Cette thèse est consacrée à l’étude haute fréquence de problèmes de Dirichlet et Neumann pour le système de l’élasticité. On y étudie le phénomène de réflexion au bord au moyen de deux techniques : la sommation de faisceaux gaussiens et les mesures de Wigner. Dans les chapitres 1 et 2, on commence par étudier le problème plus simple de l’équation des ondes scalaire à une vitesse. Sous certaines hypothèses sur les conditions initiales, on construit des solutions approchées par superposition de faisceaux gaussiens. La justification de l’asymptotique se fonde sur une estimation de normes de certains opérateurs intégraux à phases complexes. Pour des conditions initiales plus générales, on utilise les mesures de Wigner pour calculer la densité d’énergie microlocale. On calcule explicitement les transformées de Wigner d’intégrales de faisceaux gaussiens. Le comportement de la densité d’énergie microlocale de la solution exacte se déduit de celui établi pour la solution approchée. Dans le chapitre 3, on utilise les résultats établis pour les sommes infinies de faisceaux gaussiens pour construire une solution approchée pour les équations de l’élasticité et calculer sa densité d’énergie microlocale. L’existence de deux vitesses différentes dans le système de l’élasticité introduit de nouvelles difficultés qui sont traitées dans ce chapitre. / This thesis is devoted to the study of the high frequency Dirichlet and Neumann problems for the elasticity system. We study the reflection phenomenon at the boundary by means of two techniques: Gaussian beams summation and Wigner measures. In chapters 1 and 2, we start by studying the simpler problem of the scalar wave equation with one speed. Under some hypotheses on the initial conditions, we build an approximate solution by a Gaussian beams superposition. Justification of the asymptotics is based on norms estimate of some integral operators with complex phases. For more general initial conditions, we use Wigner measures to compute the microlocal energy density. We compute Wigner transforms of Gaussian beams integrals in an explicit way. The behaviour of the microlocal energy density for the exact solution is deduced from the one for the approximate solution. In chapter 3, we use the established results on infinite sums of Gaussian beams to build an approximate solution for the elasticity equations and to compute its microlocal energy density. We treat new difficulties arising from the existence of two different speeds in the elasticity system.

Hannover, Universiẗat, Diss., 2000.

In this thesis we examine the Elko field dark matter candidate, its interactions, and possible theoretical origins. We discuss important areas in which Elko Field Theory is incomplete and propose what we consider to be the most natural ways of plugging the holes in the theory. The way we propose to plug these holes enables Elko fields to interact with Standard Model gauge quanta. Any possible Elko darkness may be then due to Elko non-locality. The possible existence of Elko gauge interactions constitutes a significant result in this thesis. We also explore how Elko quantum fields might arise on the state space. We show that the Elko field is not a quantum field in the sense of Weinberg and that the Elko field violates the symmetries of the Lorentz group; another significant result altering how we think about Elko Field Theory. We also show that subgroups of the Lorentz group do not give rise to Elko fields (or their VSR counterparts) on the state space. We also examine the non-standard Wigner classes and show that in the context of our most natural ways of plugging the holes present in Elko Field Theory, Elko fields do not arise there either. We also show that in one of the non-standard Wigner classes, under certain conditions, there can exist a local massive spin-1/2 quantum field Majorana type dark matter candidate that is a well-defined quantum field in the sense of Weinberg. We give the dynamics of this new quantum field and also specify under what conditions this quantum field can exist. We finish the thesis by exploring Elko fields and their left and right-handed components in the context of the Electroweak Theory, in a more speculative way. We take the general concept of mass dimension transmutation introduced for Classical Spinor Theory by J.M. Hoff da Silva and R. da Rocha and apply it to the state space in the most natural way. We use this to derive a formula linking Dirac fields to the left-handed components of Elko fields and suggest the possibility of mass dimension transmutation being involved in electroweak interactions. Finally, we point out that although Elko fields cannot enter the Standard Model doublets, they can form their own doublets, the resulting symmetry currents of which can couple to the symmetry currents of the Standard Model.

No description available.

It is a common belief that there are invariant acoustic patterns in speech signals, which can be related to their phonetic description. These patterns are expected to remain invariant, independent of the language, speaker, phonetic context, etc. Although many investigations based on short-time spectral analysis have established the feasibility of extracting invariant cues in certain contexts, they could not provide a set of invariant cues in any given phonetic context. In this thesis, the Wigner distribution (WD) was used to analyze speech signals for the first time, to investigate acoustic invariance. The WD, like the spectrogram, provides a time-frequency description of the signal. Unlike the spectrogram, it provides correct marginals in the time and frequency domains, but it is not a positive distribution. It is demonstrated here that the partially smoothed WD, in which both the properties of positivity and correct marginals are sacrificed to some extent, provides a better time-frequency resolution than short-time spectral analyses methods. An implementation and an interpretation of the partially smoothed WD are presented. The choice of smoothing parameters and the nature of cross-term suppression in a partially smoothed WD are discussed in detail. It is shown that the cross-terms in a partially smoothed WD do not mask the underlying nature of a signal in the time-frequency plane. A partially smoothed WD was used to investigate acoustic invariance in voiceless, unaspirated stop consonants spoken by native speakers of English, Telugu and French. Contrary to reports in the literature, it was shown that the features "diffuse-rising" and "compact" spectral shapes were not unique to alveolar and velar places of articulation, respectively, but depended on the vowel context. The resulting ambiguities when specifying the place of articulation were resolved using Formant Onset Duration (time taken for the steady state formants to occur in the vocal tract after the consonantal release) and F₂ of the following vowel. The place of articulation was specified correctly for 86% of the tokens. Unlike in other investigations, the errors in specifying the place of articulation were uniformly distributed over all vowel contexts. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

Yes / Two fractional Fourier transforms are used to define bi-fractional displacement operators, which interpolate between displacement operators and parity operators. They are used to define bi-fractional coherent states. They are also used to define the bi-fractional Wigner function, which is a two-parameter family of functions that interpolates between the Wigner function and the Weyl function. Links to the extended phase space formalism are also discussed.

No description available.

No / Large-scale data are analysed using the Wigner function. It is shown that the ‘frequency variable’ provides important information, which is lost with other techniques. The method is applied to ‘sentiment analysis’ in data from social networks and also to financial data.

No presente trabalho propomos e estudamos um modelo teórico que denominamos Cristal de Wigner Blindado. Assumindo para este sistema uma estrutura ordenada, nos foi possível verificar a ocorrência de uma transição de fase entre as estruturas bcc e fcc, para este modelo em função da densidade e/ou do parâmetro de blindagem. Após esta análise estática nos estendemos aos aspectos dinâmicos. Determinamos os modos normais para estas estruturas obtendo espectros de frequência para diversas blindagem e/ou densidade. Levando o parâmetro de blindagem para o limite zero, recuperamos diversos resultados conhecidos para o Cristal de Wigner. Isto era esperado urna vez que este modelo apenas difere do nosso pela natureza das interações, que neste caso são puramente coulombianas, sem blindagem. Além disto, nos foi possível efetuar comparação com sistemas reais formados por esferas de poliestireno em suspensão aquosa, permitindo-nos concluir que o modelo por nós proposto é aplicável aos mesmos / We present and develop a theoretical model which we designate Screened Wigner Lattice (SWL). In the ordered phase of this system we were able to predict a bcc-fcc transition, by varying the screening parameter and/or the density. After this static analysis we calculated the normal modes of such crystals and got the frequency spectra in function of the screening and/or density. Taking for the screening parameter the limit zero we reproduced several results already known for the Wigner Lattice (WL). This was expected since the only difference between the SWL and WL models consists on the nature of the interaction, some of our theoretical results with experimental data obtained for crystals formed by polystyrene spheres in aqueous suspension. The agreement allows us to conclude that the SWL model applies for such systems

RAMOS, Igor Rochaid Oliveira. Estudo de um sistema clássico de dipolos magnéticos carregados em estruturas de bicamadas. 2010. 75 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2010. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2014-10-31T20:38:15Z No. of bitstreams: 1 2010_dis_iroramos.pdf: 3512055 bytes, checksum: ba5eb29d22412048c4f8a2972b874c7e (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2014-10-31T21:08:54Z (GMT) No. of bitstreams: 1 2010_dis_iroramos.pdf: 3512055 bytes, checksum: ba5eb29d22412048c4f8a2972b874c7e (MD5) / Made available in DSpace on 2014-10-31T21:08:54Z (GMT). No. of bitstreams: 1 2010_dis_iroramos.pdf: 3512055 bytes, checksum: ba5eb29d22412048c4f8a2972b874c7e (MD5) Previous issue date: 2010 / We study the structural and dynamical properties of a two-dimensional (2D) classical bi-layer crystal of charged magnetic dipolar particles in a setup where the dipoles are oriented perpendicular to the layers and equal density of charged dipolar particles in each layer. The energy of the system is due to the charge - charge interaction (Coulomb interaction) and the dipole - dipole interaction. Due to the long-range nature of the interactions, we use the Ewald summation method to obtain an expression for the energy involving rapidly convergent sums. By comparing the energies of a number of possible crystal geometries, we determine the phase diagram of the system as a function of the parameter η (which is related to the separation between the layers of charged magnetic dipoles and the particle density) and the relative intensity of the magnetic and electrical interactions. By changing the relative intensity of the dipole - dipole interaction with respect to electrical one, we are able to find six diferent stable crystalline structures as a function of η. An interesting feature of the present model system is the possibility to tune between the matched and staggered arrangements by varying the magnetic interaction between the dipoles, e.g. through an external magnetic field. The phase boundaries of the crystalline structures consist of both continuous and discontinuous transitions. In order to investigate the stability of the minimum energy arrangements we also calculate the phonon spectra of the system within the harmonic approximation. In this case, we resort again on the Ewald technique to obtain the rapidly convergent sums. The analysis of the phonon spectra reveals interesting features which are useful in the study of melting. / Estudamos as estruturas e as propriedades dinâmicas de um cristal clássico bidimensional (2D) em bicamadas de partículas dipolares magnéticas carregadas em um arranjo no qual os dipolos são perpendiculares às camadas e com mesma densidade de partículas em cada camada. A energia do sistema é devido à interação carga - carga (interação coulom- biana) e a interação dipolo - dipolo. Devido ao fato dessas interações serem de longo alcance, usamos o método da soma de Ewald para obter uma expressão para a energia envolvendo somas que convergem rapidamente. Comparando as energias de possíveis geometrias do cristal, determinamos o diagrama de fase do sistema em função do parâmetro η (que está relacionado com a distância entre as camadas de dipolos magnéticos carregados e a densidade de partículas) e da intensidade relativa das interações elétrica e magnética. Mudando a intensidade relativa da interacão dipolo - dipolo com respeito à interação elétrica, podemos encontrar seis diferentes estruturas cristalinas estáveis em função de η. Uma característica interessante desse sistema é a possibilidade de permanecer em arranjos nos quais as camadas são ou não deslocadas uma em relação a outra, apenas variando a interação magnética entre os dipolos, por exemplo, através de um campo magnético externo. As transições entre as estruturas cristalinas podem ser contínuas e descontínuas. No intuito de investigar a estabilidade das configurações de mínima energia, calculamos o espectro dos fônons do sistema usando a aproximação harmônica. Para isto, recorremos novamente a técnica de Ewald para obter somas que convergem rapidamente. A análise da relação de dispersão (fônons) revela características do sistema que são de grande utilidade no estudo da transição sólido-líquido (fusão).