This thesis is concerned with a constructivist approach to the introduction of the cosine and sine theorems at the secondary school. The aim was to develop recommendations for teaching which are based on the idea of motivating teaching cosine and sine theorems. This approach is based on available literature and builds on experience from my own teaching of this topic. By motivating teaching, I mean an approach that is consistent with the principles of constructivism and emphasizes pupils' active learning. Current textbooks for secondary schools were analyzed from a mathematical and didactic point of view. The aim of this analysis is to describe how the topic is elaborated in publications available to teachers, and to get inspiration for my own approach. My own teaching approach was based on the theory of generic models and has been implemented in two classes of the secondary grammar school. Data collected during teaching cosine and sine theorems (video recordings of lessons, field notes from teaching and pupil artifacts) were analyzed in a qualitative way. The thesis describes the teaching in detail, with an emphasis on key phases of the discovery of the two theorems. Pupils' involvement in this process is closely followed. Where teaching did not work as planned, possible reasons are found and...

Les lanceurs spatiaux sont soumis à un certain nombre d’excitations complexes durant les différentes phases de vie du produit. Ces excitations sont transmises à la charge utile par voie solidienne ou aérienne. Pour assurer la protection de la charge utile, l’architecture du lanceur étant figée au début du projet, l’amélioration des comportements dynamiques passe par l’introduction de systèmes secondaires. La partie essentielle des travaux de thèse est donc consacrée à l’implantation optimale de systèmes capables de diminuer les réponses vibratoires en utilisant des modèles adaptés. C’est pourquoi une méthode de double synthèse modale est mise en place, permettant ainsi de calculer la réponse vibratoire de la structure à l’aide de bases réduites et offrant des performances améliorées par rapport aux méthodes classiques. L’ajout d’un dispositif amortissant local nécessite la prise en compte d’une ou plusieurs modifications structurales dans le modèle, une méthode dédiée est alors développée. Le choix du dissipateur se porte sur un dissipateur frottant. Un prototype est conçu et réalisé. Il est dans un premier temps caractérisé seul et le modèle de comportement identifié est un modèle constitué d’un ressort en série avec un patin ; la loi de frottement adaptée est une loi de Coulomb simple. En parallèle, une maquette représentative du dernier étage d’un lanceur est dimensionnée et réalisée. Le frotteur est alors monté en pied de propulseur de la maquette et permet une diminution significative des vibrations de la charge utile au passage du mode de propulseur. / Space launchers undergo a certain amount of complex excitations during their lifecycle. These excitations are transmitted to the payload in a structure-born or air-born way. To improve the dynamic behaviour and thus ensure the protection of the payload, secondary systems must be added to the launcher – indeed, the architecture of the launcher is fixed at the beginning of the project. The essential part of this thesis work is dedicated to the optimal fitting of a system capable of reducing the vibration response of the payload, using appropriate models. Therefore a double modal synthesis method is implemented, allowing to calculate the vibrational response of the structure with reduced bases and offering improved performances over conventional methods. The addition of a local damping device requires the consideration of one or more structural modifications in the model, a dedicated method is thus developped along with a specific continuation algorithm. A friction damper is retained, a prototype is designed and built. It is first characterized alone ; the identified behaviour is that of a spring in series with a dry friction element, a simple Coulomb friction law enables to reproduce the experimental curves. A scale model of the launcher’s last stage is designed and built. The friction device is then mounted inside the scale model and leads to a significant reduction of the payload vibration levels.

Le basin du Qaidam, situé sur la bordure nord du Plateau Tibétain est unique au monde en ce qu’il représente le bassin intracontinental le plus profond bien que situé sur le plus haut plateau et la plus épaisse croute continentale actuels. Comprendre le développement et l’évolution de ce bassin en lien avec la collision Inde-Asie a des implications multiples pour la géologie du Tibet en particulier et la tectonique continentale en général. De nombreuses études incluant de la thermochronologie, de la paléobotanique, du paléomagnétisme, de la paléoaltimétrie, de la sédimentologie et de la géologie structurale se sont intéressées à l’histoire tectonique et topographique de cette région. Toutefois la topographie initiale de la région actuellement représentée par le Plateau Tibétain ainsi que les premiers stades de développement du plateau restent méconnus et très débattus. Les travaux présentés ici sont basés sur des données de terrain, de sismique 2D et 3D, de géochimie, de géochronologie détritique, de sédimentologie et d’analyse d’images satellitaires. Ils décrivent: 1) l’évolution cénozoïque conjointe du bassin du Qaidam et de la chaine des Eastern Kunlun ; 2) les relations entre la sédimentation dans le bassin du Qaidam et la tectonique le long de la faille de l’Altyn Tagh ; 3) une estimation quantitative de l’extrusion latérale du nord Tibet les long du système Altyn Tagh – Qilian Shan ; 4) la nature et la typologie du bassin du Qaidam. Je démontre que la chaîne du Kunlun formait un relief en érosion au Paléocène et que la zone de dépôt du bassin du Qaidam s’est élargie vers le sud jusqu’à l’Oligocène. Dès le Miocène inférieur le SO du bassin du Qaidam était limité par un système tectonique décrochant. L’accroissement du relief dans les chaines du Kunlun et de l’Altyn Tagh entraine alors un isolement puis un rétrécissement du bassin. Je suggère que la faille de l’Altyn Tagh qui forme la bordure nord du Plateau, a accommodé environs 360 km de déplacement depuis sont initiation au Miocène inférieur. Cette déformation est prise en compte par du décrochement et de l’épaississement dans les Qilian Shan, de l’épaississement crustal dans les Qinling et de l’extension dans le système de grabens de Chine du Nord. Enfin, je conclu que le bassin du Qaidam est contrôlé conjointement par les failles décrochantes de l’Altyn Tagh et du Kunlun Est. La superposition dans le temps et l’espace des effets de ces deux décrochements majeurs durant le Cénozoïque a contrôlé l’évolution du bassin et la répartition des réserves d’huile et de gaz. / The Qaidam basin, located within the northern Tibetan plateau, is the deepest intracontinental basin, yet located in the highest plateau with the thickest continental crust. Understanding how this peculiar basin developed has broad implications for the Tibetan geology in particular and for continental tectonics in general. Many approaches have been used to decipher the tectonic and topographic history of that region, however, the initial topography of the area now represented by the northern Tibetan plateau, as well as the early stages of development of the present day topography remain poorly constrained and highly debated. In order to better understand the Cenozoic evolution of the Qaidam basin and its surrounding regions (including Eastern Kunlun Range to the south, Altyn Tagh Range to the northwest, and Qilian Shan to the northeast), four critical issues are addressed in this thesis: 1) the Cenozoic joint tectonic evolution of the Qaidam basin and the Eastern Kunlun Range; 2) the interplay between the sedimentation within the Qaidam basin and the active tectonics within the Altyn Tagh Range; 3) a quantitative estimate of the lateral extrusion along the Altyn Tagh Fault-Qilian Shan tectonic system; 4) the nature and classification of the Qaidam basin. I suggest that the SW Qaidam basin has been bordered by a series of strike-slip faults to the south since the Early Miocene, rather than, as previously suggested by a continuous northward or southward thrusting system. Based on U-Pb dating (LA-ICP-MS) of detrital zircons collected from 4 sections (Paleocene to Holocene) within the southwestern Qaidam basin combined with provenance analysis and new seismic profile interpretation, I demonstrated that the Eastern Kunlun Range was already exhumed prior to the Paleocene. I show that the Qaidam basin was widening southward during thet early Cenozoic period (Paleocene to Oligocene). From Oligocene the relief of the Eastern Kunlun and Altyn Tagh ranges increased, leading to isolation and narrowing of the Qaidam basin from Miocene to the present. Along the northern edge of the basin, I identified the Tula-Huatugou and Anxi-Eboliang regions as residual parts of the original Qaidam basin. I suggest that the Altyn Tagh Fault has experienced a total of ~360 km of displacement since its Early Eocene initiation. Based on this ~360 km northeastward migration of the relatively rigid Qaidam block along the Altyn Tagh Fault and 3D isovolumetric balance of the crustal deformation within the Altyn Tagh Fault – Qilian Shan system, I demonstrate that 250 ± 28 km (43.8~49.4 %) of N20E directed crustal shortening and an additional ~250 to ~370 km of eastward motion of the Qilian Shan crust must be accounted for by strike-slip faulting in the Qilian Shan and crustal thickening in the Qinling area, as well as extension in the adjoining North China block graben systems.

Made available in DSpace on 2016-04-27T16:58:20Z (GMT). No. of bitstreams: 1 vera martins.pdf: 540342 bytes, checksum: cce5bbd0100c27ec63e22cb37816c3f8 (MD5) Previous issue date: 2003-05-22 / The objective of this work is to introduce the concepts of sine and cosine in a coordinated form, starting from right-angled triangles, passing through the trigonometric cycle and ending with the graphs of the corresponding functions, aiming to provide conditions which would enable students to attribute meaning to these concepts. To this end, a teaching sequence comprised of seven activities was devised as a means to investigate whether students of the 2nd year of Ensino Médio (High School), who had already studied trigonometry of the right-angled triangles and the trigonometric cycle, would use this knowledge, during the teaching sequence and with the help of the software Cabri-Géomètre, in the construction of graphs of the sine and cosine functions. The design and analysis of the teaching sequence is based on elements of the tool-object dialectic and the notion of the interaction between frameworks of Régine Douady. The activities were administered to a group of 16 students from a state school in the centre of the city of São Paulo during the year of 2002. In the problem-solving processes developed to solve the proposed questions and through the results obtained, the software Cabri-Géomètre demonstrated its efficiency, helping the students to associate the concepts already studied with respect to the right-angled triangle and the trigonometric cycle with the sine and cosine functions. The results also indicated that the majority of students perceived that the sine and cosine studied in the case of right-angled triangle do not differ from those studied in relation to the trigonometric cycle and, moreover, that the sine-curve and cosine-curve provide accurate portrayals of these concepts / O objetivo deste trabalho é introduzir o conceito de seno e cosseno de forma coordenada, partindo do triângulo retângulo, passando pelo ciclo trigonométrico e finalizando com os gráficos das funções correspondentes, tentando propiciar aos alunos, condições para atribuir significado a tais conceitos. Para isto foi elaborada uma seqüência didática composta de sete atividades, com intuito de investigar se alunos do 2° ano do ensino médio, que já trabalharam com trigonometria no triângulo retângulo e no ciclo trigonométrico, possam, por meio dela e com auxílio do software Cabri-Géomètre, utilizar estes conhecimentos, na construção dos gráficos das funções seno e cosseno. A elaboração e análise da seqüência de ensino, apoiam-se em elementos da dialética ferramenta-objeto e na noção de interação entre domínios, de Régine Douady. A aplicação das atividades ocorreu no ano de 2002 em uma escola da rede estadual de ensino, da região central da cidade de São Paulo. O grupo participante era composto por 16 alunos. No decorrer da resolução das questões propostas e pelos resultados obtidos verificou-se que, o software Cabri-Géomètre se mostrou bastante eficaz, auxiliando os alunos a associar os conceitos já estudados no triângulo retângulo e no ciclo trigonométrico, com as funções seno e cosseno. Os resultados obtidos também apontam que, a maioria dos alunos percebeu que o seno e o cosseno estudados no triângulo retângulo não diferem daqueles estudados no ciclo trigonométrico, e mais, que a senóide e a cossenóide retratam fielmente estes conceitos

Cette thèse regroupe une série de travaux ayant tous trait à des systèmes hamiltoniens non linéaires spatialement étendus présentant une bifurcation nœud-col. Elle est constituée de deux parties. Nous étudions dans une première partie la transition à la dissipation de systèmes unidimensionnels soumis à un forçage local et régis par des équations de type sine-Gordon ou Schrödinger non linéaire (ESNL). Nous en calculons analytiquement les solutions stationnaires et caractérisons le comportement dynamique au voisinage de celles-ci près de la bifurcation. Lorsque la relation de dispersion des systèmes possède une fréquence de coupure, le comportement dynamique est caractéristique de systèmes hamiltoniens. A contrario, lorsque la relation de dispersion ne possède pas de fréquence de coupure, la dynamique du système se couple avec l'émission d'ondes sonores qui joue le rôle d'un amortissement effectif. Elle devient alors typique de systèmes dissipatifs. En outre, les modes propres temporels du système subissent une délocalisation spatiale. La seconde partie de la thèse concerne l'étude de deux types d'écoulements bidimensionnels de fluides parfaits barotropes autour d'un obstacle : un écoulement décrit par l'ESNL et un écoulement à surface libre dans l'approximation eau peu profonde, où sont pris en compte les effets dispersifs dus aux effets de tension de surface. Lorsque la longueur caractérisant la dispersion des ondes sonores tend vers zéro, ces deux écoulements se réduisent à l'écoulement autour d'un disque d'un fluide eulérien compressible, auquel se superpose une couche limite que nous calculons analytiquement. Par des méthodes de suivi de branches fondés sur des développements pseudo-spectraux, nous calculons le diagramme de bifurcation complet des deux écoulements. En étudiant la dynamique des deux systèmes au-delà de la bifurcation, nous mettons en évidence une émission d'excitations (dans le cas de l'ESNL) dont la nature dépend du rapport de la longueur de cohérence sur la taille de l'obstacle. Dans le cadre de l'écoulement en eau peu profonde, cette émission est remplacée par une singularité à temps fini de démouillage.

In this essay I defend the notion of deductive explanation mainly against two types of putative counterexamples: those found in genuinely indeterministic systems and those found in complex dynamic systems. Using Railton's notions of explanatory information and ideal explanatory text, deductivism is defended in an indeterministic setting. Furthermore, an argument against non-deductivism that hinges on peculiarities of probabilistic causality is presented. The use of the notion of an ideal explanatory text gives rise to problems in accounting for explanations in complex dynamic systems, regardless of whether they are deterministic or not. These problems are considered in the essay and a solution is suggested. This solution forces the deductivist to abandon the requirement that an explanation consists of a deductive argument, but it is argued that the core of deductivism is saved in so far as we, for full explanations, can still adhere to the fundamental requirement: If A explains B, then A is inconsistent with anything inconsistent with B.

Artificial magnetic materials (AMMs) are a type of metamaterials which are engineered to exhibit desirable magnetic properties not found in nature. AMMs are realized by embedding electrically small metallic resonators aligned in parallel planes in a host dielectric medium. In the presence of a magnetic field, an electric current is induced on the inclusions leading to the emergence of an enhanced magnetic response inside the medium at the resonance frequency of the inclusions. AMMs with negative permeability are used to develop single negative, or double negative metamaterials. AMMs with enhanced positive permeability are used to provide magneto-dielectric materials at microwave or optical frequencies where the natural magnetic materials fail to work efficiently. Artificial magnetic materials have proliferating applications in microwave and optical frequency region. Such applications include inversely refracting the light beam, invisibility cloaking, ultra miniaturizing and frequency bandwidth enhancing low profile antennas, planar superlensing, super-sensitive sensing, decoupling proximal high profile antennas, and enhancing solar cells efficiency, among others. AMMs have unique enabling features that allow for these important applications. Fundamental limitations on the performance of artificial magnetic materials have been derived. The first limitation which depends on the generic model of permeability functions expresses that the frequency dispersion in an AMM is limited by the desired operational bandwidth. The other constraints are derived based on the geometrical limitations of inclusions. These limitations are calculated based on a circuit model. Therefore, a formulation for permeability and magnetic susceptibility of the media based on a circuit model is developed. The formulation is in terms of a geometrical parameter that represents the geometrical characteristics of the inclusions such as area, perimeter and curvature, and a physical parameter that represents the physical, structural and fabrication characteristics of the medium. The effect of the newly introduced parameters on the effective permeability of the medium and the magnetic loss tangent are studied. In addition, the constraints and relations are used to methodically design artificial magnetic material meeting specific operational requirements. A novel design methodology based on an introduced analytical formulation for artificial magnetic material with desired properties is implemented. The synthesis methodology is performed in an iterative four-step algorithm. In the first step, the feasibility of the design is tested to meet the fundamental constraints. In consecutive steps, the geometrical and physical factors which are attributed to the area and perimeter of the inclusion are synthesized and calculated. An updated range of the inclusion's area and perimeter is obtained through consecutive iterations. Finally, the outcome of the iterative procedure is checked for geometrical realizability. The strategy behind the design methodology is generic and can be applied to any adopted circuit based model for AMMs. Several generic geometries are introduced to realize any combination of geometrically realizable area and perimeter (s,l) pairs. A realizable geometry is referred to a contour that satisfies Dido's inequality. The generic geometries introduced here can be used to fabricate feasible AMMs. The novel generic geometries not only can be used to enhance magnetic properties, but also they can be configured to provide specific permeability with desired dispersion function over a certain frequency bandwidth with a maximum magnetic loss tangent. The proposed generic geometries are parametric contours with uncorrelated perimeter and area function. Geometries are configured by tuning parameters in order to possess specified perimeter and surface area. The produced contour is considered as the inclusion's shape. The inclusions are accordingly termed Rose curve resonators (RCRs), Corrugated rectangular resonators (CRRs) and Sine oval resonators (SORs). Moreover, the detailed characteristics of the RCR are studied. The RCRs are used as complementary resonators in design of the ground plane in a microstrip stop-band filter, and as the substrate in design of a miniaturized patch antenna. The performance of new designs is compared with the counterpart devices, and the advantages are discussed.

A voltage source inverter is commonly used to supply a variable frequency variable voltage to a three phase induction motor in a variable speed application. A suitable pulse width modulation (PWM) technique is employed to obtain the required output voltage in the line side of the inverter. Real-time methods for PWM generation can be broadly classified into triangle comparison based PWM (TCPWM) and space vector based PWM (SVPWM). In TCPWM methods such as sine-triangle PWM, three phase reference modulating signals are compared against a common triangular carrier to generate the PWM signals for the three phases. In SVPWM methods, a revolving reference voltage vector is provided as voltage reference instead of three phase modulating waves. The magnitude and frequency of the fundamental component in the line side are controlled by the magnitude and frequency, respectively, of the reference vector. The fundamental line side voltage is proportional to the reference magnitude during linear modulation. With sine-triangle PWM, the highest possible peak phase fundamental voltage is 0.5Vdc, where Vdc is the DC bus voltage, in the linear modulation zone. With techniques such as third harmonic injection PWM and space vector based PWM, the peak phase fundamental voltage can be as high as (formula) (i.e., 0:577Vdc)during linear modulation. To increase the line side voltage further, the operation of the VSI must be extended into the overmodulation region. The overmodulation region extends upto the six-step mode, which gives the highest possible ac voltage for a given (formula). In TCPWM based methods, increasing the reference magnitude beyond a certain level leads to pulse dropping, and gradually leads to six-step operation. However, in SVPWM methods, an overmodulation algorithm is required for controlling the line-side voltage during overmodulation and to achieve a smooth transition from PWM to six-step mode. Numerous overmodulation algorithms have been proposed in the literature for space vector modulated inverter. A well known algorithm among these divides the overmodulation zone into two zones, namely zone-I and zone-II. This is termed as the 'existing overmodulation algorithm' here. This algorithm is modified in the present work to reduce computational burden without much increase in the line current distortion. During overmodulation, the fundamental line side voltage and the reference magnitude are not proportional, which is undesirable from the control point of view. The present work ensures a linear relationship between the two. Apart from the fundamental component, the inverter output voltage mainly consists of harmonic components at high frequencies (around switching frequency and the integral multiples) during linear modulation. However, during overmodulation, low order harmonic components such as 5th, 7th, 11th, 13th etc., are also present in the output voltage. These low order harmonic voltages lead to low order harmonic currents in the motor. The sum of the lower order harmonic currents is termed as 'lower order current ripple'. The present thesis proposes a method for estimation of lower order current ripple in real-time. In closed loop current control, the motor current is fed back to the current controller. During overmodulation, the motor current contains low order harmonics, which appear in the current error fed to the controller. These harmonic currents are amplified by the current error amplifier deteriorating the performance of the drive. It is possible to filter the lower order harmonic currents before being fed back. However, filtering introduces delay in the current loop, and reduces the bandwidth even during linear modulation. In the present work, the estimated lower order current ripple is subtracted from the measured current before the latter is fed back to the controller. The estimation of lower order current ripple and the proposed current control are verified through simulation using MATLAB/SIMULINK and also experimentally on a laboratory prototype. The experimental setup comprises of a field programmable gate arrays (FPGA) based digital controller, an IGBT based inverter and a four-pole squirrel cage induction motor. (Pl refer the original document for formula)

On étudie, dans cette thèse, la diffusion d'ondes dans différents milieux nonlinéaires possédant une bande interdite naturelle. On montre, en particulier, l'existence d'un comportement de bistabilité dans les milieux régis, soit par l'équation de sine-Gordon (chaîne de pendules courte, réseaux de jonctions Josephson, double couches à effet Hall quantique), soit par l'équation de Schrödinger nonlinéaire (milieu Kerr et milieu de Bragg), dans les cas discrets et continus. Ces différents milieux sont soumis à des conditions aux bords périodiques, dont la fréquence est prise dans la bande interdite et avec une amplitude déterminant l'état de stabilité du système. En effet, pour une amplitude suffisante (supratransmission), le milieu n'est plus réfléchissant et absorbe de l'énergie, faisant passer le signal de sortie d'un état d'amplitude évanescente vers un état de très grande amplitude. On donne, par ailleurs, une description analytique complète de la bistabilité qui permet de comprendre les différents états stationnaires observés dans ces milieux et de prédire le passage d'un état à un autre.

I. L'équation décrivant la dynamique des ondes courtes à la surface d'un fluide après une réduction de Green-Naghdi des équations d'Euler se trouve être un nouveau système intégrable exhibant des propriétés remarquables. Une relation insoupçonnée avec le modèle de sine-Gordon, au travers de transformations impliquant une quantité conservée, nous permet en effet d'obtenir des solutions singulières et multivaluées pour la nouvelle équation intégrable et, par la suite, d'en construire une description en termes du Lagrangien d'un champ relativiste. L'existence de modèles très similaires au système hydrodynamique et partageant les mêmes propriétés nous pousse à rechercher les conditions d'apparition d'une telle relation dans un cadre plus général puis à construire un modèle non relativiste mélangeant deux des équations obtenues auparavant. Cette partie se clôt sur une étude aux premiers ordres quantiques des effets de ces transformations responsables de l'apparition de champs relativistes multivalués.<br />II. Dans l'optique d'arriver à une théorie cohérente décrivant des champs de spin élevé en interaction, nous présentons dans la seconde partie une construction, basée sur la théorie des champs de cordes, qui mélange tous les niveaux de spin. Grâce à des contraintes d'hermiticité, on détermine dans un premier temps les éléments d'un groupe de jauge et leur loi de composition. Les champs de jauge sont choisis comme la représentation adjointe du groupe puis modifiés pour se rapprocher des définitions usuelles. Finalement, l'étude du spin 3 nécessite l'introduction de champs auxiliaires qui nous permettent d'obtenir un Lagrangien pour le champ de spin 2 massif en généralisant une méthode introduite par Veltman dans le cas de Yang-Mills.