Made available in DSpace on 2014-06-11T19:24:45Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-04-07Bitstream added on 2014-06-13T20:12:58Z : No. of bitstreams: 1 tragueta_nl_me_botfca.pdf: 596662 bytes, checksum: f79930749f3e9ad077ff75e918264150 (MD5) / O Sistema de Posicionamento Global (GPS – Global Positioning System) permite o conhecimento da posição, via satélite, de localidades específicas como um ponto topográfico, um carro em movimento ou de uma pessoa caminhando. A precisão do posicionamento pode variar, já que ela está diretamente relacionada ao tipo de receptor utilizado e aos objetivos em questão. Os receptores de navegação, por apresentarem menos precisão, são normalmente utilizados na obtenção de dados aproximados, que não exigem a mesma acurácia dos receptores topográficos ou geodésicos. No entanto, diante da existência de diferentes elipsóides para diferentes regiões do globo terrestre, admitiu-se a hipótese de que a configuração de um elipsóide inadequado para nossas condições poderia provocar erros ainda maiores na determinação de um posicionamento. Neste contexto, foi desenvolvido o presente trabalho, tendo como principais objetivos avaliar, comparar e analisar o desempenho de seis receptores GPS de navegação idênticos com respeito ao cálculo de áreas, perímetros e afastamentos horizontais. Em função dos resultados obtidos, nas condições em que o trabalho foi conduzido, conclui-se que a utilização de receptor GPS de navegação sem conhecimento de suas limitações e configurações básicas, pode levar o usuário a considerar direções e distâncias incompatíveis com o trajeto pretendido ou demarcado. O usuário comum deve saber, no mínimo, que elipsóide está considerando. Quando comparados com o posicionamento real da área (receptor geodésico configurado para SAD 69), a utilização de receptor de navegação configurado para os elipsóides SAD 69, WGS 84 e Córrego Alegre apresentam deslocamento da área no sentido médio de 224º54’43”, 225º10’51” e 206º04’24”, respectivamente, com distância média de 67,49 m; 129,67 m e 90,57 m, respectivamente... / The Global Positioning System allows the knowledge of the position, through satellite, of specific places as a topographical point, a car in movement or of a person walking. The precision of the positioning may vary, because it is directly related to the type of used receiver and to the objectives in subject. The navigation receivers, for present less precision, are usually used in the obtaining of approximate data, that don't demand accuracy compared to the topographical or geodesic receivers. However, in function of the existence of different ellipsoids for different regions of the earth, the hypothesis admitted was that the configuration of an inadequate ellipsoid for our conditions could still provoke big mistakes in the determination of a positioning. In this context, the present work was developed, having as main objectives to evaluate, to compare and to analyze the performance of six identical navigation GPS receivers with regard to the calculation of areas, perimeters and horizontal removals. In function of the obtained results, in the conditions in that the work was developed, it is ended that the use of navigation GPS receivers without knowledge of its limitations and basic configurations, it can take the user to consider directions and incompatible distances with the intended itinerary or demarcated. The common user should know, at least, what ellipsoid is considering. When compared with the real positioning of the area (geodesic receiver configured for SAD 69), the use of navigation receiver configured for the ellipsoids SAD 69, WGS 84 and Córrego Alegre present displacement of the area on the average sense of 224º54'43, 225º10'51 and 206º04'24, respectively, with on the average distance of 67,49 m; 129,67 m and 90,57 m, respectively. The area and perimeters values obtained by navigation GPS receivers, when compared to the area and perimeter obtained by geodesic...(Complete abstract, click electronic access below)

Orientador: Lincoln Gering Cardoso / Banca: Zacarias Xavier de Barros / Banca: Vilmar Antonio Rodrigues / Resumo: O Sistema de Posicionamento Global (GPS - Global Positioning System) permite o conhecimento da posição, via satélite, de localidades específicas como um ponto topográfico, um carro em movimento ou de uma pessoa caminhando. A precisão do posicionamento pode variar, já que ela está diretamente relacionada ao tipo de receptor utilizado e aos objetivos em questão. Os receptores de navegação, por apresentarem menos precisão, são normalmente utilizados na obtenção de dados aproximados, que não exigem a mesma acurácia dos receptores topográficos ou geodésicos. No entanto, diante da existência de diferentes elipsóides para diferentes regiões do globo terrestre, admitiu-se a hipótese de que a configuração de um elipsóide inadequado para nossas condições poderia provocar erros ainda maiores na determinação de um posicionamento. Neste contexto, foi desenvolvido o presente trabalho, tendo como principais objetivos avaliar, comparar e analisar o desempenho de seis receptores GPS de navegação idênticos com respeito ao cálculo de áreas, perímetros e afastamentos horizontais. Em função dos resultados obtidos, nas condições em que o trabalho foi conduzido, conclui-se que a utilização de receptor GPS de navegação sem conhecimento de suas limitações e configurações básicas, pode levar o usuário a considerar direções e distâncias incompatíveis com o trajeto pretendido ou demarcado. O usuário comum deve saber, no mínimo, que elipsóide está considerando. Quando comparados com o posicionamento real da área (receptor geodésico configurado para SAD 69), a utilização de receptor de navegação configurado para os elipsóides SAD 69, WGS 84 e Córrego Alegre apresentam deslocamento da área no sentido médio de 224º54'43", 225º10'51" e 206º04'24", respectivamente, com distância média de 67,49 m; 129,67 m e 90,57 m, respectivamente...(Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The Global Positioning System allows the knowledge of the position, through satellite, of specific places as a topographical point, a car in movement or of a person walking. The precision of the positioning may vary, because it is directly related to the type of used receiver and to the objectives in subject. The navigation receivers, for present less precision, are usually used in the obtaining of approximate data, that don't demand accuracy compared to the topographical or geodesic receivers. However, in function of the existence of different ellipsoids for different regions of the earth, the hypothesis admitted was that the configuration of an inadequate ellipsoid for our conditions could still provoke big mistakes in the determination of a positioning. In this context, the present work was developed, having as main objectives to evaluate, to compare and to analyze the performance of six identical navigation GPS receivers with regard to the calculation of areas, perimeters and horizontal removals. In function of the obtained results, in the conditions in that the work was developed, it is ended that the use of navigation GPS receivers without knowledge of its limitations and basic configurations, it can take the user to consider directions and incompatible distances with the intended itinerary or demarcated. The common user should know, at least, what ellipsoid is considering. When compared with the real positioning of the area (geodesic receiver configured for SAD 69), the use of navigation receiver configured for the ellipsoids SAD 69, WGS 84 and Córrego Alegre present displacement of the area on the average sense of 224º54'43", 225º10'51" and 206º04'24", respectively, with on the average distance of 67,49 m; 129,67 m and 90,57 m, respectively. The area and perimeters values obtained by navigation GPS receivers, when compared to the area and perimeter obtained by geodesic...(Complete abstract, click electronic access below) / Mestre

Submitted by Marlene Santos (marlene.bc.ufg@gmail.com) on 2016-09-15T14:07:03Z No. of bitstreams: 2 Dissertação - Luis Felipe Narvaez Plaza - 2016.pdf: 3790150 bytes, checksum: 40cc7247bbdbbb26d25f05bd967a463e (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-09-15T14:46:20Z (GMT) No. of bitstreams: 2 Dissertação - Luis Felipe Narvaez Plaza - 2016.pdf: 3790150 bytes, checksum: 40cc7247bbdbbb26d25f05bd967a463e (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-09-15T14:46:20Z (GMT). No. of bitstreams: 2 Dissertação - Luis Felipe Narvaez Plaza - 2016.pdf: 3790150 bytes, checksum: 40cc7247bbdbbb26d25f05bd967a463e (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-03-14 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / This work is divided in four parts, in the first chapter we give an introduction. In the next chapter we study basic theory of geometry and differential equations, we study some results of geodesics theory on surfaces in R3; based in the works of R. Garcia and J. Sotomayor in [10] and W. Klingenberg in [15]. These ones provide a study of the behavior of the geodesic in the ellipsoid. The third chapter is inspired by the famous question given in 1905, in his famous article “Sur les lignes géodésiques des surfaces convexes” H. Poincaré posed a question on the existence of at least three geometrically different closed geodesics without self-intersections on any smooth convex two-dimensional surface (2-surface) M homeomorphic to the two-dimensional sphere (2-sphere) S2. We study this question for convex polyhedral surfaces following the paper [9] by G. Galperin and the books [1],[4]. In the last topic we will address the behavior of geodesics on Lorentz surfaces, focusing our study on the ellipsoid based mainly on the book of Tilla Weinstein [25] and in the paper [11] by S. Tabachnikov, Khesin and Genin. / Este trabalho se divide em quatro partes principais, no primeiro capítulo fazemos uma breve introdução. No segundo capítulo estudamos teoria básica de geometria e equações diferenciais, estudamos também geodésicas em superfícies no R3 baseados nos trabalhos de R. Garcia e J. Sotomayor em [10] e de W. Klingenberg em [15], estes fornecem um estudo rigoroso do comportamento das geodésicas no elipsóide. O terceiro capítulo é inspirado na famosa conjectura dada em em 1905 em seu artigo “Sur les lignes géodésiques des surfaces convexes” H. Poincaré fez uma pergunta sobre a existência de pelo menos três geodésicas simples fechadas sobre superfícies suaves convexas homeomorfas à esfera S2, neste capítulo estudamos esta conjectura em superfícies poliedrais baseado em [9] e os textos [1],[4]. No último tema de abordagem analisamos o comportamento de geodésicas em superfícies no espaço de Lorentz, focando nosso estudo no elipsóide, este estudo é baseado principalmente no livro de Tilla Weinstein [25] e no artigo [11] de S. Tabachnikov, Khesin e Genin.

Dans le contexte des systèmes dynamiques, cette thèse développe des techniques d'estimation d'état ensemblistes pour différentes classes de systèmes. On considère pour cela le cas d'un système standard linéaire invariant dans le temps soumis à des perturbations, des bruits de mesure et des incertitudes inconnus, mais bornés. Dans une première étape, une technique d'estimation d'état ellipsoïdale est étendue, puis appliquée sur un modèle d'octorotor utilisé dans un contexte radar. Une extension de cette approche ellipsoïdale d'estimation d'état est proposée pour des systèmes descripteurs. Dans la deuxième partie, nous proposons une méthode fondée sur la minimisation du P-rayon d'un zonotope, appliquée à un modèle d'octorotor. Cette méthode est ensuite étendue pour traiter les systèmes affines par morceaux. Dans la continuité des approches précédentes, un nouveau filtre de Kalman sous contraintes zonotopiques est proposé dans la dernière partie de cette thèse. En utilisant la forme duale d'un problème d'optimisation, l'algorithme projette l'état sur un zonotope qui forme l'enveloppe de l'ensemble des contraintes auxquelles l'état est soumis. La complexité de l'algorithme est ensuite améliorée en remplaçant le zonotope initial par une forme réduite en limitant son nombre de générateurs. / In the context of dynamical systems, this thesis focuses on the development of robust set-membership state estimation procedures for different classes of systems. We consider the case of standard linear time-invariant systems, subject to unknown but bounded perturbations and measurement noises. The first part of this thesis builds upon previous results on ellipsoidal set-membership approaches. An extended ellipsoidal set-membership state estimation technique is applied to a model of an octorotor used for radar applications. Then, an extension of this ellipsoidal state estimation approach is proposed for descriptor systems. In the second part, we propose a state estimation technique based on the minimization of the P-radius of a zonotope, applied to the same model of the octorotor. This approach is further extended to deal with piecewise affine systems. In the continuity of the previous approaches, a new zonotopic constrained Kalman filter is proposed in the last part of this thesis. By solving a dual form of an optimization problem, the algorithm projects the state on a zonotope forming the envelope of the set of constraints that the state is subject to. Then, the computational complexity of the algorithm is improved by replacing the original possibly large-scale zonotope with a reduced form, by limiting its number of generators.

Title: Matter Models in General Relativity with a Decreasing Number of Sym- metries Author: Norman Gürlebeck Institute: Institute of theoretical physics Supervisor: Prof. RNDr. Jiří Bičák, DrSc., dr.h.c. Abstract: We investigate matter models with different symmetries in general relativity. Among these are thin (massive and massless) shells endowed with charge or dipole densities, dust distributions and rotating perfect fluid solutions. The electromagnetic sources we study are gravitating spherical symmetric condensers (including the implications of the energy conditions) and arbitrary gravitating shells endowed with a general test dipole distribution. For the latter the Israel formalism is extended to cover also general discontinuous tangential components of the electromagnetic test field, i.e., surface dipole densities. The formalism is applied to two examples and used to prove some general properties of dipole distributions. This is followed by a discussion of axially symmetric, stationary rigidly rotating dust with non-vanishing proper volume. The metric in the interior of such a configuration can be determined completely in terms of the mass density along the axis of rotation. The last matter models we consider are non-axially symmetric, stationary and rotating perfect fluid solutions. This is done with a...

Les systèmes critiques comme les commandes de vol peuvent entraîner des désastres en cas de dysfonctionnement. D'où l'intérêt porté à la fois par le monde industriel et académique aux méthodes de preuve formelle capable d'apporter, plus ou moins automatiquement, une preuve mathématique de correction. Parmi elles, cette thèse s'intéresse particulièrement à l'interprétation abstraite, une méthode efficacepour générer automatiquement des preuves de propriétés numériques qui sont essentielles dans notre contexte.Il est bien connu des automaticiens que les contrôleurs linéaires sont stables si et seulement si ils admettent un invariant quadratique(un ellipsoïde, d'un point de vue géométrique). Ils les appellent fonction de Lyapunov quadratique et une première partie propose d'encalculer automatiquement pour des contrôleurs donnés comme paire de matrices. Ceci est réalisé en utilisant des outils de programmation semi-définie. Les aspects virgule flottante sont pris en compte, que ce soit dans les calculs effectués par le programme analysé ou dans les outils utilisés pour l'analyse. Toutefois, le véritable but est d'analyser des programmes implémentant des contrôleurs (et non des paires de matrices), incluant éventuellement des réinitialisation ou des saturations, donc non purement linéaires. L'itération sur les stratégies est une techniqued'analyse statique récemment développée et bien adaptée à nos besoins. Toutefois, elle ne se marrie pas facilement avec lestechniques classiques d'interprétation abstraite. La partie suivante propose une interface entre les deux mondes.Enfin, la dernière partie est un travail plus préliminaire sur l'usage de l'optimisation globale sur des polynômes basée sur les polynômes deBernstein pour calculer des invariants polynomiaux sur des programmes polynomiaux. / Critical Systems such as flight commands may have disastrous results in case of failure. Hence the interest of both the industrial and theacademic communities in formal methods able to more or less automatically deliver mathematical proof of correctness. Among them, this thesis will particularly focus on abstract interpretation, an efficient method to automatically generate proofs of numerical properties which are essential in our context.It is well known from control theorists that linear controllers are stable if and only if they admit a quadratic invariant (geometrically speaking, an ellipsoid). They call these invariants quadratic Lyapunov functions and a first part offers to automatically compute such invariants for controllers given as a pair of matrices. This is done using semi-definite programming optimization tools. It is worth noting that floating point aspects are taken care of, whether they affectcomputations performed by the analyzed program or by the tools used for the analysis.However, the actual goal is to analyze programs implementing controllers (and not pairs of matrices), potentially including resets or saturations, hence not purely linears. The policy iteration technique is a recently developed static analysis techniques well suited to that purpose. However, it does not marry very easily with the classic abstract interpretation paradigm. The next part tries to offer a nice interface between the two worlds.Finally, the last part is a more prospective work on the use of polynomial global optimization based on Bernstein polynomials to compute polynomial invariants on polynomials systems.

The work presented in this doctoral thesis employs colloidal suspensions to explore key open problems in condensed matter physics. Colloidal suspensions, along with gels, polymers, emulsions and liquid crystals belong to a family of materials that are collectively labelled as soft matter. Compositionally, colloidal suspensions consist of particles whose size ranges from a few nanometers to a few microns, dispersed in a solvent. A hallmark feature of these systems is that they exhibit Brownian motion, which makes them suitable for investigating statistical mechanical phenomena. Over the last fifteen years or so, colloids have been used extensively as model systems to shed light on a wide array of such phenomena typically observed in atomic systems. The chief reason why colloids are good mimics of atomic systems is their large size and slow dynamics. Unlike atomic systems, the dynamics of colloids can be probed in real time with single-particle resolution, which allows one to establish the link between macroscopic behavior and the microscopic processes that give rise to it. Yet another important feature is that colloidal systems exhibit various phases of matter such as crystals, liquids and glasses, which makes them versatile model systems that can probe a broad class of condensed matter physics problems. The work described in this thesis takes advantage of these lucrative features of colloidal suspensions to gain deeper insights into the physics of glass formation as well as shear-induced anisotropic grain growth in polycrystalline materials. The thesis is organized into two preliminary chapters, four work chapters and a concluding chapter, as follows. Chapter 1 provides an introduction to colloidal suspensions and reviews the chief theo-retical concepts regarding glass formation and grain boundary dynamics that form an integral part of subsequent chapters. Chapter 2 describes the experimental methods used for performing the work presented in the thesis and consists of two parts. The first part describes the protocols followed for synthesizing the size-tunable poly (N-isoprolypacrylamide) (PNIPAm) particles used in our study of shear-induced grain growth. The second part describes the instrumentation and techniques, such as holographic optical tweezers, confocal microscopy, rheology and Bragg diffraction microscopy, used to perform the measurements described in the thesis. Chapter 3 deals with our work on the dynamical facilitation (DF) theory of glass forma-tion. Despite decades of research, it remains to be established whether the transformation of a liquid into a glass is fundamentally thermodynamic or dynamic in origin. While obser-vations of growing length scales are consistent with thermodynamic perspectives, the purely dynamic approach of the DF theory has thus far lacked experimental support. Further, for glass transitions induced by randomly freezing a subset of particles in the liquid phase, theory and simulations support the existence of an underlying thermodynamic phase transi-tion, whereas the DF theory remains unexplored. In Chapter 3, using video microscopy and holographic optical tweezers, we show that dynamical facilitation in a colloidal glass-forming liquid grows with density as well as the fraction of pinned particles. In addition, we observe that heterogeneous dynamics in the form of string-like cooperative motion, which is consid-ered to be consistent with thermodynamic theories, can also emerge naturally within the framework of facilitation. These findings suggest that a deeper understanding of the glass transition necessitates an amalgamation of existing theoretical approaches. In Chapter 4, we further explore the question of whether glass formation is an intrinsi-cally thermodynamic or dynamic phenomenon. A major obstacle in answering this question lies in determining whether relaxation close to the glass transition is dominated by activated hopping, as espoused by various thermodynamic theories, or by the correlated motion of localized excitations, as proposed in the Dynamical Facilitation (DF) approach. In Chapter 4, we surmount this central challenge by developing a scheme based on real space micro-scopic analysis of particle dynamics and applying it to ascertain the relative importance of hopping and facilitation in a colloidal glass-former. By analysing the spatial organization of excitations within cooperatively rearranging regions (CRRs) and examining their parti-tioning into shell-like and core-like regions, we establish the existence of a crossover from a facilitation-dominated regime at low area fractions to a hopping-dominated one close to the glass transition. Remarkably, this crossover coincides with the change in morphology of CRRs predicted by the Random First-Order Transition theory (RFOT), a prominent ther-modynamic framework. Further, we analyse the variation of the concentration of excitations with distance from an amorphous wall and find that the evolution of these concentration profiles with area fraction is consistent with the presence of a crossover in the relaxation mechanism. By identifying regimes dominated by distinct dynamical processes, our study offers microscopic insights into the nature of structural relaxation close to the glass transi-tion. In Chapter 5, we extend our investigation of the glass transition to systems composed of anisotropic particles. The primary motivation for this is to bridge a long-standing di-vide between theories and simulations on one hand, and experiments on molecular liquids on the other. In particular, theories and simulations predominantly focus on simple glass-formers composed of spherical particles interacting via isotropic interactions. Indeed, even the prominent theory of Dynamical Facilitation has not even been formulated to account for anisotropic shapes or interactions. On the other hand, an overwhelming majority of liquids possess considerable anisotropy, both in particle shape as well as interactions. In Chapter 5, we mitigate this situation by developing the DF theory further and applying it to systems with orientational degrees of freedom as well as anisotropic attractive interactions. By analyzing data from experiments on colloidal ellipsoids, we show that facilitation plays a pivotal role in translational as well as orientational relaxation. Further, we demonstrate that the introduction of attractive interactions leads to spatial decoupling of translational and rotational facilitation, which subsequently results in the decoupling of dynamical het-erogeneities. Most strikingly, the DF theory can predict the existence of reentrant glass transitions based on the statistics of localized dynamical events, called excitations, whose duration is substantially smaller than the structural relaxation time. Our findings pave the way for systematically testing the DF approach in complex glass-formers and also establish the significance of facilitation in governing structural relaxation in supercooled liquids. In Chapter 6, we turn our attention away from the glass transition and address the problem of grain growth in sheared polycrystalline materials. The fabrication of functional materials via grain growth engineering implicitly relies on altering the mobilities of grain boundaries (GBs) by applying external fields. While computer simulations have alluded to kinetic roughening as a potential mechanism for modifying GB mobilities, its implications for grain growth have remained largely unexplored owing to difficulties in bridging the disparate length and time scales involved. In Chapter 6, by imaging GB particle dynamics as well as grain network evolution under shear, we present direct evidence for kinetic roughening of GBs and unravel its connection to grain growth in driven colloidal polycrystals. The capillary fluctuation method allows us to quantitatively extract shear-dependent effective mobilities. Remarkably, our experiments reveal that for sufficiently large strains, GBs with normals parallel to shear undergo preferential kinetic roughening resulting in anisotropic enhancement of effective mobilities and hence directional grain growth. Single-particle level analysis shows that the anisotropy in mobility emerges from strain-induced directional enhancement of activated particle hops normal to the GB plane. Finally, in Chapter 7, we present our conclusions and discuss possible future directions.

This thesis presents the development of a fault detection and diagnosis (FDD) procedure capable of capturing, isolating and identifying multiple abrupt parametric faults. The proposed method relies on parameter estimation deployed in a set membership framework. This approach presupposes the utilization of a linearly parametrizable model and the a priori knowledge of bounded noise errors and parameter perturbations. Under these assumptions, a data-hyperspace is generated at every time instant. The goal of set membership identification (SMI) is the determination of the parametric set, formed as an orthotope or ellipsoid, within which the nominal parameter vector resides and intersects with the data-hyperspace. The fault detection mechanism is activated when the normal operation of the SMI procedure is interrupted due to an empty intersection of the data-hyperspace and the estimated parametric set. At the detection instant, a resetting procedure is performed in order to compute the parameter set and the data-hyperspace that contain the varied nominal parameter vector, allowing the SMI algorithm to continue its operation. During the fault isolation, consistency tests are executed, relying on the projections of the worst case parametric sets and the ones arisen from the normal operation of SMI. A faulty component is indicated when these projections do not intersect, while the distance of their centers is used for fault identification. In case of the ellipsoidal SMI-based FDD and under the assumption of a time invariant parameter vector, a new fault detection criterion is defined based on the intersection of support orthotopes of ellipsoids. A more accurate estimation of the time instant of fault occurrence is proposed based on the application of a backward-in-time procedure starting from the fault detection instant, while the conditions under which a fault will never be detected by the orthotopic and ellipsoidal SMI based FDD are provided. This dissertation explores the efficiency of the proposed FDD methodology for capturing failure modes of two microelectromechanical systems; an electrostatic parallel-plate microactuator and a torsionally resonant atomic force microscope. From an engineering point of view, failure modes appeared in the microcomponents of the microactuator and the TR-AFM are encountered as parameter variations and are captured, isolated and identified by the proposed FDD methodology. / Σε αυτή την διατριβή, παρουσιάζεται η ανάπτυξη μιας διαδικασίας Ανίχνευσης και Διάγνωσης Σφαλμάτων, η οποία είναι ικανή να εντοπίζει, απομονώνει και αναγνωρίζει πολλαπλά, απότομα παραμετρικά σφάλματα. H προτεινόμενη μέθοδος βασίζεται στην αναγνώριση του συνόλου συμμετοχής των παραμέτρων. Ο στόχος της Αναγνώρισης Συνόλου Συμμετοχής είναι ο καθορισμός του παραμετρικού συνόλου εντός του οποίου κείται το ονομαστικό διάνυσμα παραμέτρων, δεδομένου ότι το ονομαστικό διάνυσμα παραμέτρων ανήκει επίσης σε έναν υπερχώρο δεδομένων. Το παραμετρικό σύνολο απεικονίζεται ως ένα ορθότοπο ή ένα ελλειψοειδές, λόγω της εύκολης μαθηματικής τους περιγραφής. Έτσι, η διαδικασία Αναγνώρισης Συνόλου Συμμετοχής αντιστοιχεί σε ένα πρόβλημα βελτιστοποίησης, το οποίο αποσκοπεί στον υπολογισμό του ορθοτόπου ή ελλειψοειδούς το οποίο περιέχει το ονομαστικό διάνυσμα παραμέτρων και τέμνεται με τον υπερχώρο δεδομένων. Ο μηχανισμός Ανίχνευσης Σφαλμάτων ενεργοποιείται όταν διακόπτεται η φυσιολογική λειτουργία της Αναγνώρισης Συνόλου Συμμετοχής, λόγω της κενής τομής μεταξύ των εκτιμώμενου παραμετρικού συνόλου και του υπερχώρου δεδομένων. Τη χρονική στιγμή ανίχνευσης ενός σφάλματος, εφαρμόζεται μια διαδικασία επαναρύθμισης που σκοπεύει στον υπολογισμό του νέου παραμετρικού συνόλου, το οποίο περιέχει το μεταβεβλημένο ονομαστικό διάνυσμα παραμέτρων και τέμνεται με το υπερχώρο δεδομένων. Κατά τη διάρκεια της διαδικασίας απομόνωσης του σφάλματος, εκτελούνται τεστ συμβατότητας, τα οποία βασίζονται στις προβολές των νέων παραμετρικών συνόλων και στις προβολές των παραμετρικών συνόλων χείριστης περίπτωσης, ενώ η απόσταση των κέντρων των προβολών χρησιμοποιείται για αναγνώριση σφάλματος. Στην περίπτωση που η Ανίχνευση και Διάγνωση Σφαλμάτων πραγματοποιείται βασιζόμενη στην Αναγνώριση Συνόλου Συμμετοχής με ελλειψοειδή και θεωρώντας το ονομαστικό διάνυσμα παραμέτρων χρονικά αμετάβλητο, ορίζεται ένα νέο κριτήριο ανίχνευσης σφαλμάτων, χρησιμοποιώντας την τομή των περιβαλλόντων ορθοτόπων των ελλειψοειδών. Σε αυτή την περίπτωση, ένα σφάλμα ανιχνεύεται όταν η τομή αυτή είναι κενή. Ακόμη, προτείνεται μια πιο ακριβής εκτίμηση της χρονικής στιγμής εμφάνισης του σφάλματος, ενώ παρατίθενται οι συνθήκες υπό τις οποίες ένα σφάλμα μπορεί να μην ανιχνευθεί ποτέ με την εφαρμογή των προτεινόμενων μεθόδων. Η συγκεκριμένη διατριβή επίσης ερευνά την αποτελεσματικότητα της προτεινόμενης μεθοδολογίας Ανίχνευσης και Διάγνωσης Σφαλμάτων για τον εντοπισμό των τρόπων εκδήλωσης σφαλμάτων σε δύο μικροηλεκτρομηχανικά συστήματα (ΜΗΜΣ), έναν ηλεκτροστατικό μικροεπενεργητή παράλληλων πλακών και ένα ατομικό μικροσκόπιο συντονισμού στρέψης. Από πλευράς μηχανικής, οι τρόποι εκδήλωσης σφαλμάτων στα δομικά στοιχεία του μικροεπενεργητή ή του ατομικού μικροσκοποίου αντιμετωπίζονται ως απότομες παραμετρικές, οι οποίες εντοπίζονται και διαγιγνώσκονται από τις προτεινόμενες μεθόδους.

Les matériaux granulaires sont omniprésents, ils se trouvent aussi bien dans la nature que dans quelques applications industrielles. Parmi les applications industrielles utilisant les matériaux granulaires, on cite le mélange des poudres dans les industries agro-alimentaires, chimiques, métallurgiques et pharmaceutiques. La caractérisation et l'étude du comportement de ces matériaux sont nécessaires pour la compréhension de plusieurs phénomènes naturels comme le mouvement des dunes et les avalanches de neige, et de processus industriels tel que l'écoulement et le mélange des grains dans un mélangeur. Le comportement varié des matériaux granulaires les rend inclassables parmi les trois états de la matière : solide, liquide et gazeux. Ceci a fait dire qu'il s'agit d'un ``quatrième état'' de la matière, situé entre solide et liquide. L'objectif de ce travail est de concevoir et de mettre en oeuvre des méthodes efficaces d'éléments discrets pour la simulation et l'analyse des processus de mélange et de ségrégation des particules ellipsoïdales dans des mélangeurs culbutants industriels tels que le mélangeur à cerceaux. Dans la DEM l'étape la plus critique en terme de temps CPU est celle de la détection et de résolution de contact. Donc pour que la DEM soit efficace il faut optimiser cette étape. On se propose de combiner le modèle du potentiel géométrique et la condition algébrique de contact entre deux ellipsoïdes proposée par Wang et al., pour l'élaboration d'un algorithme efficace de détection de contact externe entre particules ellipsoïdales. Puis de de prouver un résultat théorique et d'élaborer un algorithme pour le contact interne. D'autre part, le couplage DEM-chaîne de Markov permet de diminuer très sensiblement le temps de simulation en déterminant la matrice de transition à partir d'une simulation à courte durée puis en calculant l'état du système à l'aide du modèle de chaîne de Markov. En effet, en utilisant la théorie des matrices strictement positives et en se basant sur le théorème de Perron-Frobenius on peut approximer le nombre de transitions nécessaires pour la convergence vers un état donné. / The importance of granular mixing for many process industries dealing with powders and grains can hardly be exaggerated. For example, chemical, food, and pharmaceutical industries usually require blending different particulate materials. High-quality products ranging from polymers and pharmaceuticals to ceramics and semiconductors increasingly depend on reliable granular flow and high quality and controllable granular mixing processes. In this work we implement a discrete element method for the simulation and analysis of mixing and segregation of ellipsoidal particles inside industrial tumbling blenders. The most critical step in term of time CPU in a discrete element simulation is the detection and resolution of contact. We use the algorithm of separating plane of ellipsoids and the algebraic condition on the separation of two ellipsoid algebraic conditions for the development of an efficient contact detection algorithm for ellipsoidal particles and to prove a theoretical result and a new algorithm for the internal contact. However, the coupling between DEM and Marckov chain makes it possible to very appreciably decrease the simulation time by determining the transition matrix of a short time simulation then by calculating the state from the system using the model from chain from Markov. Indeed, by using the theory of the strictly positive matrices and while basing oneself on the theorem of Perron-Frobenius we can approximate the number of transitions necessary for convergence towards a given state.