the residual stress inversion. Finally, a hybrid method including body and surface wave inspections is proposed. The hybrid method can reduce the efforts of inversion significantly.

碩士
國立交通大學
應用數學系數學建模與科學計算碩士班
104
Solving large scale eigenvalue problems is always very difficult, it is efficient by using the Iteration method to solve this problem. In this thesis, we mean the iterative projection methods, Jacobi-Davidson (JD) and Shift-Invert Residual Arnoldi (SIRA) methods, which using inexact iteration. The problem be projection onto subspace, in order to reduce dimension, then we can obtain approximate by solve the smaller eigenvalue problem. We provide two package, jdsiraSEP and jdsiraGEP, which were primarily written by Chien-Chih Huang via MATLAB, these can solve the standard eigenvalue problems and generalized eigenvalue problems, respectively. The jdsiraSEP and jdsiraGEP based on Jacobi-Davidson and Shift-Invert Residual Arnoldi methods are applied to restarting and locking techniques. User can choose JD or SIRA method to find the desired eigenpairs. We then describe the algorithm about the jdsiraSEP andjdsiraGEP and how to operate in MATLAB. At the end of this thesis, we take the photonic crystals for example to show how to solve the eigenproblem.

This dissertation focuses on a novel approach for characterizing the mechanical behavior of an elastic body. In particular, we develop a mathematical tool for the estimation of residual stress field in an elastic body that has mechanical properties similar to that of the arterial wall, by making use of intravascular ultrasound (IVUS) imaging techniques. This study is a preliminary step towards understanding the progression of a cardiovascular disease called atherosclerosis using ultrasound technology. It is known that residual stresses play a significant role in determining the overall stress distribution in soft tissues. The main part of this work deals with developing a nonlinear inverse spectral technique that allows one to accurately compute the residual stresses in soft tissues. Unlike most conventional experimental, both in vivo and in vitro, and theoretical techniques to characterize residual stresses in soft tissues, the proposed method makes fundamental use of the finite strain non- linear response of the material to a quasi-static harmonic loading. The arterial wall is modeled as a nonlinear, isotropic, slightly compressible elastic body. A boundary value problem is formulated for the residually stressed arterial wall, the boundary of which is subjected to a constant blood pressure, and then an idealized model for the IVUS interrogation is constructed by superimposing small amplitude time harmonic infinitesimal vibrations on large deformations via an asymptotic construction of its solution. We then use a semi-inverse approach to study the model for a specific class of deformations. The analysis leads us to a system of second order differential equations with homogeneous boundary conditions of Sturm-Liouville type. By making use of the classical theory of inverse Sturm-Liouville problems, and root finding and optimization techniques, we then develop several inverse spectral algorithms to approximate the residual stress distribution in the arterial wall, given the first few eigenfrequencies of several induced blood pressures.

碩士
國立交通大學
應用數學系所
105
For the large and sparse eigenvalue problems, we usually want to find the eigenvalues in a specific region. Since we need to solve the linear system at each step, we use the inexactly Jacobi-Davidson method or the inexactly Shift and Invert Residual Arnoldi method which can reduce the accuracy of the linear systems and compute the eigenpairs which we want. Notice that the only difference between the algorithms of the Jacobi-Davidson and the shift and invert residual Arnoldi methods is the correction equations, so we combine these two methods by adjusting the correction equations to construct a program JDSIRA with MATLAB. In addition to solving the standard eigenvalue problem, this program can also solve polynomial eigenvalue problem and nonlinear eigenvalue problem. Moreover, we also develop the function of harmonic Rayleigh-Ritz method which can be used to solve the approximate eigenpairs. In the numerical experiment, we test the large and sparse matrices, some polynomial eigenvalue problems, and some nonlinear eigenvalue problems and also record the convergence processes of the program. In addition, when we test the eigenvalue problem of the Maxwell equations in the specific photonic crystal, there are some problems to make the program become unstable. Based on the numerical results, we can adjust the appropriate parameters and add some strategies in the program so that the program can solve the desired eigenvalues more efficiently.

Inverse spectral techniques are developed in this dissertation for recovering the shear modulus and residual stress of soft tissues. Shear modulus is one of several quantities for measuring the stiffness of a material, and hence estimating it accurately is an important factor in tissue characterization. Residual stress is a stress that can exist in a body in the absence of externally applied loads, and beneficial for biological growth and remodeling. It is a challenge to recover the two quantities in soft tissues both theoretically and experimentally. The current inverse spectral techniques recover the two unknowns invasively, and are theoretically based on a novel use of the intravascular ultrasound technology (IVUS) by obtaining several natural frequencies of the vessel wall material. As the IVUS is interrogating inside the artery, it produces small amplitude, high frequency time harmonic vibrations superimposed on the quasistatic deformation of the blood pressure pre-stressed and residually stressed artery. The arterial wall is idealized as a nonlinear isotropic cylindrical hyperelastic body for computational convenience. A boundary value problem is formulated for the response of the arterial wall within a specific class of quasistatic deformations reflexive of the response due to imposed blood pressures. Subsequently, a boundary value problem is developed from intravascular ultrasound interrogation generating small amplitude, high frequency time harmonic vibrations superimposed on the quasistatic finite deformations via an asymptotic construction of the solutions. This leads to a system of second order ordinary Sturm-Liouville problems (SLP) with the natural eigenfrequencies from IVUS implementation as eigenvalues of the SLP. They are then employed to reconstruct the shear modulus and residual stress in a nonlinear approach by inverse spectral techniques. The shear modulus is recovered by a multidimensional secant method (MSM). The MSM avoids computing the Jacobian matrix of the equations and is shown to be convenient for manipulation. Residual stress is recovered via an optimization approach (OA) instead of the traditional equation-solving method. The OA increases the robustness of the algorithms by overdetermination of the problem, and comprehensive tests are performed to guarantee the accuracy of the solution. Numerical examples are displayed to show the viability of these techniques.

Nuclear magnetic resonance (NMR) spectroscopy is an established technique for macromolecular structure determination at atomic resolution. However, the majority of the current structure determination approaches require a large set of experiments and use large amount of data to elucidate the three dimensional protein structure. While current structure determination protocols may perform well in data-rich settings, protein structure determination still remains to be a difficult task in a sparse-data setting. Sparse data arises in high-throughput settings, for larger proteins, membrane proteins, and symmetric protein complexes; thereby requiring novel algorithms that can compute structures with provable guarantees on solution quality and running time.

In this dissertation project we made an effort to address the key computational bottlenecks in NMR structural biology. Specifically, we improved and extended the recently-developed techniques by our laboratory, and developed novel algorithms and computational tools that will enable protein structure determination from sparse NMR data. An underlying goal of our project was to minimize the number of NMR experiments, hence the amount of time and cost to perform them, and still be able to determine protein structures accurately from a limited set of experimental data. The algorithms developed in this dissertation use the global orientational restraints from residual dipolar coupling (RDC) and residual chemical shift anisotropy (RCSA) data from solution NMR, in addition to a sparse set of distance restraints from nuclear Overhauser effect (NOE) and paramagnetic relaxation enhancement (PRE) measurements. We have used tools from algebraic geometry to derive analytic expressions for the bond vector and peptide plane orientations, by exploiting the mathematical interplay between RDC- or RCSA-derived sphero-conics and protein kinematics, which in addition to improving our understanding of the geometry of the restraints from these experimental data, have been used by our algorithms to compute the protein structures provably accurately. Our algorithms, which determine protein backbone global fold from sparse NMR data, were used in the high-resolution structure determination protocol developed in our laboratory to solve the solution NMR structures of the FF Domain 2 of human transcription elongation factor CA150 (RNA polymerase II C-terminal domain interacting protein), which have been deposited into the Protein Data Bank. We have developed a novel, sparse data, RDC-based algorithm to compute ensembles of protein loop conformations in the presence of a moderate level of dynamics in the loop regions. All the algorithms developed in this dissertation have been tested on experimental NMR data. The promising results obtained by our algorithms suggest that our algorithms can be successfully applied to determine high-quality protein backbone structures from a limited amount of experimental NMR data, and hence will be useful in automated NOE assignments and high-resolution protein backbone structure determination from sparse NMR data. The algorithms and the software tools developed during this project are made available as free open-source to the scientific community.

Dissertation

Section 33(1)(b) is fraught with borrowed provisions. The end-product marries German and Canadian features. The failure of the German Constitutional Courts to interpret the "essential content of a right" precipitated the adopted infant's bumpy landing in South Africa. That the sibling still lacks identity is evidenced by our Constitutional Court's evasive and superficial treatment of the clause. Section 33(1)(a) - proportionality prong enables judges to justify their neglect of Section 33(1)(b). The opinion is expressed that Section 33(1){b) demands interpretation but to date it has been shrouded in vagueness. After all without demarcating boundaries with sufficient precision and highlighting where the State may not tread the State may trespass. Alternatively the limitable nature of human rights could become a myth as Section 33(1)(b) could be transformed into an insurmountable hurdle for the State, rendering every right absolute in practice. A workable conceptual framework proposes an inverted, porous and value imbibing solution.
Law
LL.M.

Dissertação de Mestrado Integrado em Engenharia do Ambiente apresentada à Faculdade de Ciências e Tecnologia
Due to the characteristics of the wastewaters resulting from domestic, commercial and industrial effluents produced in urban agglomerations, the solid transport, natural or artificial ventilation and the multiphase flows have special relevance in sanitation systems. The flow in the general network of collectors carrying wastewater is processed predominantly by gravity and with a free surface. However, complementary installations with pipelines with flow under pressure that may have various specificities and incorporate various risks associated with their normal operation are usually indispensable, particularly in large systems. In the case of ascending pipelines, the air injection in steady flow at their base may, not only facilitate the aeration of the liquid mass and prevent the creation of septic conditions, but also improve the hydraulic operation and the process of lifting or transporting the solids present in the wastewater.The current dissertation is part of a set of works that have been developed within the scope of an ongoing research project at the Laboratory of Hydraulics, Water Resources and Environment, LHRHA, of the Department of Civil Engineering of the Faculty of Sciences and Technology of Coimbra University, DEC-FCTUC, which aims to study and model the various particularities of steady multiphase flows in sanitation systems. The main focus of research in this case was centered on a predominantly experimental work of establishment, measurement and analysis of the solid transport that occurs in two-phase (water-sand) and three-phase (water-sand) steady (permanent) flows in under pressure ascending pipes, in order to be able to evaluate the effects and possible benefits on solid transport, caused by the injection of compressed air at the base of ascending ducts. For this purpose, an existing experimental installation at LHRHA was used, which allowed the introduction, collection and measurement of solid flow rates for various water and injected air flow rates, different inclinations of the ascending duct and different diameters of the transported solid particles. The possibility of applying a simplified two-phase (water-air) model proposed in previous work, for the characterization of the hydraulic functioning of the three-phase (water-air-solid) flows now experimentally observed, considering the solid phase included in the liquid phase, is analyzed, as well as a first approach to the modeling of the critical conditions, or of solid transport start, in the observed two and three-phase flows. The introduction of air at the base of an ascending duct in steady flow, whether it is the impulsion duct of a pumping system, or the ascending branch of an inverted siphon, shows to be extremely favorable in the observed solid transport, which is facilitated or incremented when the introduced air flow rate increases, for a given installation geometry. The characteristics of the flow and the observed solid flow rate are greatly influenced by the slope of the pipe and the diameter of the transported particles. The application of the simplified water-air model previously proposed allows for a reasonable approximation for the description of the hydraulic functioning of the three-phase flow in the ascending duct; the critical or solid transport starting conditions appear to be describable to a good approximation based on Shields and Reynolds numbers, using appropriate characteristic quantities.
Devido às caracteristicas das águas residuais comunitárias resultantes das contribuições domiciliárias, comerciais e industriais produzidas nos aglomerados urbanos, o transporte sólido, a ventilação natural ou artificial e os escoamentos multifásicos apresentam especial relevância nos sistemas de saneamento. O escoamento na rede geral de colectores que transportam águas residuais processa-se predominantemente por gravidade e com superfície livre. No entanto, instalações complementares com condutas com escoamento sob pressão que podem apresentar diversas especificidades e incorporar vários riscos associados ao seu normal funcionamento são normalmente indispensáveis, particularmente em sistemas de grandes dimensões. No caso de condutas ascendentes, a injecção de ar na base das mesmas poderá, não apenas facilitar o arejamento da massa líquida e prevenir a criação de condições de septicidade, como também melhorar o funcionamento hidráulico e o processo de elevação ou de transporte dos sólidos presentes nas águas residuais.A presente dissertação insere-se num universo de trabalhos que têm vindo a ser desenvolvidos no âmbito de um projecto de investigação em curso no Laboratório de Hidráulica, Recursos Hídricos e Ambiente, LHRHA, do Departamento de Engenharia Civil da Faculdade de Ciências e Tecnologia da Universidade de Coimbra, DEC-FCTUC, que pretende estudar e modelar as diversas particularidades dos escoamentos multifásicos em sistemas de saneamento. O principal foco de investigação neste caso centrou-se num trabalho predominantemente experimental de estabelecimento, medição e análise do transporte sólido que ocorre nos escoamentos em regime permanente de duas fases (água-areia) e de três fases (água-ar-areia) em condutas sob pressão ascendentes, de forma a poder avaliar os efeitos e possíveis benefícios no transporte sólido, causados pela injecção de ar comprimido na base de condutas ascendentes. Para o efeito, foi utilizada uma instalação experimental existente no LHRHA que permitiu a introdução, recolha e medição de caudais sólidos para vários caudais de água e de ar injectado, diferentes inclinações da conduta ascendente e diferentes diâmetros das partículas sólidas transportadas.É analisada a possibilidade de aplicação de um modelo simplificado de duas fases (água-ar) proposto em trabalho anterior, para a caracterização do funcionamento hidráulico dos escoamentos de três fases (água-ar-sólidos) agora observados experimentalmente, considerando a fase sólida incluída na fase líquida, bem como uma primeira abordagem à modelação das condições críticas, ou de início do transporte sólido, nos escoamentos de duas e três fases observados. A introdução de ar na base de uma conduta ascendente, seja a conduta de impulsão de um sistema de bombagem, ou o ramo ascendente de um sifão invertido, mostra-se extremamente favorável no transporte sólido observado que surge facilitado ou incrementado quando aumenta o caudal de ar introduzido, para um dada geometria da instalação. As características do escoamento e o caudal sólido observado são muito influenciados pela inclinação da tubagem e pelo diâmetro das partículas transportadas. A aplicação do modelo simplificado água-ar anteriormente proposto permite uma razoável aproximação para a descrição do funcionamento hidráulico do escoamento de três fases na conduta ascendente; as condições críticas ou de início de transporte sólido aparentam poder ser descritas com boa aproximação com base nos números de Shields e de Reynolds, utilizando grandezas características adequadas.

Le problème inverse en électroencéphalographie (EEG) est la localisation de sources de courant dans le cerveau utilisant les potentiels de surface sur le cuir chevelu générés par ces sources. Une solution inverse implique typiquement de multiples calculs de potentiels de surface sur le cuir chevelu, soit le problème direct en EEG. Pour résoudre le problème direct, des modèles sont requis à la fois pour la configuration de source sous-jacente, soit le modèle de source, et pour les tissues environnants, soit le modèle de la tête. Cette thèse traite deux approches bien distinctes pour la résolution du problème direct et inverse en EEG en utilisant la méthode des éléments de frontières (BEM): l’approche conventionnelle et l’approche réciproque. L’approche conventionnelle pour le problème direct comporte le calcul des potentiels de surface en partant de sources de courant dipolaires. D’un autre côté, l’approche réciproque détermine d’abord le champ électrique aux sites des sources dipolaires quand les électrodes de surfaces sont utilisées pour injecter et retirer un courant unitaire. Le produit scalaire de ce champ électrique avec les sources dipolaires donne ensuite les potentiels de surface. L’approche réciproque promet un nombre d’avantages par rapport à l’approche conventionnelle dont la possibilité d’augmenter la précision des potentiels de surface et de réduire les exigences informatiques pour les solutions inverses. Dans cette thèse, les équations BEM pour les approches conventionnelle et réciproque sont développées en utilisant une formulation courante, la méthode des résidus pondérés. La réalisation numérique des deux approches pour le problème direct est décrite pour un seul modèle de source dipolaire. Un modèle de tête de trois sphères concentriques pour lequel des solutions analytiques sont disponibles est utilisé. Les potentiels de surfaces sont calculés aux centroïdes ou aux sommets des éléments de discrétisation BEM utilisés. La performance des approches conventionnelle et réciproque pour le problème direct est évaluée pour des dipôles radiaux et tangentiels d’excentricité variable et deux valeurs très différentes pour la conductivité du crâne. On détermine ensuite si les avantages potentiels de l’approche réciproquesuggérés par les simulations du problème direct peuvent êtres exploités pour donner des solutions inverses plus précises. Des solutions inverses à un seul dipôle sont obtenues en utilisant la minimisation par méthode du simplexe pour à la fois l’approche conventionnelle et réciproque, chacun avec des versions aux centroïdes et aux sommets. Encore une fois, les simulations numériques sont effectuées sur un modèle à trois sphères concentriques pour des dipôles radiaux et tangentiels d’excentricité variable. La précision des solutions inverses des deux approches est comparée pour les deux conductivités différentes du crâne, et leurs sensibilités relatives aux erreurs de conductivité du crâne et au bruit sont évaluées. Tandis que l’approche conventionnelle aux sommets donne les solutions directes les plus précises pour une conductivité du crâne supposément plus réaliste, les deux approches, conventionnelle et réciproque, produisent de grandes erreurs dans les potentiels du cuir chevelu pour des dipôles très excentriques. Les approches réciproques produisent le moins de variations en précision des solutions directes pour différentes valeurs de conductivité du crâne. En termes de solutions inverses pour un seul dipôle, les approches conventionnelle et réciproque sont de précision semblable. Les erreurs de localisation sont petites, même pour des dipôles très excentriques qui produisent des grandes erreurs dans les potentiels du cuir chevelu, à cause de la nature non linéaire des solutions inverses pour un dipôle. Les deux approches se sont démontrées également robustes aux erreurs de conductivité du crâne quand du bruit est présent. Finalement, un modèle plus réaliste de la tête est obtenu en utilisant des images par resonace magnétique (IRM) à partir desquelles les surfaces du cuir chevelu, du crâne et du cerveau/liquide céphalorachidien (LCR) sont extraites. Les deux approches sont validées sur ce type de modèle en utilisant des véritables potentiels évoqués somatosensoriels enregistrés à la suite de stimulation du nerf médian chez des sujets sains. La précision des solutions inverses pour les approches conventionnelle et réciproque et leurs variantes, en les comparant à des sites anatomiques connus sur IRM, est encore une fois évaluée pour les deux conductivités différentes du crâne. Leurs avantages et inconvénients incluant leurs exigences informatiques sont également évalués. Encore une fois, les approches conventionnelle et réciproque produisent des petites erreurs de position dipolaire. En effet, les erreurs de position pour des solutions inverses à un seul dipôle sont robustes de manière inhérente au manque de précision dans les solutions directes, mais dépendent de l’activité superposée d’autres sources neurales. Contrairement aux attentes, les approches réciproques n’améliorent pas la précision des positions dipolaires comparativement aux approches conventionnelles. Cependant, des exigences informatiques réduites en temps et en espace sont les avantages principaux des approches réciproques. Ce type de localisation est potentiellement utile dans la planification d’interventions neurochirurgicales, par exemple, chez des patients souffrant d’épilepsie focale réfractaire qui ont souvent déjà fait un EEG et IRM.
The inverse problem of electroencephalography (EEG) is the localization of current sources within the brain using surface potentials on the scalp generated by these sources. An inverse solution typically involves multiple calculations of scalp surface potentials, i.e., the EEG forward problem. To solve the forward problem, models are needed for both the underlying source configuration, the source model, and the surrounding tissues, the head model. This thesis treats two distinct approaches for the resolution of the EEG forward and inverse problems using the boundary-element method (BEM): the conventional approach and the reciprocal approach. The conventional approach to the forward problem entails calculating the surface potentials starting from source current dipoles. The reciprocal approach, on the other hand, first solves for the electric field at the source dipole locations when the surface electrodes are reciprocally energized with a unit current. A scalar product of this electric field with the source dipoles then yields the surface potentials. The reciprocal approach promises a number of advantages over the conventional approach, including the possibility of increased surface potential accuracy and decreased computational requirements for inverse solutions. In this thesis, the BEM equations for the conventional and reciprocal approaches are developed using a common weighted-residual formulation. The numerical implementation of both approaches to the forward problem is described for a single-dipole source model. A three-concentric-spheres head model is used for which analytic solutions are available. Scalp potentials are calculated at either the centroids or the vertices of the BEM discretization elements used. The performance of the conventional and reciprocal approaches to the forward problem is evaluated for radial and tangential dipoles of varying eccentricities and two widely different skull conductivities. We then determine whether the potential advantages of the reciprocal approach suggested by forward problem simulations can be exploited to yield more accurate inverse solutions. Single-dipole inverse solutions are obtained using simplex minimization for both the conventional and reciprocal approaches, each with centroid and vertex options. Again, numerical simulations are performed on a three-concentric-spheres model for radial and tangential dipoles of varying eccentricities. The inverse solution accuracy of both approaches is compared for the two different skull conductivities and their relative sensitivity to skull conductivity errors and noise is assessed. While the conventional vertex approach yields the most accurate forward solutions for a presumably more realistic skull conductivity value, both conventional and reciprocal approaches exhibit large errors in scalp potentials for highly eccentric dipoles. The reciprocal approaches produce the least variation in forward solution accuracy for different skull conductivity values. In terms of single-dipole inverse solutions, conventional and reciprocal approaches demonstrate comparable accuracy. Localization errors are low even for highly eccentric dipoles that produce large errors in scalp potentials on account of the nonlinear nature of the single-dipole inverse solution. Both approaches are also found to be equally robust to skull conductivity errors in the presence of noise. Finally, a more realistic head model is obtained using magnetic resonance imaging (MRI) from which the scalp, skull, and brain/cerebrospinal fluid (CSF) surfaces are extracted. The two approaches are validated on this type of model using actual somatosensory evoked potentials (SEPs) recorded following median nerve stimulation in healthy subjects. The inverse solution accuracy of the conventional and reciprocal approaches and their variants, when compared to known anatomical landmarks on MRI, is again evaluated for the two different skull conductivities. Their respective advantages and disadvantages including computational requirements are also assessed. Once again, conventional and reciprocal approaches produce similarly small dipole position errors. Indeed, position errors for single-dipole inverse solutions are inherently robust to inaccuracies in forward solutions, but dependent on the overlapping activity of other neural sources. Against expectations, the reciprocal approaches do not improve dipole position accuracy when compared to the conventional approaches. However, significantly smaller time and storage requirements are the principal advantages of the reciprocal approaches. This type of localization is potentially useful in the planning of neurosurgical interventions, for example, in patients with refractory focal epilepsy in whom EEG and MRI are often already performed.