給定兩個有限離散型條件分配，我們可以去探討有關相容性及唯一性的問題。Tian et al.(2009)提出一個統合的方法，將相容性的問題轉換成具限制條件的線性方程系統(以邊際機率為未知數)，並藉由 l_2-距離測量解之誤差，進而求出最佳解來。他們也提出了電腦數值計算法在檢驗相容性及唯一性時的準則。 由於 Tian et al.(2009)的方法是把邊際機率和為 1 的條件放置在線性方程系統中，從理論的觀點來看，我們認為該條件在此種做法下未必會滿足。因此，本文中將邊際機率和為 1 的條件從線性方程系統中抽離出來，放入限制條件中，再對修正後的問題求最佳解。 我們提出了兩個解決問題的方法：(一) LRG 法；(二) 干擾參數法。LRG 法是先不管機率值在 0 與 1 之間的限制，在邊際機率和為 1 的條件下，利用 Lagrange 乘數法導出解的公式，之後再利用 Rao-Ghangurde 法進行修正，使解滿足機率值在 0 與 1 之間的要求。干擾參數法是在 Lagrange 乘數法公式解中有關廣義逆矩陣的計算部份引進了微量干擾值，使近似的逆矩陣及解可快速求得。理論證明，引進干擾參數所增加的誤差不超過所選定的干擾值，易言之，由干擾參數法所求出的解幾近最佳解。故干擾參數法在處理相容性問題上，是非常實用、有效的方法。從進一步分析Lagrange 乘數法公式解的過程中，我們也發現了檢驗條件分配"理論"相容的充分條件。 最後，為了驗證 LRG 法與干擾參數法的可行性，我們利用 MATLAB 設計了程式來處理求解過程中的運算，並以 Tian et al.(2009)文中四個可涵蓋各種情況的範例來解釋說明處理的流程，同時將所獲得的結果和 Tian et al. 的結果做比較。 / Given two finite discrete conditional distributions, we could study the compatibility and uniqueness issues. Tian et al.(2009) proposed a unified method by converting the compatibility problem into a system of linear equations with constraints, in which marginal probability values are assumed unknown. It locates the optimum solution by means of the error of l_2 - discrepancy. They also provided criteria for determining the compatibility and uniqueness. Because the condition of sum of the marginal probability values being equal to one is in Tian et al.s’linear system, it might not be fulfilled by the optimum solution. By separating this condition from the linear system and adding into constraints, we would look for the optimum solution after modification. We propose two new methods: (1) LRG method and (2) Perturbation method. LRG method ignores the requirement of the probability values being between zero and one initially, it then uses the Lagrange multipliers method to derive the solution for a quadratic optimization problem subject to the sum of the marginal probability values being equal to 1. Afterward we use the Rao-Ghangurde method to modify the computed value to meet the requirement. The perturbation method introduces tiny perturbation parameter in finding the generalized inverse for the optimum solution obtained by the Lagrange multipliers method. It can be shown that the increased error is less than the perturbation value introduced. Thus it is a practical and effective method in dealing with compatibility issues. We also find some sufficient conditions for checking the compatibility of conditional distributions from further analysis on the solution given by Lagrange multipliers method. To show the feasibilities of LRG method and Perturbation method, we use MATLAB to device a program to conduct them. Several numerical examples raised by Tian et al.(2009) in their article are applied to illustrate our methods. Some comparisons with their method are also presented.

In our age in which the use of electronic devices is expanding all over the world, their reliability and miniaturization have become very crucial. The thesis is based on the study of one of the most frequent failure mechanisms in semiconductor packages, the delamination of interface or the separation of two bonded materials, in order to improve their adhesion and a fortiori the reliability of microelectronic devices. It focuses on the metal (-oxide) / polymer interfaces because they cover 95% of all existing interfaces. Since several years, research activities at mesoscopic scale (1-10µm) have proved that the more roughened the surface of the interface, i.e., presenting sharp asperities, the better the adhesion between these two materials. Because roughness exhibits extremely complex shapes, it is difficult to find a description that can be used for reliability analysis of interfaces. In order to investigate quantitatively the effect of roughness variation on adhesion properties, studies have been carried out involving analytical fracture mechanics; then numerical studies were conducted with Finite Element Analysis. Both were done in a deterministic way by assuming an ideal profile which is repeated periodically. With the development of statistical and stochastic roughness representation on the one hand, and with the emergence of probabilistic fracture mechanics on the other, the present work adds a stochastic framework to the previous studies. In fact, one of the Stochastic Finite Element Methods, the Perturbation method is chosen for implementation, because it can investigate the effect of the geometric variations on the mechanical response such as displacement field. In addition, it can carry out at once what traditional Finite Element Analysis does with numerous simulations which require changing geometric parameters each time. This method is developed analytically, then numerically by implementing a module in a Finite Element package MSc. Marc/Mentat. In order to get acquainted and to validate the implementation, the Perturbation method is applied analytically and numerically to the 3 point bending test on a beam problem, because the input of the Perturbation method in terms of roughness parameters is still being studied. The capabilities and limitations of the implementation are outlined. Finally, recommendations for using the implementation and for furture work on roughness representation are discussed.

Στην παρούσα διατριβή υπολογίζονται σχετικιστικά πολυτροπικά μοντέλα περιστρεφομένων αστέρων νετρονίων, καθώς και μοντέλα που περιγράφονται από ρεαλιστικές καταστατικές εξισώσεις. Σκοπός αυτής της μελέτης είναι να υπολογιστούν σημαντικές φυσικές ποσότητες ενός αστέρα νετρονίων, στην περίπτωση της υδροστατικής ισορροπίας, της ομοιόμορφης αλλά και της διαφορικής περιστροφής, καθώς και στην περίπτωση που ο αστέρας έχει μαγνητικό πεδίο με πολοειδή και τοροειδή συνιστώσα. Μία σύντομη περιγραφή της αριθμητικής διαπραγμάτευσης έχει ως εξής. Καταρχάς, επιλύεται το σύστημα διαφορικών εξισώσεων Oppenheimer-Volkov (OV). Το σύστημα αυτό περιγράφει την υδροστατική ισορροπία μη περιστρεφομένων πολυτροπικών μοντέλων. Στη συνέχεια, θεωρείται η ομοιόμορφη περιστροφή ως διαταραχή, σύμφωνα με την «μέθοδο διαταραχής Hartle» και υπολογίζονται διορθώσεις στην μάζα και την ακτίνα, διορθώσεις που οφείλονται σε σφαιρικές και τετραπολικές παραμορφώσεις. Ακολούθως, εφαρμόζεται μία διαταρακτική προσέγγιση με όρους τρίτης τάξης στην γωνιακή ταχύτητα, Ω. Η στροφορμή, J, η ροπή αδράνειας, I, η περιστροφική κινητική ενέργεια, T, και η βαρυτική δυναμική ενέργεια, W, είναι ποσότητες που υφίστανται σημαντικές διορθώσεις από την προσέγγιση τρίτης τάξης. Η διαφορική περιστροφή ϑεωρείται ότι (i) υπακούει σε έναν συγκεκριμένο νόμο, ή (ii) επάγεται από το συνδυασμό ομοιόμορφης περιστροφής και ακτινικών ταλαντώσεων του αστέρα· ο στόχος είναι να υπολογισθεί η μεταβολή σημαντικών φυσικών ποσοτήτων που οφείλεται στη διαφορική περιστροφή. Στο δεύτερο μέρος, μελετάται η επίδραση του μαγνητικού πεδίου, το οποίο αποτελείται από πολοειδή και τοροειδή συνιστώσα, με τη «μέθοδο διαταραχής κατά Ioka-Sasaki» (IS). Στην παρούσα διαπραγμάτευση, το πρόβλημα περιγράφεται από μία «γενικευμένη διαφορική εξίσωση Grad-Shafranov» (GS),η επίλυση της οποίας δίνει τη συνάρτηση ροής (flux function), ψ. Μέσω αυτής της συνάρτησης υπολογίζονται οι συνιστώσες του μαγνητικού πεδίου και η γεωμετρική παραμόρφωση που υφίσταται ο αστέρας λόγω του μαγνητικού πεδίου. Η αντιμετώπιση του προβλήματος γίνεται και σε αυτήν την περίπτωση με τη ϑεωρία διαταραχών. ΄Εχοντας υπολογίσει μοντέλα περιστρεφομένων αστέρων νετρονίων και διάφορα μοντέλα με μαγνητικό πεδίο, μπορούμε να συνθέσουμε τα αποτελέσματά μας και να προσδιορίσουμε μοντέλα αστέρων νετρονίων μηδενικής φαινόμενης παραμόρφωσης (equalizers), δηλαδή αστέρων νετρονίων που η περιστροφή και το μαγνητικό πεδίο προκαλούν ίσες και αντίθετες γεωμετρικές παραμορφώσεις στο σχήμα του αστέρα. / We compute relativistic polytropic models as well as models obeying realistic equations of state, of rotating neutron stars. The purpose of this study is to calculate significant physical quantities of a neutron star, in the case of hydrostatic equilibrium, rigid and differential rotation, as well as in the case of a magnetic neutron star with both poloidal and toroidal components. A short description of the numerical treatment has as follows. First, we solve the Oppenheimer-Volkov system of differential equations. This system refers to hydrostatic equilibrium of non rotating polytropic models. Then, solid rotation is added as a perturbation, according to "Hartle’s perturbation method" and corrections to mass and radius are calculated, as also corrections due to spherical and quadrupole deformations. In addition a third order perturbation in angular velocity, Ω, is implemented. Angular momentum, J, moment of inertia, I, rotational kinetical energy, T, and gravitational potential energy, W, are quantites that are significally corrected by the third order approximation. Differential rotation is assumed that (i) obeys a specific law, or (ii) follows as a result of the solid rotation and radial oscillations combination; our purpose is the calculation of the main physical quantities that are altered by differential rotation. In the second part the effect of magnetic field is studied, which consists of a poloidal and a toroidal component. The "Ioka-Sasaki perturbation method" (IS) is implemented. This problem is described by the quantification of the flux function ψ, which comes as a solution of the "Grad-Shafranov" (GS) differential equation. Then the components of the magnetic field and the quadrupole deformation of the star are calculated. This method is also a perturbative method similar to "Hartle’s perturbation method". Having calculated models of rotating neutron stars, as also various models of magnetic fields, we can compose our results and determine models of neutron stars with zero deformation, the equalizers, these are neutron stars that are rotating and also have a magnetic field in a way that they, rotation and magnetic field, produce equal but opposite geometrical deformations in the shape of the star.

Submitted by JÚLIO HEBER SILVA (julioheber@yahoo.com.br) on 2017-06-20T18:27:52Z No. of bitstreams: 2 Dissertação - Rosane Gonçalves Ferreira - 2016.pdf: 4272548 bytes, checksum: a5f44a1be60a4ace1d85167dc75c33c4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Cláudia Bueno (claudiamoura18@gmail.com) on 2017-07-07T19:47:39Z (GMT) No. of bitstreams: 2 Dissertação - Rosane Gonçalves Ferreira - 2016.pdf: 4272548 bytes, checksum: a5f44a1be60a4ace1d85167dc75c33c4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-07-07T19:47:39Z (GMT). No. of bitstreams: 2 Dissertação - Rosane Gonçalves Ferreira - 2016.pdf: 4272548 bytes, checksum: a5f44a1be60a4ace1d85167dc75c33c4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-03-04 / Vibrations of mechanical systems have a wide field of research, where many work have been dedicated. Such importance is due to the fact that most human activities involve vibrations. It is worth noting that many device can suffer or produce vibrations, such as, machines, structures, motors, turbines. Vibratory systems, generally can produce complex behavior, thus the analysis of such dynamics behavior needs to use sophisticated mathematical tools. The mathematical model assigns important features of real processes with respect to linear and non-linear differential equations. In this work we are interested in the analysis of behavior of delayed mechanical systems. Time delayed can compromise the performance of controls even adding instability in the systems. On the other hand, write choose of delays can improve its performance. Systems with time delay, similar to ordinary systems, are molded by ordinary and/or partial differential equations, but, unlikely ordinary differential equations, delayed differential equations, also known as functional differential equations, are molded on Banach spaces with infinite dimension, which introduce serious difficulty in analysis of stability, since that, the spectra of solution semi-group associated with the linear part of the model can presents infinite eigenvalues. Thus, our contribution of the study of dynamics behavior of such systems will be in two directions. In the first one, we apply the perturbation method of multiple scales in themodel of differential equations, since that the system shows nonlinear vibrations. It is worth noting that the differential analysis used in the stage regarding differential equations in Banach spaces, which has infinite dimension, this approach differ substantially from standards approaches. Then we obtain numerical solutions for the amplitude at steady state using the Newton Raphson method and then we made a numerical analysis of the model of stability with delay and without delay to different parameters, using the Runge-Kuttamethod. / As vibrações possuem um campo extenso de estudos, ao quais trabalhos inteiros têm sido dedicados. Tamanha importância deve-se ao fato de que a maioria das atividades humanas envolve vibrações. Muitos sistemas construídos sofrem ou produzem vibração, tais como máquinas, estruturas, motores, turbinas e sistemas de controle. Umsistema vibratório geralmente apresenta comportamento complexo, assim a análise do comportamento dinâmicos envolve o uso de ferramentas matemáticas sofisticadas. O modelo matemático incorpora os aspectos importantes do processo real, em termos de equações diferenciais lineares ou não lineares. Neste trabalho nosso objetivo é analisar o comportamento de um modelo de sistemas mecânicos. Os tempos de atrasos quando presentes em controladores e atuadores podem ser motivo de ineficiência ou mesmo causar a instabilidade do sistema. Porém, o controle adequado desses atrasos pode melhorar o desempenho de sistemas mecânicos. Os sistemas com tempo de atraso, assim como os sistemas ordinários, são modelados por equações diferenciais ordinárias ou parciais, mas diferentemente das equações ordinárias, equações com tempo de atraso, também conhecidas como equações funcionais, são modeladas em espaços de dimensão infinita, o que dificulta enormemente a análise de estabilidade, uma vez que, o espectro do semigrupo solução associado à parte linear do modelo pode apresentar infinitos autovalores. Assim, nossa contribuição ao estudo do comportamento dinâmico de tais sistemas foi feito em duas partes. Na primeira, aplicamos o método de perturbação das múltiplas escalas no sistema de equações diferenciais do modelo, uma vez que o sistema apresenta vibrações não lineares. Nesta parte, é importante ressaltar que a análise diferencial usada foi em um espaço de dimensão infinita, também conhecido como espaço de Banach; esta análise difere substancialmente daquela usada no caso ordinário. Em seguida obtemos soluções numéricas para a amplitude em estado estacionário usando o método de Newton Raphson e depois fizemos uma análise numérica da estabilidade do modelo com atraso e sem atraso para diferentes parâmetros, usando o método de Runge- Kutta.

La maintenance aéronautique est fortement régulée, notamment à travers l’établissement d’un planning de maintenance obligatoire, permettant de garantir la sureté structurale. La fréquence des arrêts en maintenance est déterminée de manière très conservative en vue d’assurer les exigences de fiabilité. Développer des stratégies de maintenance moins conservatives et plus efficaces peut alors représenter une voie pour une nouvelle croissance des compagnies aériennes. Les systèmes de monitoring embarqué de structures, sont progressivement introduits dans l’industrie aéronautique. Ces développements pourraient alors permettre de nouvelles stratégies de maintenance structurale basées sur la prévision de l’état de santé de chaque élément structural, plutôt que basée sur une maintenance programmée, tel qu’implémentée actuellement. Dans ce cadre général, ce travail se concentre sur le suivi par un système embarqué de la propagation de fissures de fatigue dans les panneaux de fuselage. Une nouvelle méthode de prévision des fissures basée sur des modèles de propagation est développée, qui permet de filtrer le bruit des mesures du système embarqué, identifier la taille actuelle de la fissure et prédire son évolution future et par conséquent la fiabilité des panneaux. Cette approche prédictive est intégrée dans le processus de maintenance structurale aéronautique et deux types de maintenances prédictives sont proposés. L’étude numérique montre que ces stratégies de maintenance prédictive peuvent réduire de manière significative les coûts de maintenance en réduisant le nombre d’arrêts en maintenance et le nombre de réparations inutiles. / Aircraft maintenance represents a major economic cost for the aviation industry. Traditionally, the aircraft maintenance is highly regulated based on fixed schedules (thus called scheduled maintenance) in order to ensure safety. The frequency of scheduled maintenance is designed to be very conservative to maintain a desirable level of reliability. Developing efficient maintenance can be an important way for airlines to allow a new profit growth. With the development of sensor technology, structural health monitoring (SHM) system, which employ a sensor network sealing inside aircraft structures to monitor the damage state, are gradually being introduced in the aviation industry. Once it is possible to monitor the structure damage state automatically and continuously by SHM systems, it enables to plan the maintenance activities according to the actual or predicted health state of the aircraft rather than a fixed schedule. This work focus on the fatigue crack propagation in the fuselage panels. The SHM system is assumed to be employed. A model-based prognostics method is developed, which enables to filter the noise of SHM data to estimate the crack size, and to predict the future health state of the panels. This predictive information is integrated into the maintenance decision-making and two types of predictive maintenance are developed. The numerical study shows that the predictive maintenance significantly reduces the maintenance cost by reducing the number of maintenance stop and the repaired panels.

This dissertation focuses on the scattering phenomena by well-polished optical mirror surfaces. Specifically, predicting image degradation by surface scatter from rough mirror surfaces for a two-mirror telescope operating at extremely short wavelengths (9nm~30nm) is performed. To evaluate image quality, surface scatter is predicted from the surface metrology data and the point spread function in the presence of both surface scatter and aberrations is calculated. For predicting the scattering intensity distribution, both numerical and analytic methods are considered. Among the numerous analytic methods, the small perturbation method (classical Rayleigh-Rice surface scatter theory), the Kirchhoff approximation method (classical BeckmanKirchhoff surface scatter theory), and the generalized Harvey-Shack surface scatter theory are adopted. As a numerical method, the integral equation method (method of moments) known as a rigorous solution is discussed. Since the numerical method is computationally too intensive to obtain the scattering prediction directly for the two mirror telescope, it is used for validating the three analytic approximate methods in special cases. In our numerical comparison work, among the three approximate methods, the generalized Harvey-Shack model shows excellent agreement to the rigorous solution and it is used to predict surface scattering from the mirror surfaces. Regarding image degradation due to surface scatter in the presence of aberrations, it is shown that the composite point spread function is obtained in explicit form in terms of convolutions of the geometrical point spread function and scaled bidirectional scattering distribution functions of the individual surfaces of the imaging system. The approximations and assumptions in this iv formulation are discussed. The result is compared to the irradiance distribution obtained using commercial non-sequential ray tracing software for the case of a two-mirror telescope operating at the extreme ultra-violet wavelengths and the two results are virtually identical. Finally, the image degradation due to the surface scatter from the mirror surfaces and the aberration of the telescope is evaluated in terms of the fractional ensquared energy (for different wavelengths and field angles) which is commonly used as an image quality requirement on many NASA astronomy programs.

[pt] Uma fase crítica do processo de obtenção do petróleo é a perfuração do solo para o acesso ao reservatório. Um dos problemas, em particular, é compreender o comportamento dinâmico da coluna de perfuração durante o processo de perfuração diante de diversos fatores como a interação broca-rocha, choques da coluna de perfuração contra a parede do poço, estratégias de controle da velocidade angular de operação e outros fatores. Uma etapa fundamental para lidar com este problema é a representação do sistema dinâmico para caracterizar a coluna de perfuração, isto é, o modelo matemático que representará a resposta dinâmica da estrutura diante dos carregamentos. Neste contexto, este trabalho abordará o problema da dinâmica de uma coluna de perfuração através de um modelo matemático baseado na teoria de Cosserat, que resultará em um sistema de seis equações diferenciais parciais que descrevem a resposta dinâmica de uma estrutura unidimensional, inserida no espaço euclidiano tridimensional, em termos das variáveis de deslocamento linear da curva e angular das seções. O modelo é capaz de descrever uma dinâmica não-linear, incluindo flexão, torsão, extensão e cisalhamento. Inicialmente, o sistema de EDPs é resolvido na forma quase estática, satisfazendo as condições de contorno, utilizando o método de Perturbação Regular. As soluções aproximadas são utilizadas como funções base para implementação no método de Elementos Finitos. Estas funções base são conhecidas como elemento de Cosserat Modificado (Modfied Cosserat Rod Element - MCRE). Verifica-se a limitação destas funções base para problemas que não envolvam grandes deslocamentos, não sendo adequadas para o problema proposto. Diante deste fato, o sistema de EDPs é escrito na forma fraca e resolvido por um software comercial de análise de Elementos Finitos considerando as condições de contorno, o modelo de interação broca-rocha, a estratégia de controle da velocidade angular e eventuais contatos da coluna contra a parede do poço. O modelo proposto produziu resultados que estão de acordo com a literatura e se mostrou capaz de lidar com grandes deslocamentos. / [en] A critical step in the oil exploration process is drilling the soil for access to the petroleum reservoir. One of the problems is understanding the dynamic behavior of the drill string during the drilling process in the face of various factors such as drill bit-rock interaction, drill string shocks against the well wall, angular velocity control strategies and other factors. A key part of dealing with this problem is the representation of the dynamic system to characterize the drill string, e.g., the mathematical model that will represent the dynamical response of the structure when facing different types of loads. In this context, this work will address the problem of the dynamics of a drill string using a mathematical model based on Cosserat theory that will result in a system of six partial differential equations that describe the dynamic response of a one-dimensional structure, inserted in three-dimensional Euclidean space, in terms of the linear displacement variables of the curve and angular displacement of the cross sections. The model is able to describe nonlinear dynamics, including flexure, torsion, extension and shear. Initially, the system of partial differential equations is solved in a quasi-static sense, satisfying the boundary conditions, using the Regular Perturbation method. The approximate solutions are used as shape functions for implementation in the Finite Element method. These shape functions are known as Modified Cosserat Rod Element (MCRE). It is verified that these shape functions are restricted to problems that do not involve large displacements and for this reason they are not suitable for the proposed problem. Given this fact, the system of partial differential equations is written in a weak form and solved by a commercial software based on Finite Element analysis, considering the boundary conditions, the drill bit-rock interaction model, the angular velocity control strategy and for any string contacts against the well wall. The proposed model produced results that are in agreement with the literature and is capable of dealing with large displacements.

El continuo af'an por reducir la cantidad de act'¿nidos minoritarios (MA) procedentes del combustible quemado en los reactores de agua ligera (Light Water Reactor, LWR) y de esa forma reducir la radiotoxicidad, ha llevado a desarrollar nuevos conceptos de combustible nuclear. El nuevo combustible por empaquetamiento de esferas (Sphere-Pac, SP) ofrece la oportunidad de reintroducir los MA en una matriz y quemarlos en un reactor r'apido de neutrones, donde se facilitan ciclos mu'ltiples por transmutaci'on de elemen- tos. Este combustible se puede utilizar tambi'en en un sistema subcr'¿tico r'apido de neutrones, es decir, un sistema nuclear accionado por un acelera- dor de part'¿culas (Accelerator Driven System, ADS), donde la subcriticidad (seguridad de parada del reactor) permite utilizar combustibles con mayor contenido de MA que en un reactor normal, reduciendo eficazmente en un solo paso la radiotoxicidad. El combustible SP se produce a partir de una soluci'on base (formada por metales y elementos qu'¿micos) mediante un proceso de gelificaci'on in- terna. Este proceso garantiza una buena homogeneidad del producto final y un riesgo de contaminaci'on mucho menor si se compara con la fabricaci'on cl'asica de pellets (combustible comprimido), puesto que se evita el uso de prensas y amoladoras. La gelificaci'on interna es una reacci'on qu'¿mica acu- osa que se produce al calentar la soluci'on hasta 80 ± 5¿ C. Cuando se realiza el proceso por calentamiento electromagn'etico, se observan algunas venta- jas con respecto al calentamiento tradicional por conducci'on (contacto de la muestra con aceite de silicio precalentado): se evita la etapa de reciclado del aceite y de los disolventes org'anicos necesarios para eliminar el aceite de la superficie de las part'¿culas producidas. En la unidad de gelificaci'on in- terna por microondas (Microwave Internal Gelation, MIG), las microondas representan una alternativa mucho m'as simple y segura: el calentamiento volum'etrico sin contacto facilita la producci'on a distancia del combustible en celdas calientes y adem'as reduce los residuos de l'¿quido contaminado. Esta tesis se enmarca dentro del proyecto Platform for Innovative Nu- clear FuEls (PINE), que tiene como objetivo fundamental la producci'on de combustible SP por MIG. En el sistema MIG, el tiempo de calentamiento es muy corto (del orden de decenas de milisegundos), por lo que se deben optimizar los par'ametros que contribuyen al calentamiento por microondas y es necesario conocer en profundidad la interacci'on entre las microondas y las muestras. En la primera parte de este trabajo se investiga un modelo t'ermico basado en diferencias finitas en el dominio del tiempo (FDTD), el cual es capaz de determinar, en cada instante durante el proceso de calentamiento, el comportamiento t'ermico de un punto definido dentro del material que se calienta. Adem'as se presenta una descripci'on detallada de los par'ametros m'as relevantes del modelo, incluyendo las condiciones de contorno (entre ellas la convecci'on). Por otra parte, se implementa anal'¿ticamente y se valida con diferentes t'ecnicas: una basada en teor'¿a de la f'¿sica, otra basada en la herramienta de ecuaciones diferenciales parciales (PDEtools) y la u'ltima basada en ejemplos encontrados en la literatura. En segundo lugar, se investigan los posibles disen¿os de cavidades de microondas para su aplicaci'on en MIG. Tanto las cavidades (selecci'on de los modos, frecuencia de resonancia, factores de calidad, etc.) como su posterior caracterizaci'on, se detallan con el objetivo de especificar el acoplamiento de energ'¿a. Los mecanismos de transferencia de energ'¿a de las cavidades se explican utilizando el m'etodo de perturbaci'on, con el que adem'as se analizan las p'erdidas de la cavidad cuando se coloca una muestra diel'ectrica en su interior. Con el modelo de transferencia de energ'¿a desar- rollado, se obtiene la tasa de generaci'on de calor por microondas, que se aplica al modelo t'ermico FDTD mencionado anteriormente. Los resultados anal'¿ticos demuestran la viabilidad de producir esferas gelificadas por MIG. Seguidamente se introducen los principales par'ametros relacionados con el calentamiento de un material por microondas, es decir, las propiedades diel'ectricas. Se desarrolla un nuevo procedimiento que permite medir estas propiedades en gotas que caen libremente a trav'es de una cavidad de mi- croondas. Se presenta el montaje experimental, cuya viabilidad se prueba a trav'es de diferentes experimentos. Las propiedades diel'ectricas medidas se incluyen en los modelos (perturbacional y t'ermico) con la intenci'on de determinar la potencia absorbida por la sustancia (en forma de gotas) y la temperatura que alcanza. En la u'ltima parte se presenta la implementaci'on del sistema MIG apli- cada al proyecto PINE, fundamental para la pr'actica de calentamiento (basado en frecuencias altas) dentro del laboratorio. Las propiedades de cada dispositivo se evaluan para realizar un estudio de potencia antes del ensamblaje del sistema MIG. De esa forma se evitan fallos al poner el sis- tema en funcionamiento. Adem'as se aportan las t'ecnicas experimentales y los resultados. La producci'on con 'exito de esferas gelificadas demuestra, sin duda, el uso favorable de las microondas en la producci'on de combustible SP por gelificaci'on interna. / In the continuous aim to reduce the amount of minor actinides (MA) from the spent fuel of Light Water Reactors (LWR) and therefore reduce its radiotoxicity (radioactive toxicity), new nuclear fuel concepts have been developed. Sphere-Pac (SP) fuel gives the opportunity to reintroduce the MA in a fuel matrix and to burn them in a fast reactor, which facilitates a multi-cycle because of its breeding feature, or in a subcritical fast system, i.e. an Accelerator Driven System (ADS) where its sub-criticality allows higher MA contents than a normal fast reactor reducing efficiently the radiotoxicity in one step. SP fuel is produced from the base solution (already containing all the elements) by internal gelation, which guarantees a good material homo- geneity and a lower contamination risk compared to the classical pellet fabrication, avoiding presses and grinding machines. The internal gelation is an aqueous chemical reaction occurring when the solution is heated up to 80 ± 5¿C. When performing the internal gelation process with electro- magnetic heating, some advantages appear with respect to the traditionally heating through conduction by contact of the sample with hot silicon oil: the recycling step of the oil and the organic solvents necessary to clean the particles from oil are avoided. In the Microwave Internal Gelation (MIG) unit, the microwaves represent a much simpler and safer alternative: the contactless volumetric heating facilitates the remote production of the fuel in hot cells and furthermore reduces the contaminated liquid waste. The fuel related project called Platform for Innovative Nuclear FuEls (PINE), in which this thesis is embedded, aims for the production of SP- fuel by MIG. In the MIG system, the heating time is very short (in the order of tens of milliseconds), therefore the microwave heating parameters have to be optimized and a good knowledge of the interaction between the microwaves and the samples must be achieved. In the first part of this dissertation a finite difference time domain (FDTD) thermal model capable to determine over each instant about the thermal behaviour of a definite point inside a material during heat process- ing is investigated. A detailed overview of the most relevant parameters on the model including the boundary conditions (e.g. convection) is pre- sented. Furthermore, the model is analytically implemented and validated with different techniques: a theoretical based physically validation, a par- tial differential equations (PDEtools) based validation and a validation with examples from the literature. Secondly, possible microwave cavity designs for MIG are researched. The cavities (selection of modes, resonant frequency, Q-factor, etc.) and its subsequent characterization for the coupling of energy are explained. Furthermore, the power transfer mechanisms of the cavities are explained using the perturbation method to analyse the losses when a dielectric sam- ple is placed inside a cavity. The developed power transfer model delivers the microwave heat generation rate which is applied to the FDTD thermal model mentioned in the previous paragraph. The analytical results provide a positive impression about the feasibility of producing gelated spheres by MIG. Next, the main parameters dealing with the heating of a material by microwaves are introduced. A new procedure that enables the measure- ment of dielectric properties of aqueous droplets freely falling through a microwave cavity is developed. The experimental setup is presented and several experiments prove its feasibility. The measured dielectric properties are afterwards included in the perturbation and thermal models with the main intention of determining the absorbed power by the material in form of drops and the reached temperature. In the last part the MIG system for the laboratory practice of the high frequency heating applied to the PINE project is implemented. Each device is characterized for a power study precedent to the MIG system assembly, avoiding then failures when putting the system into operation. In addition, the experimental techniques and the results are reported. Successful pro- duction of gelated spheres shows the favourable usage of microwave for the production of SP-fuel by internal gelation. / Cabanes Sempere, M. (2013). Innovative production of nuclear fuel by microwave internal gelation [Tesis doctoral]. Editorial Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/31641 / Alfresco

Turbulent boundary layers approximating those found on the NASA Orion Multi-Purpose Crew Vehicle (MPCV) thermal protection system during atmospheric reentry from the International Space Station have been studied by direct numerical simulation, with the ultimate goal of reducing aerothermodynamic heating prediction uncertainty. Simulations were performed using a new, well-verified, openly available Fourier/B-spline pseudospectral code called Suzerain equipped with a ``slow growth'' spatiotemporal homogenization approximation recently developed by Topalian et al. A first study aimed to reduce turbulence-driven heating prediction uncertainty by providing high-quality data suitable for calibrating Reynolds-averaged Navier--Stokes turbulence models to address the atypical boundary layer characteristics found in such reentry problems. The two data sets generated were Ma[approximate symbol] 0.9 and 1.15 homogenized boundary layers possessing Re[subscript theta, approximate symbol] 382 and 531, respectively. Edge-to-wall temperature ratios, T[subscript e]/T[subscript w], were close to 4.15 and wall blowing velocities, v[subscript w, superscript plus symbol]= v[subscript w]/u[subscript tau], were about 8 x 10-3 . The favorable pressure gradients had Pohlhausen parameters between 25 and 42. Skin frictions coefficients around 6 x10-3 and Nusselt numbers under 22 were observed. Near-wall vorticity fluctuations show qualitatively different profiles than observed by Spalart (J. Fluid Mech. 187 (1988)) or Guarini et al. (J. Fluid Mech. 414 (2000)). Small or negative displacement effects are evident. Uncertainty estimates and Favre-averaged equation budgets are provided. A second study aimed to reduce transition-driven uncertainty by determining where on the thermal protection system surface the boundary layer could sustain turbulence. Local boundary layer conditions were extracted from a laminar flow solution over the MPCV which included the bow shock, aerothermochemistry, heat shield surface curvature, and ablation. That information, as a function of leeward distance from the stagnation point, was approximated by Re[subscript theta], Ma[subscript e], [mathematical equation], v[subscript w, superscript plus sign], and T[subscript e]/T[subscript w] along with perfect gas assumptions. Homogenized turbulent boundary layers were initialized at those local conditions and evolved until either stationarity, implying the conditions could sustain turbulence, or relaminarization, implying the conditions could not. Fully turbulent fields relaminarized subject to conditions 4.134 m and 3.199 m leeward of the stagnation point. However, different initial conditions produced long-lived fluctuations at leeward position 2.299 m. Locations more than 1.389 m leeward of the stagnation point are predicted to sustain turbulence in this scenario. / text