Η υστέρηση είναι ένα μη γραμμικό φαινόμενο, το οποίο είναι πολύ κοινό σε διάφορους κλάδους της επιστήμης, συμπεριλαμβανομένων της φυσικής, της μηχανικής και της βιολογίας. Η μαθηματική θεμελίωση του φαινομένου της υστέρησης οφείλεται σε διάφορες εφαρμογές, οι οποίες αποτελούν και τα πρακτικά παραδείγματα, τα οποία την υποστηρίζουν. Για το λόγο αυτόν πλήθος μοντέλων, τα οποία πήραν την ονομασία τους από τους επιστήμονες που τα πρότειναν (π.χ Duhem, Weiss, Preisach κ.ο.κ), πρώτα χρησιμοποιήθηκαν για συγκεκριμένες εφαρμογές και μετά θεωρήθηκαν ως μοντέλα υστέρησης. Το φαινόμενο της υστέρησης, όπως και η μαθηματική του ανάλυση, έχει μελετηθεί διεξοδικά [1,2] και για το λόγο αυτό έχουν προταθεί αρκετά μαθηματικά εργαλεία. Εντούτοις, το πρόβλημα της αναγνώρισης (επίτευξη μαθηματικών μοντέλων επί τη βάση πειραματικών μετρήσεων) συστημάτων με υστέρηση δεν έχει λάβει τη δέουσα προσοχή ακόμα. Στις περισσότερες των περιπτώσεων, η αναγνώριση περιορίζεται σε πρακτικά ζητήματα (κυρίως για προσομοιώσεις συστημάτων με υστέρηση), κατά τα οποία επιλέγεται ένα συγκεκριμένο μοντέλο υστέρησης και χρησιμοποιείται μία μέθοδος εκτίμησης (π.χ μη-γραμμική βελτιστοποίηση), δίχως να δαπανάται επιπλέον προσπάθεια σε βαθύτερα θεωρητικά θέματα (π.χ κατά πόσο η εκτίμηση είναι η βέλτιστη ή αν είναι μοναδική κ.ο.κ). Αξίζει να σημειωθεί ότι το πρόβλημα της αναγνώρισης είναι βαθύτερο και χρήζει επιπλέον θεωρητικής ανάλυσης βάσει αρχών και εργαλείων από το γνωστικό αντικείμενο της “Θεωρίας Αναγνώρισης Συστημάτων”, έτσι ώστε να επιτυγχάνονται τα βέλτιστα αποτελέσματα. O πρώτος στόχος της παρούσα διατριβής είναι η ανάπτυξη μεθοδολογίας ανίχνευσης μη γραμμικής συμπεριφοράς (όπως για παράδειγμα η υστέρηση) αποκλειστικά επί τη βάση πειραματικών μετρήσεων. Η βασική ιδέα για την επίτευξη του σκοπού αυτού είναι η χρήση της Συνάρτησης Συνάφειας (Coherence Function), η οποία αναμένεται να μειωθεί με την ύπαρξη μη γραμμικοτήτων [3]. Μετά την ανίχνευση, ο στόχος είναι η ανάπτυξη ολοκληρωμένης μεθοδολογίας για την αναγνώριση φυσικών συστημάτων με υστέρηση, βάσει του μοντέλου ολίσθησης του Maxwell (Maxwell Slip model – [4]). Ο συγκεκριμένος στόχος αντιμετωπίζεται υπό το πρίσμα της θεωρίας αναγνώρισης συστημάτων (System Identification) και ως εκ τούτου τα βασικά θέματα θεωρητικής φύσεως τα οποία αντιμετωπίζονται είναι, τα ακόλουθα:  Η εκ των προτέρων αναγνωρισιμότητα (μοναδικότητα της παραμετροποίησης – uniqueness of representation) της δομής του μοντέλου ολίσθησης του Maxwell.  Η επίδραση των αρχικών καταστάσεων στην εκτίμηση του μοντέλου ολίσθησης του Maxwell.  Ο σχεδιασμός της διεγέρσεως έτσι ώστε τα διαθέσιμα δεδομένα να περιέχουν όλη τη δυνατή πληροφορία για την επιτυχή αναγνώριση του μοντέλου ολίσθησης του Maxwell.  H επιλογή και η αριθμητική εφαρμογή κατάλληλης εκτιμήτριας των παραμέτρων του μοντέλου ολίσθησης του Maxwell.  Η μελέτη της εκ των υστέρων αναγνωρισιμότητας (a posteriori identifiability) του Μοντέλου ολίσθησης του Maxwell.  Η μελέτη της ποιότητας της εκτίμησης του μοντέλου ολίσθησης του Maxwell, το οποίο συνεπάγεται την μελέτη της συνέπειας (consistency) και της ασυμπτωτικής κανονικότητας των εκτιμήσεων (asymptotic normality).  Η διαδικασία επιλογής της δομής (model structure selection) του μοντέλου ολίσθησης του Maxwell.  Ο έλεγχος εγκυρότητας (model validation) του εκτιμώμενου μοντέλου ολίσθησης του Maxwell. Επί τη βάση των παραπάνω βασικών θεμάτων, αναπτύσσονται κατάλληλα εργαλεία και λεπτομερείς διαδικασίες με σκοπό να δοθούν απαντήσεις. Προκειμένου να φανερωθεί η πρακτικότητα και εφαρμοσιμότητα των προαναφερθέντων θεωρητικών θεμάτων, είναι αναγκαία η εφαρμογή τους σε ένα πραγματικό σύστημα με υστέρηση. Από το πλήθος των διαθέσιμων συστημάτων αυτού του είδους, επιλέγεται ένα πραγματικό μηχανικό σύστημα με τριβή. Αξίζει να σημειωθεί ότι συστήματα αυτού του είδους όχι μόνο είναι πολύ κοινά σε μηχανολογικές εφαρμογές, άλλα η αναγνώριση τους αποτελεί πρόκληση, λόγω της πολύπλοκης φύσης της υστέρησης που παρουσιάζουν. Συγκεκριμένα τα εν λόγω συστήματα παρουσιάζουν διαφορετικό είδος υστέρησης ανάλογα με την περιοχή λειτουργίας τους. Έτσι, όταν λειτουργούν στην περιοχή προολίσθησης (δεν παρουσιάζεται μακροσκοπική κίνηση, η σχετική μετατόπισης μεταξύ των επιφανειών που έρχονται σε επαφή είναι της τάξεως των 2 - 5 μm (presliding regime [5]) εμφανίζεται υστέρηση (σχεδόν) ανεξάρτητη του ρυθμού, με χαρακτηριστικά μακράς μνήμης (hysteresis with nonlocal memory) μεταξύ της (μικρο)μετατόπισης και της δύναμης τριβής [6,7,8]. Όσο η σχετική μετατόπιση των επιφανειών που έρχονται σε επαφή αυξάνεται, τότε όλο και περισσότεροι δεσμοί (junctions) σπάνε και τελικά παρατηρείται μακροσκοπική μετατόπιση με αποτέλεσμα το σύστημα να εισέρχεται στην περιοχή ολίσθησης (sliding regime). Στην περιοχή αυτή, ο προηγούμενος τύπος της υστέρησης εξαφανίζεται και εμφανίζεται υστέρηση, μεταξύ της μετατόπισης και της δύναμης τριβής, ρυθμού εξαρτώμενης [8,9,4]. Αξίζει να σημειωθεί ότι ένα σύστημα με τριβή μεταβαίνει από την μια περιοχή λειτουργίας στην άλλη (π.χ κατά την αλλαγή στη φορά της κίνησης) αρκετές φορές ακόμα και κατά την τυπική του λειτουργία. Το γεγονός αυτό καταδεικνύει τη δυσκολία του προβλήματος. Προκειμένου να επιλυθεί το πρόβλημα της αναγνώρισης μηχανικών συστημάτων με τριβή, αρχικά μελετάται το σύστημα μόνο στην περιοχή προολίσθησης. Για το λόγο αυτό διεξάγονται κατάλληλα πειράματα στην περιοχή αυτή, μετρώνται τα σήματα της μετατόπισης και της τριβής προολίσθησης και εφαρμόζεται αναγνώριση του συστήματος επί τη βάση του Μοντέλου ολίσθησης του Maxwell. Η εφαρμογή της προτεινόμενης μεθοδολογίας οδηγεί σε σχεδόν άψογα αποτελέσματα, καταδεικνύοντας την ικανότητα του μοντέλου ολίσθησης του Maxwell να περιγράφει τη δυναμική του συστήματος στην περιοχή προολίσθησης. Αφού μελετήθηκε το σύστημα εντός της περιοχής προολίσθησης, το επόμενο βήμα περιλαμβάνει τη γενικότερη (και πιο πιθανή) περίπτωση, κατά την οποία το σύστημα λειτουργεί στη συνδυασμένη περιοχή προολίσθησης - ολίσθησης. Όπως και πριν, διεξάγονται πειράματα και μετρώνται τα σήματα μετατόπισης και τριβής. Αν και η αναγνώριση του συστήματος, μέσω του μοντέλου ολίσθησης του Maxwell στη συνδυασμένη περιοχή, δίνει χειρότερα συγκρινόμενα με τα προηγούμενα, αποτελέσματα, η χρήση του μοντέλου παρουσιάζεται αρκετά υποσχόμενη. Το γεγονός ότι η αναγνώριση, μέσω του μοντέλου ολίσθησης του Maxwell, στη συνδυασμένη περιοχή προολίσθησης - ολίσθησης οδηγεί σε χειρότερα αποτελέσματα οφείλεται στο ότι η εν λόγω δομή του μοντέλου δεν είναι σε θέση να ερμηνεύσει πλήρως την πολυπλοκότητα της υστέρησης που εμφανίζεται στην περίπτωση αυτή. Έτσι, κρίνεται απαραίτητη η κατάλληλη επέκταση της βασικής δομής. Για το λόγο αυτό προτείνεται κατάλληλη, επί τη βάση της βασική δομής, επέκταση. Η χρήση της νέας δομής του μοντέλου για την αναγνώριση του συστήματος στη συνδυασμένη περιοχή προολίσθησης - ολίσθησης οδηγεί σε εξαιρετική βελτίωση των αποτελεσμάτων, καταδεικνύοντας την καταλληλότητά της. Προκειμένου οι δυνατότητες της νέας δομής να παρουσιαστούν καλύτερα, αναπτύσσεται ένα απλό σύστημα ελέγχου πρόσω-αντιστάθμισης (feedforward), βασισμένο στην προτεινόμενη νέα δομή. Ο παραπάνω έλεγχος έχει ως αποτέλεσμα την επίτευξη εξαιρετικά χαμηλού σφάλματος εντοπισμού (tracking error), υποδεικνύοντας την εξαιρετική αντιστάθμιση της αναπτυσσόμενης τριβής και ως εκ τούτου την ικανότητα της προτεινόμενης δομής να ερμηνεύει τη δυναμική του συστήματος με τριβή, όταν αυτό δουλεύει στην συνδυασμένη περιοχή προολίσθησης - ολίσθησης. / Hysteresis is a nonlinear phenomenon which is common in various branches of science and technology, including physics, mechanics, biology, civil and mechanical engineering. It is well known that many applications stimulate and provide lively support to mathematical construction. For instance, several well - known models which named after the physicists and engineers who proposed them (Rayleigh, Duhem, Weiss, Prandtly, Preisach, Bouc and so on) was entangled with applications before being viewed as models of hysteresis. The study of hysteresis phenomena as well as their mathematical analysis have been systematically researched [1,2] and several mathematical modelling tools have been proposed. Nevertheless the problem of inverse modelling (that is identifying from available experimental data a model that provides the optimum representation of the system under study) of a system with hysteresis have not been investigated thoroughly. In the most of the cases the hysteresis identification is often limited to practical issues such that postulating a hysteresis model and applying an estimation technique (i.e. nonlinear optimization) for obtaining its parameters. However the problem is much deeper and a more theoretical analysis, employing principles and tools from the "System Identification Theory", should be applied in order the optimum results to be obtained. The dissertation aims at proposing a methodology for detecting nonlinearities (such as hysteresis) utilizing experimentally obtained excitation - response data only. The key feature for doing so is the Coherence Function, which is expected to be decreased with the appearance of nonlinear behavior [3]. Following this a complete methodology for identifying systems with hysteresis based upon the Maxwell Slip model [4] is established. This problem is addressed from the ``System Identification" point of view, and therefore the critical issues primarily addressed here are:  The a priori identifiability (or uniqueness of representation) of the Maxwell Slip model structure.  The excitation design for achieving ``rich" enough data for the Maxwell Slip model identification purpose.  The selection and numerical implementation of an estimator  The a posteriori identifiability (whether the model can be identified from a actual experiment under real conditions) of the Maxwell Slip model.  The estimator asymptotic statistical properties, such that consistency and asymptotic normality  The model structure selection  The model validation Based upon these questions, answers are provided and detailed guidelines are established. In order the established theoretical findings to be solidify and their practicality to be revealed, their application to an actual system with hysteresis is required. From the huge number of the available systems with hysteresis, a real (experimental) mechanical system with friction is selected. This kind of systems are not only quite common in mechanical engineering applications (friction perhaps is the most common source of nonlinearities in mechanical systems), but also extremely challenging due to its complicated hysteresis nature (different types of hysteresis appear according to the operational regime). In order the latter to be more clear consider that whenever a system with friction operates within presliding regime (no macroscopic movement between the two surface in contact - the relative displacement is approximately 2 – 5 μm for steel materials [5], then there is a (almost) rate-independent hysteresis with nonlocal memory between the displacement and friction force [6,7,4]. As the relative displacement increases then more and more junctions break and finally there is a macroscopic relative motion and therefore the sliding regime begins. In this case the previous type of hysteresis disappears, and a new rate-dependent hysteresis between the displacement and friction force appears [8,9,4]. However, the system transits from the one regime to the other, (i.e at velocity reversals) several time during its typical operation, thus the type of hysteresis appears depends on the operational regime and thus to the system motion. Unavoidably this makes the identification problem quite challenging. Firstly the system under study is considered within the presliding regime only. Experiments were carried out and actual presliding displacement - friction force signals were obtained. The application of the proposed methodology yields almost excellent results, indicating its ability of capturing the underlying presliding frictional dynamics. The obvious next step is to consider the most common case, which is operation within both presliding - sliding dynamics. Experiments were implemented and displacement - friction force signals were collected. In this case the identification results based upon the Maxwell Slip model, though not so good as before, appear to be very promising. For that reason a proper extension of the basic Maxwell Slip model structure is proposed and implemented. This modification yields to significant improvement, and excellent results are achieved. In order the potentiality of the proposed extended Maxwell Slip model to be demonstrated better, a simple feedforward friction compensation scheme, based upon the extended model, is implemented. The results demonstrate excellent friction compensation, yielding extremely low tracking error, not only in each operational regime but also during regime transitions.

No description available.

Made available in DSpace on 2016-12-12T20:15:53Z (GMT). No. of bitstreams: 1 Resumo - Denilso.pdf: 6952 bytes, checksum: d64faf1cec322aeb51d49ed61bf9358e (MD5) Previous issue date: 2009-05-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work the two-component spinor formulation of the classical theory of electromagnetic fields is presented. In particular, we obtain explicitly the wave equa-tion for photons of both helicities. For this purpose, we present first the formulation of the theory in Minkowski spacetime together with the homomorphism between SL(2;C) and the restricted Lorentz group. / Neste trabalho apresentaremos a formulação da teoria eletromagnética clássica em termos de espinores de duas componentes. Em particular, obteremos explicitamente as equações de onda para fotons de ambas helicidades. Para isso, primeiro trataremos explicitamente da formulação covariante da teoria eletromagnética clássica. Explicitaremos também o homomorfismo entre o grupo SL(2,C) e o grupo de Lorentz restrito.

Atualmente o potencial vetor é geralmente tratado no eletromagnetismo clássico como um artifício para o cálculo dos campos elétricos e magnéticos sem um significado claro. No entanto, quando foi proposto na metade do século XIX, ele possuía um significado físico claro e desempenhava um papel central para Faraday, Maxwell e outros físicos britânicos. Um dos objetivos deste trabalho é entender como se deu esta mudança na interpretação do conceito de potencial vetor. Para isto foi realizado um estudo histórico analisando as diferentes interpretações para este conceito partindo dos trabalhos de Faraday sobre indução eletromagnética, onde propôs o conceito de estado eletrotônico. Analisamos as contribuições de William Thomson que fortemente inspiraram Maxwell a sugerir diferentes interpretações para o conceito em trabalhos publicados ao longo de cerca de duas décadas até a publicação do Treatise on Electricity and Magnestism em 1873. No final do século XIX a interpretação dada por Maxwell ao conceito de potencial vetor começou a ser questionada por vários físicos. Uma das questões envolvidas neste processo foi a realidade das grandezas físicas. Nomes como Heaviside, Hertz e outros defendiam que as grandezas dotadas de realidade física na teoria eletromagnética eram os campos elétrico e magnético e não o potencial vetor. Com essa nova visão desenvolveram uma nova teoria eletromagnética próxima da que conhecemos atualmente. No entanto, este processo não foi linear e aceito acriticamente. Ao longo do século XX foram publicados trabalhos propondo uma interpretação física para o potencial vetor, ainda no contexto clássico. O estudo histórico aqui desenvolvido priorizou a abordagem desenvolvida na Grã-Bretanha / Currently the vector potential generally is considered in the classical electromagnetic theory as an artifice for the calculation of the electric and magnetic fields and without a clear physical meaning. However, when it was proposed in the mid-nineteenth century, it used to have a clear physical meaning and played a central role for Faraday, Maxwell and other British physicists. One of the goals of this dissertation is to understand how the meanings attributed to the vector potential changed along years. In order to answer to this question, we developed a historical study analyzing the different interpretations for this concept starting with the works of Faraday on electromagnetic induction, where he introduced the concept of electrotonic state. We analyzed the contributions of William Thomson that inspired strongly Maxwell to suggest different interpretations for the concept in works published along the next two decades until the publication of the Treatise on Electricity and Magnestism in 1873. In the end of the nineteenth century Maxwells interpretations for the vector potential began to be questioned by several physicists. One of the issues involved in this questioning was the reality of the physical quantities. People as Heaviside, Hertz and others defended that electric and magnetic fields, not the vector potential, were quantities endowed with physical reality. With this new approach they developed a new electromagnetic theory closer to the currently accepted. Nevertheless, this process was not linear and uncritically accepted. Throughout the twentieth century papers and books were published defending a physical interpretation for the vector potential considering a classical context for the electromagnetic theory. The historical study developed here focused the developments in Great-Britain although some mentions to Continental physics are made

O presente trabalho trata do cálculo da força contra eletromotriz em carga de uma máquina síncrona com ímãs na superfície do rotor (cuja forma de onda de força contra eletromotriz é não senoidal) sendo esta alimentada por correntes de fase cujas forma de onda são quadradas. Para conduzir esta investigação e calcular a força contra eletromotriz da máquina em estudo, faz-se uma revisão sobre o Método da Permeabilidade Fixa, método este que permite a linearização do ponto de operação da máquina. Dessa forma, as simulações são conduzidas por meio do método dos elementos finitos e do Método da Permeabilidade Fixa, levando-se em conta a forma de onda da corrente de alimentação. Atenção especial é dada ao modo que se analisa o fluxo concatenado e a forma de obtenção da força contra eletromotriz uma vez que as formas de onda do fluxo concatenado sofrem variações abruptas a cada 60º elétricos. Além destes parâmetros, analisa-se também cada uma das parcelas do torque eletromagnético, i.e., torque mútuo, torque de relutância e torque de borda, sendo realizado ao final do trabalho, uma comparação entre a soma da estimativa de cada parâmetro com o valor do torque eletromagnético obtido por meio de uma simulação não linear. / This work deals with the assessment of a surface mounted magnet synchronous machine\'s parameters (whose back-EMF is approximately trapezoidal) and that is fed by an ideal square current waveform. In order to investigate and describe each machine\'s parameter, a review on Frozen Permeability Method is presented. Some simulation by means of finite element method with the aid of Frozen Permeability Method are carried out taking into account that the machine is fed by an ideal square current waveform. The results for flux-linkage wave-form and back-EMF waveform are shown and analyzed. A special attention is given to back-EMF calculation since the linkage flux of each phase has an abrupt change every sixty electrical degrees due to the phase commutation. In addition, an attention is given to each torque component on load condition, i.e., mutual torque, reluctance torque, cogging torque and a comparison between the electromagnetic torque and the summation of these components.

[pt] Nos Institutos Nacionais de Metrologia para a medição da grandeza de indutância com alta exatidão usam-se circuitos especiais, desenvolvidos e montados pelos próprios laboratórios. Esta dissertação de mestrado descreve o desenvolvimento e a realização de uma nova construção da ponte de Maxwell-Wien, usada para a padronização e disseminação da unidade henry do Instituto Nacional de Metrologia, Normalização e Qualidade Industrial - INMETRO. Na parte teórica do trabalho o conceito do erro complexo é introduzido e, usando este método mais generalizado, os erros nos circuitos de medição e o efeito de impedâncias parasitas internas e externas são analisados. Métodos de compensação para minimizar estes erros são tratados. Na parte prática da dissertação, a partir das características de indutores padrão, os esquemas mais conhecidos de pontes de Maxwell-Wien são estudados. Os conceitos de inovação para desenvolver uma nova ponte de estrutura não tradicional, os métodos aplicados e a construção realizada são descritos detalhadamente. O trabalho é completado por um programa de avaliação das medições, desenvolvido em linguagem C, no ambiente de LabWindows/CVI (C for Virtual Instrumentation, produto da National Instruments). Os resultados de calibrações sistemáticas e de comparações internacionais são resumidos, comprovando que, apesar das soluções e métodos simples, a nova ponte está oferecendo boa repititividade e alta exatidão, atingindo o desempenho das pontes de laboratórios Primários. / [en] In national institutes of metrology, for the high precision measurement of inductance special circuits are used, developed and constructed by the laboratories themselves. This dissertation for a master degree describes the development and realisation of a new Maxwell-Wien bridge that is used for the standardisation and dissemination of the unit of inductance in the National Institute of Metrology, Standardization and Industrial Quality - INMETRO. In the theoretical part of this work the concept of the complex error is introduced and, using this generalised method, the errors of measurement circuits as well as the effects of internal and external stray impedance are analysed. Methods of compensation to minimise these errors are also treated. In the practical part of the dissertation, starting from the characteristics of standard inductors, the most known arrangements of Maxwell-Wien bridges are studied. The innovative concepts to develop a new bridge of non-traditional structure, the methods applied and the realised construction are described in details. The work is completed by a computer program to evaluate measurement data, developed in language C, in the environment of LabWindows/CVI, (C for Virtual Instrumentation, product of National Instruments). The results of systematic calibrations and that of international comparisons are resumed, proving that, in spite of simple solutions and methods, the new bridge is offering high accuracy and repeatability, attaining the performance of the bridges of primary laboratories. / [es] En los Institutos Nacionales de Metrologia para la medición de inductancia con alta exatitud se usan circuitos especiales, desarrollados y montados por los proprios laboratorios. Esta disertación de maestría describe el desarrollo y la realización de una nueva construcción del puente de Maxwell-Wien, usada para la padronización y diseminación de la unidad henry del Instituto Nacional de Metrologia, Normalización y Calidad Industrial - INMETRO. En la parte teórica del trabajo, se introduce el concepto de error complejo y, utilizando este método mas generalizado, se analizan los errores en los circuitos de medición y el efecto de impedancias parásitas internas y externas. Son discutidos métodos de compensación para minimizar estos errores. En la parte práctica de la disertación se estudian, a partir de las características de inductores padrón, los esquemas mas conocidos de puentes de Maxwell-Wien. Se descriven detalladamente los conceptos de innovación para desarrollar un nuevo puente de extructura no tradicional, los métodos aplicados y la construcción realizada. EL trabajo es completado por un programa de avaliación de las mediciones, desarrollado en lenguaje C, en el ambiente de LabWindows/CVI (C for Virtual Instrumentation, producto de la National Instruments). Se resumen los resultados de calibraciones sistemáticas y de comparaciones internacionales, comprobando que, apesar de las soluciones y métodos simples, el nuevo puente ofrece buena repititividad y alta exatitud, alcanzando el desempeño de los puentes de laboratorios Primarios.

Este trabalho apresenta um método numérico para simular escoamentos viscoelásticos tridimensionais com superfícies livres governados pela equação constitutiva de Maxwell. O método numérico é uma extensão da técnica newtoniana GENSMAC3D para escoamentos viscoelásticos. As equações governantes para escoamentos incompressíveis cartesianos isotérmicos são apresentadas em detalhes. O tratamento do tensor não-newtoniano em contornos rígidos tridimensionais é apresentado em detalhes, bem como o cálculo da condição de contorno na superfície livre. As equações governantes são resolvidas pelo método de diferenças finitas numa malha deslocada tridimensional. O fluido é modelado pela técnica das partículas marcadoras e tratado como uma superfície linear por partes. O método numérico desenvolvido foi implementado no sistema Freeflow3D, e resultados numéricos obtidos na simulação de escoamentos tridimensionais governados pela equação constitutiva de Maxwell são apresentados. Adicionalmente, apresentamos uma validação mostrando a convergência do método desenvolvido nesse trabalho / This work presents a numerical method for solving three-dimensional viscoelastic flows with free surfaces governed by the Maxwell constitutive equation. The numerical method is an extension of the Newtonian technique GENSMAC3D to viscoelastic flows. The governing equations for Cartesian incompressible isothermic flows are presented in details. The treatment of the non-Newtonian tensor on three-dimensional rigid boundaries is given in details as well as the calculation of the boundary conditions on the free surface. The governing equations are solved by a finite difference method using a three-dimensional staggered grid. The fluid is described by marker particles and is represented by a piecewise linear surface. The numerical method developed in this work was implemented into the Freeflow3D system, and numerical results obtained from the simulation of complex three-dimensional flows are presented. Additionally, we present validation results and demonstrate the convergence of the method by performing mesh refinement

The Maxwell equations of electromagnetism form the foundation of classical electromagnetism, and are of interest to mathematicians, physicists, and engineers alike. The first part of this thesis concerns boundary value problems for the anisotropic Maxwell equations in Lipschitz domains. In this case, the material parameters that arise in the Maxwell system are matrix valued functions. Using methods from functional analysis, global in time solutions to initial boundary value problems with general nonzero boundary data and nonzero current density are obtained, only assuming the material parameters are bounded and measurable. This problem is motivated by an electromagnetic inverse problem, similar to the classical Calder\'on inverse problem in Electrical Impedance Tomography. The second part of this thesis deals with materials having negative refractive index. Materials which possess a negative refractive index were postulated by Veselago in 1968, and since 2001 physicists were able to construct these materials in the laboratory. The research on the behavior of these materials, called metamaterials, has been extremely active in recent years. We study here refraction problems in the setting of Negative Refractive Index Materials (NIMs). In particular, it is shown how to obtain weak solutions (defined similarly to Brenier solutions for the Monge-Amp\`ere equation) to these problems, both in the near and the far field. The far field problem can be treated using Optimal Transport techniques; as such, a fully nonlinear PDE of Monge-Amp\`ere type arises here. / Mathematics

<p align="justify">Ce travail consiste à étudier des systèmes constitués par un grand nombre de grains, auxquels de l’énergie cinétique est fournie, et à étudier leurs similarités et leurs différences avec des fluides traditionnels. Je me concentre principalement sur la nature de non-équilibre de ces fluides granulaires, en montrant que, même si les méthodes de méchanique statistique y sont applicables, leurs propriétés sont très différentes de celles de systèmes à l’équilibre ou proches de l’équilibre :</p><p><p><ul><li>Les fluides granulaires présentent des phénomènes de transport qui n’ont pas d’équivalent dans des fluides moléculaires, tels qu’un couplage spécifique entre flux de chaleur et gradient de densité.<p><li>Leur distribution de vitesse est en général différente de la distribution de Maxwell-Boltzmann, et présente une surpopulation pour les grandes vitesses. <p><li>Dans le cas de mélanges, différentes espèces de grains sont en général caractérisées par des énergies cinétiques différentes, i.e. ces systèmes sont sujet à une non-equipartition de leur énergie.<p><li>Ces fluides ont tendance à former des inhomogénéités spatiales spontanément. Cette propriété est illustrée en étudiant l’expérience du Demon de Maxwell appliquée aux systèmes granulaires.</ul><p><p align="justify">Chacune de ces particularités est discutée en détail dans des chapitres distincts, où l’on applique différentes méthodes de méchanique statistique (équation de Boltzmann, transition de phase, mean field models…) et où l’on vérifie les prédictions théoriques par simulations numériques (MD, Monte Carlo…).</p> / Doctorat en sciences, Spécialisation physique / info:eu-repo/semantics/nonPublished

The purpose of this chapter is to acquaint the reader with the general scope and trend of Maxwell Anderson's work in order to give a more complete conspectus for the discussion of his plays. By so doing a foundation will be laid for a more intelligible discussion of the specific aspects of the seven plays concerned in the thesis proper, the title of which is, "An Essay on Character Portrayal, Style, and Technique of' Writing in Maxwell Anderson's Biographical Plays in Verse."