A covariant Wigner-Weyl quantization formalism on the manifold that uses pseudo-differential operators is proposed. The asymptotic product formula that leads to the symbol calculus in the presence of gauge and gravitational fields is presented. The new definition is used to get covariant differential operators from momentum polynomial symbols. A covariant Wigner function is defined and shown to give gauge-invariant results for the Landau problem. An example of the covariant Wigner function on the 2-sphere is also included.

Au cours de cette étude, nous avons fait la synthèse des théories qui ont pour objet d'améliorer les thermoéléments. Nous avons ensuite étudié les propriétés thermoélectriques des composés ternaires AgTlSe, AgTlTe, AgTl_0,95TeSn_0,05 et AgTlTe_1-xSe_x avec x= 0,1 ; 0,2 et 0,3. Ces composés ont une température de fusion voisine de 500°C. C'est donc dans la même zone de température que les alliages à base de tellurure de bismuth qu'ils pourraient être utilisés comme thermoéléments. Tous les échantillons étudiés étaient de type p. Les propriétés que nous avons déterminées nous ont permis d'estimer le facteur de mérite thermoélectrique maximal que l'on peut obtenir avec chacun de ces matériaux en le dopant convenablement. Il ressort immédiatement que AgTlTe est le composé le plus intéressant, ou plutôt celui qui permet les plus grands espoirs. L'estimation que nous avons obtenue pour son facteur de mérite maximal est en effet très élevée : Elle se situe à température ambiante 20% au-dessus du facteur de mérite du meilleur élément de type p que nous connaissions : (Bi₂Te₃)₉₀(Bi₂Se₃)₅(Sb₂Se₃)₅. Par rapport à ce dernier les propriétés électriques ne sont pas très favorables mais par contre la conductibilité thermique de AgTlTe est 4 fois plus faible. Notre estimation est une indication fort encourageante pour la poursuite de cette étude. Toutefois elle ne permet pas encore d'affirmer que l'on pourra, avec AgTlTe, améliorer le rendement des dispositifs thermoélectriques existants. En effet, il suffirait d'une erreur de 10% sur la mesure du coefficient de Seebeck pour modifier l'estimation d'un facteur 2. Une telle sensibilité doit nous inciter à la plus grande prudence dans nos affirmations. De plus, en s'approchant du dopage optimum plusieurs facteurs peuvent aussi bien améliorer que détériorer les propriétés du matériau (changement de mode de diffusion des porteurs ...). Ainsi notre estimation suppose que l'on puisse ajuster le dopage, ce qui nécessite de trouver des impuretés dont la solubilité dans AgTlTe soit suffisante. Pour AgSbTe₂ par exemple, cela n'a pas été possible alors que ce composé était très prometteur. Un programme actuellement en cours pour étudier l'influence d'une quinzaine d'impuretés différentes devrait permettre d'élucider ce point. Le principe de notre estimation est d'évaluer le rôle du dopage sur le facteur de mérite. Mais il existe d'autres facteurs sur lesquels on peut agir pour l'améliorer. Ainsi a-t-on souvent recours aux solutions solides pour diminuer la conductibilité thermique. Par exemple Bi₂Te₃ optimisé possède à température ambiante un facteur de mérite Z de 0,66 10^-3K^-1 alors que par l'adjonction de 5% de Sb₂Te₃ et 5% de Sb₂Se₃ il atteint 3,4 10^-3K^-1. En ce qui concerne AgTlTe cette voie ne semble pas prometteuse car sa conductibilité thermique est déjà extrêmement faible et ne pourra sans doute pas être beaucoup diminuée. Par contre d'autres alliages pourraient permettre d'augmenter la mobilité des porteurs, qui dans AgTlTe est assez faible. Ces indications pourront servir de ligne directrice pour la poursuite de cette étude qui comprendra donc deux volets : (¤) Recherche de dopants et optimisation du dopage deAgTlTe. (¤) Recherche de matériaux voisins de AgTlTe possédant de meilleures propriétés électriques. Ces matériaux pourraient être recherchés parmi les solutions solides comportant CuTlTe. Par ailleurs, il sera utile de préciser la nature de la transformation que nous avons rencontrée à plusieurs reprises. Finalement, nous avons montré que le composé AgTlTe serait susceptible de supplanter les alliages à base de tellururede bismuth. Le travail qui reste à accomplir est important mais nous pouvons espérer qu'il débouchera sur un élargissement de l'utilisation des thermoéléments.

Ce travail développe une approche globale du problème de l'interface entre une solution électrolytique et un semiconducteur doté d'une densité d'impuretés ionisables élevée (environ 10²º/cm³). L'épaisseur réduite de la zone de charge d'espace, l'influence de la couche d'Helmhotz et l'existence de niveaux profonds sont étudiées. Une expression très générale de la capacité de charge d'espace en présence de niveaux profonds est établie. Cette approche est appliquée au cas de l'oxyde de nickel lithiné Li_xNi_1-xO et conduit à une explication originale du comportement de l'interface.

Ce travail porte sur l'élaboration et la caractérisation de cellules solaires organiques à base de nouvelles classes de matériaux donneurs dérivés de petites molécules solubles. Une première phase de ce travail a été consacrée à l'étude des cellules de type hétérojonction volumique à base de poly(3-hexylthiophène) et d'un dérivé soluble du fullerène C60, le PCBM. Le nombre considérable de travaux déjà publiés sur ces dispositifs en ont fait un système modèle particulièrement approprié à l'étude des différents paramètres expérimentaux impliqués dans la fabrication de ce type de cellules et à leur optimisation. Les protocoles expérimentaux définis sur la base de ces études ont été ensuite appliquées à l'évaluation de deux nouvelles classes de donneurs moléculaires à base du dicétopyrrolopyrrole (DPP) et de dipyrrométhène de bore (BODIPY). Les travaux sur les donneurs dérivés du DPP ont porté sur la réalisation de différentes séries de cellules solaires à hétérojonction planaire et volumique et les résultats obtenus ont permis à la fois d'atteindre des performances intéressantes et de progresser dans la compréhension des relations structure-propriétés dans cette famille de donneurs moléculaires. La dernière partie de ce travail concerne la réalisation et l'étude de cellules solaires à partir d'une classe originale de donneurs moléculaires dérivés du BODIPY. La caractérisation des propriétés électroniques de différentes familles de bodipys ainsi que la fabrication et l'étude de plusieurs séries de cellules solaires ont conduit à des avancées importantes et des rendements parmi les plus élevés obtenus jusqu'à présent sur des BHJ moléculaires à base d'accepteur dérivé du C60 ont été obtenus. Par ailleurs ces travaux ont permis de mettre pour la première fois en évidence des effets coopératifs dans des BHJ moléculaires utilisant des donneurs multiples.

Multisymplectic integration is a relatively new addition to the field of geometric integration, which is a modern approach to the numerical integration of systems of differential equations. Multisymplectic integration is carried out by numerical integrators known as multisymplectic integrators, which preserve a discrete analogue of a multisymplectic conservation law. In recent years, it has been shown that various discretisations of a multi-Hamiltonian PDE satisfy a discrete analogue of a multisymplectic conservation law. In particular, discretisation in time and space by the popular symplectic Runge–Kutta methods has been shown to be multisymplectic. However, a multisymplectic integrator not only needs to satisfy a discrete multisymplectic conservation law, but it must also form a well-defined numerical method. One of the main questions considered in this thesis is that of when a multi-Hamiltonian PDE discretised by Runge–Kutta or partitioned Runge–Kutta methods gives rise to a well-defined multisymplectic integrator. In particular, multisymplectic integrators that are explicit are sought, since an integrator that is explicit will, in general, be well defined. The first class of discretisation methods that I consider are the popular symplectic Runge–Kutta methods. These have previously been shown to satisfy a discrete analogue of the multisymplectic conservation law. However, these previous studies typically fail to consider whether or not the system of equations resulting from such a discretisation is well defined. By considering the semi-discretisation and the full discretisation of a multi-Hamiltonian PDE by such methods, I show the following: • For Runge–Kutta (and for partitioned Runge–Kutta methods), the active variables in the spatial discretisation are the stage variables of the method, not the node variables (as is typical in the time integration of ODEs). • The equations resulting from a semi-discretisation with periodic boundary conditions are only well defined when both the number of stages in the Runge–Kutta method and the number of cells in the spatial discretisation are odd. For other types of boundary conditions, these equations are not well defined in general. • For a full discretisation, the numerical method appears to be well defined at first, but for some boundary conditions, the numerical method fails to accurately represent the PDE, while for other boundary conditions, the numerical method is highly implicit, ill-conditioned and impractical for all but the simplest of applications. An exception to this is the Preissman box scheme, whose simplicity avoids the difficulties of higher order methods. • For a multisymplectic integrator, boundary conditions are treated differently in time and in space. This breaks the symmetry between time and space that is inherent in multisymplectic geometry. The second class of discretisation methods that I consider are partitioned Runge– Kutta methods. Discretisation of a multi-Hamiltonian PDE by such methods has lead to the following two major results: 1. There is a simple set of conditions on the coefficients of a general partitioned Runge– Kutta method (which includes Runge–Kutta methods) such that a general multi- Hamiltonian PDE, discretised (either fully or partially) by such methods, satisfies a natural discrete analogue of the multisymplectic conservation law associated with that multi-Hamiltonian PDE. 2. I have defined a class of multi-Hamiltonian PDEs that, when discretised in space by a member of the Lobatto IIIA–IIIB class of partitioned Runge–Kutta methods, give rise to a system of explicit ODEs in time by means of a construction algorithm. These ODEs are well defined (since they are explicit), local, high order, multisymplectic and handle boundary conditions in a simple manner without the need for any extra requirements. Furthermore, by analysing the dispersion relation for these explicit ODEs, it is found that such spatial discretisations are stable. From these explicit ODEs in time, well-defined multisymplectic integrators can be constructed by applying an explicit discretisation in time that satisfies a fully discrete analogue of the semi-discrete multisymplectic conservation law satisfied by the ODEs. Three examples of explicit multisymplectic integrators are given for the nonlinear Schr¨odinger equation, whereby the explicit ODEs in time are discretised by the 2-stage Lobatto IIIA– IIIB, linear–nonlinear splitting and real–imaginary–nonlinear splitting methods. These are all shown to satisfy discrete analogues of the multisymplectic conservation law, however, only the discrete multisymplectic conservation laws satisfied by the first and third multisymplectic integrators are local. Since it is the stage variables that are active in a Runge–Kutta or partitioned Runge– Kutta discretisation in space of a multi-Hamiltonian PDE, the order of such a spatial discretisation is limited by the order of the stage variables. Moreover, the spatial discretisation contains an approximation of the spatial derivatives, and thus, the order of the spatial discretisation may be further limited by the order of this approximation. For the explicit ODEs resulting from an r-stage Lobatto IIIA–IIIB discretisation in space of an appropriate multi-Hamiltonian PDE, the order of this spatial discretisation is r - 1 for r = 10; this is conjectured to hold for higher values of r. For r = 3, I show that a modification to the initial conditions improves the order of this spatial discretisation. It is expected that a similar modification to the initial conditions will improve the order of such spatial discretisations for higher values of r.

Submitted by MARCIA ROVADOSCHI (marciar@unifra.br) on 2018-08-20T17:59:29Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese_AndersonLuizEllwanger.pdf: 20191181 bytes, checksum: d3b7f1adf6fed73bff479e01e305a9ca (MD5) / Made available in DSpace on 2018-08-20T17:59:29Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese_AndersonLuizEllwanger.pdf: 20191181 bytes, checksum: d3b7f1adf6fed73bff479e01e305a9ca (MD5) Previous issue date: 2018-05-18 / In this work we present a study on a Dynamic Planning structured for the development of the discipline of Physics I and Physics Applied to Architecture in undergraduate classes of the faceto- face modality of the Universidade Franciscana during the year 2016. This research was initially delineated from conclusions obtained in activities previously applied in 2014 in these same disciplines, with the help of Moodle computational environment. The current didactic strategy was organized through the Teaching Plan, prepared at the beginning of the semester, having been adjusted over the period according to the needs of each class, considering previous implementations added to the researcher's experience. The initial planning and organization of the contents / activities started from the study of the curricular curriculum of the course, in which the discipline is inserted, as well as the expected profile of the egress. Subsequently, the reorganization of Dynamic Planning considered the prior knowledge of the students guiding a didactic sequence based on the use of virtual applications, videos and practical activities. The evaluation process took place on a continuous basis, in which all tasks such as participation in forums, multiple choice questions and organization / presentation of papers made up the student's final evaluation. In this way, the differential of this research was based on the constant reorganization of the planning, guided by the results collected throughout the implementation. The teaching frame is marked in the meaning of Significant Learning with emphasis on the student's autonomy in the process of formation. The analysis of the results was systematized from the participation of the students in dialog spaces in the Moodle environment, and in a semi structured interview, both methods being supported in the Content Analysis Theory of Bardin. With regard to students' use of knowledge, there was a more intense commitment to the "classroom structure" and, later, a motivation in understanding an unfinished science that is constantly advancing. In this way, this study highlights the results of a differentiated methodology called Dynamic Planning, which aims student autonomy in the teaching and learning process. / Neste trabalho apresentamos um estudo sobre um Planejamento Dinâmico estruturado para o desenvolvimento da disciplina de Física I e Física Aplicada à Arquitetura em turmas de graduação, da modalidade presencial, da Universidade Franciscana, durante o ano de 2016. Essa pesquisa foi inicialmente delineada a partir de conclusões obtidas em atividades aplicadas previamente em 2014 nessas mesmas disciplinas, com o auxílio do Moodle via o Ambiente Virtual de Aprendizagem (AVA). A atual estratégia didática foi organizada por meio do Plano de Ensino, elaborado ao iniciar o semestre, tendo sido ajustado ao longo do período de acordo com a necessidade de cada turma, considerando as implementações anteriores somadas à experiência do pesquisador. O planejamento inicial e a organização dos conteúdos/atividades partiram do estudo da grade curricular do curso, em que está inserida a disciplina, assim como o perfil esperado do egresso. Posteriormente, a reorganização do Planejamento Dinâmico considerou os conhecimentos prévios dos estudantes norteando uma sequência didática baseada no uso de aplicativos virtuais, vídeos e atividades práticas. O processo avaliativo ocorreu de forma continuada, nas quais todas as tarefas como participação em fóruns, questões de múltipla escolha e organização/apresentações de trabalhos compuseram a avaliação final do estudante. Desta forma, o diferencial desta pesquisa amparou-se na constante reorganização do planejamento, guiada pelos resultados coletados ao longo da implementação. O referencial de ensino é balizado nas acepções da Aprendizagem Significativa com ênfase na autonomia do estudante no seu processo de formação. A análise dos resultados foi sistematizada a partir da participação dos estudantes em espaços de diálogo no AVA- Moodle, e em uma entrevista semiestruturada, sendo ambos os métodos amparados na Teoria de Análise de Conteúdo de Bardin. No que se refere ao aproveitamento dos estudantes frente ao conhecimento, percebeuse um empenho mais intenso na “estrutura aula” e, posteriormente, uma motivação na compreensão de uma ciência não acabada e em contínuo avanço. Desta forma, este estudo destaca os resultados de uma metodologia diferenciada denominada Planejamento Dinâmico, que visa uma maior autonomia dos estudantes no processo de ensino e aprendizagem.

<p>As successful as the Standard Model has been in describing particle interactions, there are still many open questions it does not answer; the strong CP violation and the existence of dark matter among them. To address these issues many extensions to the Standard Model have been devised. Some of these extensions propose a new force mediating particle; a massive particle results in a potential described by a Yukawa-like interaction, while a massless exchange particle leads to power law type potentials. Limits on the strength of these interactions at the sub-micron range of separation between two particles are poorly characterized, but previous experiments conducted at IUPUI placed the best limits to date on the strength of a Yukawa-like interaction. Those experiments used a spherical test mass and a planar source mass. However, if a cylindrical test mass was used, the increased interaction volume of the cylinder would result in an increased sensitivity of about an order of magnitude over the spherical test mass experiment. Building such a system presents many challenges, namely the alignment of the cylinder with respect to the planar source mass. A capacitance based scheme to determine the alignment of a cylinder with respect to a plane will be discussed. The thesis concludes with an outline for a new type of measurement system. The new experiment attempts to induce a gravitational Π-pulse in a nanoshphere to probe extensions to the Standard Model.</p> <p> </p>

Dans ce mémoire, nous présentons une stratégie basée sur une approche hybride dans le domaine temporel, couplant une méthode de résolution des équations de Maxwell dans le domaine 3D (FDTD) avec une méthode de résolution des équations de ligne de transmission, afin de pouvoir simuler des problèmes électromagnétiques de grande échelle. Le mémoire donne les éléments d'hybridation pour deux cadres d'utilisation de cette approche : une approche multi-domaine et une approche multi-résolution ou d'échelle. L'approche multi-domaine est une extension de la méthode FDTD 3D à plusieurs sousdomaines reliés par des structures filaires sur lesquelles on résout une équation de lignes de transmission par un formalisme FDTD 1D. La difficulté est d'abord d'avoir une définition implicite du champ électromagnétique dans la théorie des lignes de transmission, et d'autre part de prendre en compte les effets du sol sur les courants induits au niveau des lignes et sur les champs électromagnétiques. L'approche multi-résolution ou d'échelle est conçue pour étendre les capacités de la méthode FDTD au traitement du routage de câbles complexes ayant une section plus petite que la taille de la cellule. Ce mémoire présente différentes techniques pour évaluer les paramètres de la ligne, basées sur la résolution d'un problème de Laplace 2D, ainsi qu'une méthode de couplage champs/câbles basée sur le courant de mode commun. L'ensemble de ce travail nous a permis de proposer une méthode numérique efficace pour calculer les effets électromagnétiques induits par une source (type onde plane ou dipolaire) sur des sites de grande dimension, composés de plusieurs bâtiments reliés entre eux par un réseau de câbles. Dans ce cadre une application à la foudre a été réalisée.

We study point particles to illustrate the various symmetries such as the Poincaré group and its non-relativistic version. In order to find the Noether charges and the Noether currents, which are conserved under physical symmetries, we study Noether’s theorem. We describe the Pauli-Lubanski spin vector, which is invariant under the Poincaré group and describes the spin of a particle in field theory. By promoting the Pauli-Lubanski spin vector to an operator in the quantized theory we will see that it describes the spin of a particle. Moreover, we find an action for a smooth spinning bosonic particle by compactifying one string dimension together with one embedding dimension. As with the Pauli-Lubanski spin vector, we need to quantize this action to confirm that it is the action for a smooth spinning particle. / Vi studerar punktpartiklar för att illustrera olika symemtrier som t.ex. Poincaré gruppen och dess icke-relativistiska version. För att hitta de Noether laddningar och Noether strömmar, vilka är bevarade under symmetrier, studerar vi Noether’s sats. Vi beskriver Pauli-Lubanksi spin vektorn, vilken har en invarians under Poincaré gruppen och beskriver spin hos en partikel i fältteori. Genom att låta Pauli-Lubanski spin vektorn agera på ett tillstånd i kvantfältteori ser vi att den beskriver spin hos en partikel. Dessutom finner vi en verkan för en spinnande partikel genom att kompaktifiera en bosonisk sträng dimension tillsammans med en inbäddad dimension. Som med Pauli-Lubanski spin vektorn, kvantiserar vi denna verkan för att bekräfta att det är en verkan för en spinnande partikel.

The theory of radiative transfer is applied to the problem of multiple wave scattering in a one-dimensional multilayer. A new mathematical model of a multilayer is presented in which both the refractive index and width of each layer are randomized. The layer widths are generated by a new probability distribution which allows for strong layer width disorder. An expression for the transport mean free path of the multilayer is derived based on its single-scattering properties. It will be shown that interference between the field reflected from adjacent layer interfaces remains significant even in the presence of strong layer width disorder. It will be proven that even when the scattering is weak, the field in a random multilayer localizes at certain frequencies. The effect of increasing layer width randomization on this form of localization is quantified. The radiative transfer model of time-harmonic scattering in multilayers is extended to narrow-band pulse propagation in weakly scattering media. The tendency of pulses to broaden in this medium is discussed. A radiative transport model of the system is developed and compared to numerical solutions of the wave equation. It is observed that pulse broadening is not described by simple transfer theory. The radiative transfer model is extended by the addition of a Laplacian term in an attempt to model the effect of ensemble average pulse broadening. Numerical simulation results in support of this proposal are given, and applications for the theory suggested. Finally, the problem of acoustic wave scattering by planar screens is considered. The study was motivated by the idea that multiple scattering experiments may prove possible in a medium composed of such scatterers. Successful multiple scattering in a medium of planar scatterers will depend on the scattering cross-section at angles away from normal incidence. The scattering cross-section is calculated for a circular disc using a new technique for solving the acoustic wave equation on planar surfaces. The method is validated by comparison with available analytic solutions and the geometric theory of diffraction.