Pour les panneaux de grande hauteur soumis à un fort gradient thermique associé à l’incendie, ils subissent des déplacements hors plan importants qui, du fait de l’excentrement du poids propre qui en résulte, vont engendrer des efforts de flexion venant s’ajouter aux efforts de compression déjà existants. Un tel changement de géométrie, d’autant plus prononcé que le panneau est de grande hauteur, combiné à une dégradation simultanée des propriétés de résistance des matériaux sous l’effet de l’élévation de température, peut conduire à un effondrement de la structure sous poids propre. L’évaluation de la résistance au feu d’éléments de structures de grandes dimensions, repose sur la théorie du calcul à la rupture, appliquée d’une part à la détermination d’un diagramme d’interaction au feu caractérisant la résistance du panneau en chacune de ses sections, d’autre part à l’analyse de la ruine globale du panneau dans sa configuration déformée. Le programme comporte deux volets complémentaires. Le premier volet concerne l’approche expérimentale. Un mur de 9 mètre a été testé sur le grand équipement Vulcain afin de valider le modèle de calcul d’une part, qui est en cours du développement, et à identifier des phénomènes locaux éventuels non accessibles par la modélisation d’autre part. Le deuxième volet concerne le développement d’outils de modélisation et de calcul performants. Basées sur une approche cinématique, des procédures itératives qui se reposent sur la méthode de perturbation ont été construit pour chercher une solution analytique pour prédire la configuration déformée d’une plaque soumis à un fort gradient thermique. Ensuite, des méthodes numériques fondées sur la discrétisation en éléments finis du panneau déformé, traité comme une coque à faible courbure, et l’utilisation de techniques d’optimisation non-linéaires, qui ont connu récemment des progrès importants, devront pouvoir être développées et appliquées à ce problème / High rise reinforced concrete walls under fire exhibit important out-of-plane displacements, which in turn lead to an eccentricity of the self-weight with respect to the initial undeformed configuration, resulting in supplementary bending moments. This geometrical change, combined with the degradation of the stiffness and strength properties of reinforced concrete due to severe temperature increase, may lead to the failure of walls under fire.Investigation on fire resistance of reinforced concrete walls will be based on the yield design approach in order to analyze the global stability of high rise walls, taking into account the geometry changes induced by the thermal loading.The program consists of two parts.Firstly, a 9-meter high reinforced concrete wall has already been tested under fire with the equipment Vulcan. This full size experiment aims at validating the modeling of plates under large out-of-plan displacement and identifying potential local phenomenon which has not been considered in the model.Secondly, a yield design approach will carried out to analyze the stability of reinforced concrete walls. By using the perturbation method, a recursive analytical procedure based on a kinematic approach is proposed to find the deformed configuration of reinforced concrete walls under fire. The deformed configuration will be later modeled as a shallow shell, on which a yield design procedure will be performed by a non-linear optimization

L'objectif de cette thèse est de développer, caractériser et analyser l'imagerie radar en configuration bistatique. Dans le cadre de notre étude, nous nous plaçons dans le cas général d'une configuration bistatique sans condition sur la configuration d'acquisition. Nous avons alors développé un algorithme de reconstruction d'images tenant compte des polarisations d'émission et de réception. Ainsi, nous avons pu caractériser les images obtenues et donner l'expression des résolutions d'une image bistatique en fonction de la configuration d'acquisition. Ensuite, nous avons étudié les images bistatiques reconstruites lors de l'observation de cibles complexes ainsi que celles obtenues lors de la détection de cibles sur une surface océanique afin de les comparer avec celles d'une configuration monostatique. Les résultats ainsi obtenus permettent de valider l'intérêt de la configuration bistatique et de présenter les nouvelles perspectives qu'offre ce sujet de recherche en imagerie radar.

In school algebra, using different methods including factorization to solve quadratic equations is one common teaching and learning topic at upper secondary school level. This study is about analyzing the algebra content related to solving quadratic equations and the method of factorization as presented in Swedish mathematics textbooks with subject matter content knowledge (CK) and pedagogical content knowledge (PCK) as analytical tools. Mathematics textbooks as educational resources and artefacts are widely used in classroom teaching and learning. What is presented in a textbook is often taught by teachers in the classroom. Similarly, what is missing from the textbook may not be presented by the teacher. The study is based on an assumption that pedagogical content knowledge is embedded in the subject content presented in textbooks. Textbooks contain both subject content knowledge and pedagogical content knowledge. The primary aim of the study is to explore what pedagogical content knowledge regarding solving quadratic equations that is embedded in mathematics textbooks. The secondary aim is to analyze the algebra content related to solving quadratic equations from the perspective of mathematics as a discipline in relation to algebra history. It is about what one can find in the textbook rather than how the textbook is used in the classroom. The study concerns a teaching perspective and is intended to contribute to the understanding of the conditions of teaching solving quadratic equations. The theoretical framework is based on Shulman’s concept pedagogical content knowledge and Mishra and Koehler’s concept content knowledge. The general theoretical perspective is based on Wartofsky’s artifact theory. The empirical material used in this study includes twelve mathematics textbooks in the mathematics B course at Swedish upper secondary schools. The study contains four rounds of analyses. The results of the first three rounds have set up a basis for a deep analysis of one selected textbook. The results show that the analyzed Swedish mathematics textbooks reflect the Swedish mathematics syllabus of algebra. It is found that the algebra content related to solving quadratic equations is similar in every investigated textbook. There is an accumulative relationship among all the algebra content with a final goal of presenting how to solve quadratic equations by quadratic formula, which implies that classroom teaching may focus on quadratic formula. Factorization method is presented for solving simple quadratic equations but not the general-formed quadratic equations. The study finds that the presentation of the algebra content related to quadratic equations in the selected textbook is organized by four geometrical models that can be traced back to the history of algebra. These four geometrical models are applied for illustrating algebra rules and construct an overall embedded teaching trajectory with five sub-trajectories. The historically related pedagogy and application of mathematics in both real world and pure mathematics contexts are the pedagogical content knowledge related to quadratic equations.

This study is an attempt to explicate Gottfried Wilhelm von Leibniz&rsquo / s search for a way out of the labyrinth of the continuum in his early years of philosophizing. The main motive of the study is the belief that it would be worthwhile to see how Leibniz initially goes into the labyrinth and comes across with the riddles contained in it. Accordingly, this thesis is intended to discuss what the problem of the composition of the continuum is for the young Leibniz, which concepts and metaphysical problems are associated with the labyrinth, and what particular difficulties challenge Leibniz in his struggle. More importantly, the study seeks to delineate how Leibniz responds to these difficulties, what kinds of solutions he suggests, and how and why he changes his mind and offers different accounts concerning the composition of the continuum in his early writings. In this search for a way out of the labyrinth, some of the early writings of Leibniz written between 1666 and 1675 were studied with a particular emphasis on those directly related with the labyrinth of the continuum. During the study, the differences and transitions between geometrical, physical, and metaphysical accounts concerning the problem of the composition of the continuum were examined with a special focus on the bridging role of &lsquo / motion&rsquo / and the notion of &lsquo / conatus.&rsquo

A novel lidar ceilometer prototype based on divided lens optics has been designed, built, characterised, and tested. The primary applications for this manufacturable ground-based sensor are the determination of cloud base height and the measurement of vertical visibility. First, the design, which was developed in order to achieve superior performance at a low cost, is described in detail, along with the process used to develop it. The primary design considerations of optical signal to noise ratio, range-dependent overlap of the transmitter and receiver channels, and manufacturability, were balanced to develop an instrument with good signal to noise ratio, fast turn-on of overlap for detection of close range returns, and a minimised number of optical components and simplicity of assembly for cost control purposes. Second, a novel imaging method for characterisation of transmitter-receiver overlap as a function of range is described and applied to the instrument. The method is validated by an alternative experimental method and a geometric calculation that is specific to the unique geometry of the instrument. These techniques allow the calibration of close range detection sensitivity in order to acquire information prior to full overlap. Finally, signal processing methods used to automate the detection process are described. A novel two-part cloud base detection algorithm has been developed which combines extinction-derived visibility thresholds in the inverted cloud return signal with feature detection on the raw signal. In addition, standard approaches for determination of visibility based on an iterative far boundary inversion method, and calibration of attenuated backscatter profile using returns from a fully-attenuating water cloud, have been applied to the prototype. The prototype design, characterisation, and signal processing have been shown to be appropriate for implementation into a commercial instrument. The work that has been carried out provides a platform upon which a wide range of further work can be built.

Cette thèse se concentre sur l'étude de composés magnétiques géométriquement frustrés où les ions magnétiques se situent aux sommets d'un réseau de tétraèdres partageant leurs sommets: les composés pyrochlores. Deux familles de formule chimique R2M2O7, où R est un lanthanide et M= Ti, Sn, sont particulièrement intéressantes puisqu'elles présentent une grande variété d'états magnétiques exotiques. Premièrement, nous avons étudié le champ cristallin agissant au site de la terre rare dans l'approximation de Stevens où uniquement le terme fondamental est considéré. Un jeu unique de paramètres a été déterminé pour chaque famille considérée grâce à une analyse globale incluant des spectres de neutrons inélastiques de plusieurs composés. Ensuite, nous avons caractérisé avec un large éventail de techniques les propriétés physiques à basse température de Nd2Sn2O7. En dessous de la température de transition Tc=0.91 K, ce composé possède un ordre magnétique à longue portée dans la configuration de spins dite "all-in-all-out". Une persistance de la dynamique de spins a été révélée dans la phase ordonnée, attribuée à des excitations unidimensionnelles de spins. Une dynamique de spins anormalement lente est également reportée dans la phase paramagnétique. Enfin, nous avons apporté quelques informations sur les deux états fondamentaux proposés pour le composé très étudié Tb2Ti2O7: premièrement, l'apparition d'une transition Jahn-Teller à basse température est suggérée mais l'absence d'élargissement des pics de Bragg réfute la présence d'une transition structurale. Enfin ce composé pourrait être un exemple d'une glace de spin quantique mais l'existence d'un plateau d'aimantation n'est pas évident jusqu'à T=20 mK. / This Phd thesis focuses on the study of magnetically frustrated compounds where magnetic ions lie at the vertices of a corner-sharing tetrahedra network: the pyrochlore compounds. The two series of chemical formula R2M2O7, where R is a lanthanide and M=Ti, Sn, are of peculiar interest since they display a large variety of exotic magnetic ground states. First, we have studied the crystal-electric-field acting at the rare earth within the Stevens approximation where only the ground state multiplet is considered. A single set of parameters for each families of interest has been determined through a global analysis including several inelastic neutron scattering spectra of various compounds. Then, we have characterised with a large panel of techniques the low temperature physical properties of Nd2Sn2O7. This compound enters a long-range magnetic order at transition temperature Tc=0.91 K with an ``all-in-all-out'' spin configuration. A persistence of spin dynamics has been found in the ordered phase, ascribed to one-dimensional spin loops excitations. Anomalously slow paramagnetic spin fluctuations are also reported. Finally, we have brought information on the two proposed ground states of the widely studied compound Tb2Ti2O7: first, a Jahn-Teller transition is claimed to occur at low temperatures but no broadening of the Bragg peaks is seen down to T=4 K precluding premises of a structural transition. Secondly, this compound could be a realisation of a quantum spin-ice but no definitive evidence of a magnetisation plateau is found down to T=20 mK.

This research studies the interaction among the following contexts: natural language, geometrical language and musical language and it can provide new instruments to accord didactical situations and for a deeper understanding of communication processes. It springs from the consideration that the geometrical transformations are usually used in the compositional processes and the “role of the music to learn geometrical transformations” is actually a new study. In the field of the theory of situations by G. Brousseau (1986) we can assume to be in front of a learning teaching-situation including non-teaching situation as the teacher of musical instruments, while transmitting the knowledge of musical language (theoretical-practical) didn’t have the intention to transmit the geometrical transformation.

In ground based high frequency (HF) radio pumping experiments, absorption of ordinary (O) mode pump waves energises the ionospheric plasma, producing optical emissions and other effects. Pump-induced or natural kilometre-scale field-aligned density depletions are believed to play a role in self-focussing phenomena such as the magnetic zenith (MZ) effect, i.e., the increased plasma response observed in the direction of Earth's magnetic field. Using ray tracing, we study the propagation of ordinary (O) mode HF radio waves in an ionosphere modified by density depletions, with special attention to transmission through the radio window (RW), where O mode waves convert into the extraordinary (X, or Z) mode. The depletions are shown to shift the position of the RW, or to introduce RWs at new locations. In a simplified model neglecting absorption, we estimate the wave electric field strength perpendicular to the magnetic field at altitudes normally inaccessible. This field could excite upper hybrid waves on small scale density perturbations. We also show how transmission and focussing combine to give stronger fields in some directions, notably at angles close to the MZ, with possible implications for the MZ effect. In a separate study, we consider electromagnetic (e-m) beams with helical wavefronts (i.e., twisted beams), which are associated with orbital angular momentum (OAM). By applying geometrical optics to each plane wave component of a twisted nonparaxial e-m Bessel beam, we calculate analytically the shift of the beam's centre of gravity during propagation perpendicularly and obliquely to a weak refractive index gradient in an isotropic medium. In addition to the so-called Hall shifts expected from paraxial theory, the nonparaxial treatment reveals new shifts in both the transverse and lateral directions. In some situations, the new shifts should be significant also for nearly paraxial beams.

Η παρούσα διπλωματική εργασία διεισδύει σε δύο χώρους. Αρχικά στον χώρο του Ηλεκτρολόγου Μηχανικού, μέσω των μηχανικών (γεωμετρικών ) ελέγχων των Ακτινολογικών μηχανημάτων, καθώς και των ελέγχων – επιδιορθώσεων στις γεννήτριες και στις Ακτινολογικές λυχνίες. Συγχρόνως διεισδύει στο χώρο της Ακτινοφυσικής και της Ακτινολογίας, αφού ασχολείται με τις δόσεις, τις παροχές ακτινοβολίας, καθώς και τις επιδράσεις αυτών στα ακτινολογικά φιλμ απεικόνισης. Σκοπός αυτής της εργασίας είναι η περιγραφή και η πλήρη ανάλυση των γεωμετρικών ελέγχων καθώς και των ελέγχων γεννητριών - ακτινολογικών λυχνιών, που πρέπει να γίνονται στα ακτινολογικά μηχανήματα. Τα μηχανήματα αυτά βρίσκονται στα Ακτινολογικά τμήματα των Δημόσιων και Ιδιοτικών Νοσοκομείων και γενικά σε χώρους παραγωγής ιοντιζουσών ακτινοβολιών. Οι έλεγχοι αυτοί, η συχνότητά τους, καθώς και ο τρόπος διεξαγωγής τους ορίζονται από τα πρωτόκολλα της Ελληνικής Επιτροπής Ατομικής Ενέργειας ( Ε.Ε.Α.Ε. ) Σκοπός των ελέγχων αυτών, βάσει των πρωτοκόλλων της Ε.Ε.Α.Ε., είναι η διασφάλιση ποιότητας των ακτινολογικών μηχανημάτων, με στόχο την βέλτιστη παροχή ιατρικών υπηρεσιών προς τους εξεταζόμενους. / This essay enters into two areas. Initially the area of Electrical Engineering, through mechanical (geometrical) tests of X-ray machines, and controls - repairs to generators and x-ray tubes. At the same time enters the field of Radiology and Radiation, after dealing with the doses, the radiation output and its effects on X-ray film imaging. The purpose of this paper is to describe and complete analysis of the geometrical controls and generator controls - X-ray tubes, which must be made in radiography machines. These machines are in the radiology department of Public Hospitals and Privacy Policy and generally in areas of production of ionizing radiation. These checks, their frequency and the pattern are defined by the protocols of the Greek Atomic Energy Commission (GAEC). The purpose of these inspections, under the protocols of GAEC, is the quality assurance of radiological equipment, to the best medical services to the examinees.

Cette thèse se concentre sur l'étude de composés magnétiques géométriquement frustrés où les ions magnétiques se situent aux sommets d'un réseau de tétraèdres partageant leurs sommets: les composés pyrochlores. Deux familles de formule chimique R2M2O7, où R est un lanthanide et M= Ti, Sn, sont particulièrement intéressantes puisqu'elles présentent une grande variété d'états magnétiques exotiques. Premièrement, nous avons étudié le champ cristallin agissant au site de la terre rare dans l'approximation de Stevens où uniquement le terme fondamental est considéré. Un jeu unique de paramètres a été déterminé pour chaque famille considérée grâce à une analyse globale incluant des spectres de neutrons inélastiques de plusieurs composés. Ensuite, nous avons caractérisé avec un large éventail de techniques les propriétés physiques à basse température de Nd2Sn2O7. En dessous de la température de transition Tc=0.91 K, ce composé possède un ordre magnétique à longue portée dans la configuration de spins dite "all-in-all-out". Une persistance de la dynamique de spins a été révélée dans la phase ordonnée, attribuée à des excitations unidimensionnelles de spins. Une dynamique de spins anormalement lente est également reportée dans la phase paramagnétique. Enfin, nous avons apporté quelques informations sur les deux états fondamentaux proposés pour le composé très étudié Tb2Ti2O7: premièrement, l'apparition d'une transition Jahn-Teller à basse température est suggérée mais l'absence d'élargissement des pics de Bragg réfute la présence d'une transition structurale. Enfin ce composé pourrait être un exemple d'une glace de spin quantique mais l'existence d'un plateau d'aimantation n'est pas évident jusqu'à T=20 mK. / This Phd thesis focuses on the study of magnetically frustrated compounds where magnetic ions lie at the vertices of a corner-sharing tetrahedra network: the pyrochlore compounds. The two series of chemical formula R2M2O7, where R is a lanthanide and M=Ti, Sn, are of peculiar interest since they display a large variety of exotic magnetic ground states. First, we have studied the crystal-electric-field acting at the rare earth within the Stevens approximation where only the ground state multiplet is considered. A single set of parameters for each families of interest has been determined through a global analysis including several inelastic neutron scattering spectra of various compounds. Then, we have characterised with a large panel of techniques the low temperature physical properties of Nd2Sn2O7. This compound enters a long-range magnetic order at transition temperature Tc=0.91 K with an ``all-in-all-out'' spin configuration. A persistence of spin dynamics has been found in the ordered phase, ascribed to one-dimensional spin loops excitations. Anomalously slow paramagnetic spin fluctuations are also reported. Finally, we have brought information on the two proposed ground states of the widely studied compound Tb2Ti2O7: first, a Jahn-Teller transition is claimed to occur at low temperatures but no broadening of the Bragg peaks is seen down to T=4 K precluding premises of a structural transition. Secondly, this compound could be a realisation of a quantum spin-ice but no definitive evidence of a magnetisation plateau is found down to T=20 mK.