Pages 6 and 7 are labelled as the same page. / <p> The purpose of this work is to calculate phonon dispersion curves in metals paying particular attention to the evaluation of a new electron-ion matrix element by use of orthogonalized plane waves (OPW). The dynamic role of the electrons in screening the electron-ion interaction has been studied. Our formalism makes use of recent developments in the theory of the many-body problem. Applications of our theory have been made to aluminum. The pseudopotential part of the OPW electron-ion matrix element produced an overscreening of the frequency modes. Comparison is made to the use of the Bardeen matrix element. Our results strongly suggest that this calculation applied to lead would explain the magnitude of Kohn kinks observed by Brockhouse et al. (B 62a).</p> / Thesis / Doctor of Philosophy (PhD)

The collision of impulsive gravitational waves, electromagnetic plane waves with collinear polarization and, especially, plane fronted parallel waves (pp waves) are considered. The solution of axisymmetric pp waves is reviewed and the structures of the resulting space-times are investigated with the help of curvature invariants.

The collision of pure electromagnetic plane waves with collinear polarization in Einstein-Maxwell theory and the collision of gravitational plane waves in vacuum Einstein theory are studied. The singularity structure of the Bell-Szekeres and the Szekeres solutions is examined by using curvature invariants. As a final work, the collision of the plane waves in dilaton gravity theory is studied and also the singularity structure of the corresponding space-time is examined.

La integración de tecnologías de ulta-wideband, radio-cognitiva y MIMO representa una herramienta podersoa para mejorar la eficiencia espectral de los sistemas de comunicación inalámbricos. En esta dirección, nuevas estrategias para el modelado de canales MIMO y su caracterización se hacen necesarias si se desea investigar cómo la frecuencia central y el acho de banda afectan el desempeño de los sistemas MIMO. Investigaciones preliminares han enfocado menos atención en cómo estos parámetros afectan las características del canal MIMO. Se presenta una caracterización del canal MIMO en función de la frecuencia, abondándose puntos de vista experimentales y teóricos. Los problemas indicados tratan cinco áreas principales: medidas, post-procesado de datos, generación sintética del canal, estadística multivariable para datos y modelado del canal. Se ha diseñado y validado un sistema de medida basado en un analizador vectorial de redes y se han ejecutado medidas entre 2 y 12 GHz en condiciones estáticas, tanto en línea de vista como no línea de vista. Se ha propuesto y validado un procedimiento confiable para post-procesado, generación sintética de canal y análisis experimental basado en medidas en el dominio de frecuencia. El procedimiento experimental se ha focalizado en matrices de transferencia del canal para casos no selectivos en frecuencia, estimándose además las matrices complejas de covarianza, aplicándose la factorización de Cholesky sobre ls CCM y obteniéndose finalmente matrices de coloreado del sistema. Se presenta un procedimiento de corrección para generación sintética del canal aplicado a casos MIMO de grandes dimensiones y cuando la CCM es indefinida. Este CP permite la factorización de Cholesky y de dichas CCM. Las características multivariables de los datos experimentales han sido investigadas, realizándose un test de normalidad compleja multivariable. / García Ariza, AP. (2009). Modelling and experimental analysis of frequency dependent MIMO channels [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/6563

The rapid expansion of major cities in the west Europeancountries has accentuated the need to exploit every potentialsite for new establishments, e.g. areas over train tunnels andnear railway tracks in general. A significant impediment toexploit such areas is the structure-borne noise generated bythe train traffic, which is transmitted into buildings via theground. Reliable prediction methods and cost-effective noisecontrol measures are therefore needed and are also the objectof the present work. In this thesis, the studied buildings areconsidered as wave-guides for the sound transmitted from theground. The work is restricted to the case of hard ground suchas granite. The chosen technique permits comparison betweendifferent potential measures to reduce the transmission ofstructure-borne sound upward in buildings. It is shown that thedesign of the load-bearing structures is important in thiscontext, and a design with relocated columns has givenpromising results. It is also shown that the stiffness of theground plays an important role in the transmission process.This leads to the idea that a sand layer between the foundationof the building and the bedrock may reduce the transmission.New methods have thus been developed in the course of this workto evaluate the stiffness of the layer using approximate andexact techniques. Results are presented and a comparison ismade with previous results for a "normal" building and it isshown that the insertion of sand layer has a potential toconsiderably reduce the sound level in the building. <b>Keywords:</b>Ground-borne noise, railway noise, in-planewaves, wave-guides, scattering, propagation constant, inputmobility, elastic stratum, dual integral equations.

<p>The rapid expansion of major cities in the west Europeancountries has accentuated the need to exploit every potentialsite for new establishments, e.g. areas over train tunnels andnear railway tracks in general. A significant impediment toexploit such areas is the structure-borne noise generated bythe train traffic, which is transmitted into buildings via theground. Reliable prediction methods and cost-effective noisecontrol measures are therefore needed and are also the objectof the present work. In this thesis, the studied buildings areconsidered as wave-guides for the sound transmitted from theground. The work is restricted to the case of hard ground suchas granite. The chosen technique permits comparison betweendifferent potential measures to reduce the transmission ofstructure-borne sound upward in buildings. It is shown that thedesign of the load-bearing structures is important in thiscontext, and a design with relocated columns has givenpromising results. It is also shown that the stiffness of theground plays an important role in the transmission process.This leads to the idea that a sand layer between the foundationof the building and the bedrock may reduce the transmission.New methods have thus been developed in the course of this workto evaluate the stiffness of the layer using approximate andexact techniques. Results are presented and a comparison ismade with previous results for a "normal" building and it isshown that the insertion of sand layer has a potential toconsiderably reduce the sound level in the building.</p><p><b>Keywords:</b>Ground-borne noise, railway noise, in-planewaves, wave-guides, scattering, propagation constant, inputmobility, elastic stratum, dual integral equations.</p>

L’anisotropie des propriétés mécaniques et acoustiques des matériaux poro-élastiques est un facteur déterminant dans le comportement de panneaux utilisés dans différents domaines de l’ingénierie. La compréhension des différents mécanismes physiques conditionnant la réponse en fréquence de ces structures est alors nécessaire. L’anisotropie intrinsèque des matériaux poreux visco-élastiques présente un potentiel particulier pour l’optimisation multi-fonctionnelle de parois multicouches. En effet, ces parois doivent souvent respecter des contraintes de raideur et isolation sonore et thermique de manière simultanée. Une méthode par superposition d’ondes planes dans des parois composées de matériaux poro-visco-élastiques est présentée afin d’analyser la sensibilité de la réponse acoustique de structures multicouches à l’alignement relative des couches poreuses anisotropes dans celles-ci. La méthode est validée et appliquée à l’étude d’un système composée d’une mousse de mélamine située entre deux parois métalliques. Cesystème permet d’illustrer des phénomènes intrinsèques aux couche poro-élastiques anisotropes, tel que le décalage en fréquence de la résonance fondamentale du système, et les couplages de compression-cisaillement dans le milieu poro-élastique. Ce phénomène de couplage est particulièrement intéressant puisqu’il n’est caractérisable que par la polarisation des ondes dans le milieu poro-élastique anisotrope. En fin, la méthode est appliquée afin d’optimiser un système multicouche pour des performances acoustiques. Les variables d’optimisation sont les orientations relatives des couches poro-élastiques anisotropes par rapport au système de coordonnées globales. Les solutions aux problèmes d’optimisation sont analysées en termes de comportement mécanique, ce qui permet d’établir une corrélation entre performances acoustiques et comportement dynamique. / The mechanical and acoustic anisotropy of media is a governing factor in the behaviour of multilayered systems including such media. The understanding of the mechanisms conditioning the dynamic behaviour of multilayered systems is of paramount importance. In particular, the intrinsicanisotropy of poroelastic media presents a potential for the optimal design of systems for multifunctional performances. Indeed, these multilayered systems are bound by stiffness, thermal and acoustic performance constraints in simultaneously. A plane wave method is presented to study theinfluence of material orientation in the dynamic behaviour of multilayered systems composed of anisotropic poroelastic media. The method is applied to a system composed of an anisotropic open-celled melamine foam core in between two metal sheets. This particular multilayered configuration allows to shed light on phenomena intrinsic to layers composed of anisotropic poroelastic materials, such as the frequency shift of the fundamental resonance of the panel, or the compression-shear coupling effects taking place in the poroelastic core layers. The latter phenomena is of particular importance, as it is evidenced on the unconventional polarisation of waves in anisotropic poroelastic media. Finally, the method is adapted to the optimisation of multi-layered systems for acoustic performance. the design variables are consequently the core material orientations with respect to the global coordinate system. The solutions to the optimisation problem are analysed in terms of dynamic behaviour, thus allowing to correlate acoustic performanceof the overall structure, and the response of each individual layer.

Cette thèse est consacrée à l'étude de la méthode PAW (projector augmented-wave) et d'une de ses modifications, baptisée méthode PAW variationnelle (VPAW), pour le calcul de l'état fondamental d'Hamiltoniens en géométrie périodique. Ces méthodes visent à améliorer la vitesse de convergence des méthodes d'ondes planes (ou méthodes de Fourier) en appliquant une transformation inversible au problème aux valeurs propres initial agissant au voisinage de chaque site atomique. Cette transformation permet de capter une partie des difficultés dues aux singularités coulombiennes. La méthode VPAW est analysée pour un opérateur de Schr\"odinger unidimensionnel avec des potentiels de Dirac. Les fonctions propres de ce modèle comprennent des sauts de dérivées similaires aux cusps électroniques. Le saut de dérivée des fonctions propres du problème aux valeurs propres issu de la méthode VPAW est réduit de façon importante. Cela entraîne une accélération de convergence en ondes planes du calcul des valeurs propres corroborée par une étude numérique. Une étude de la méthode VPAW est conduite pour des Hamiltoniens 3D périodiques avec des singularités coulombiennes, parvenant à des conclusions similaires. Pour la méthode PAW, la transformation inversible comporte des sommes infinies qui sont tronquées en pratique. Ceci introduit une erreur, qui est rarement quantifiée en pratique. Elle est analysée dans le cas de l'opérateur de Schrödinger unidimensionnel avec des potentiels de Dirac. Des bornes sur la plus basse valeur propre en fonction des paramètres PAW sont prouvées conformes aux tests numériques. / This thesis is devoted to the study of the PAW method (projector augmented-wave) and of a variant called the variational PAW method (VPAW). These methods aim to accelerate the convergence of plane-wave methods in electronic structure calculations. They rely on an invertible transformation applied to the eigenvalue problem, which acts in a neighborhood of each atomic site. The transformation captures some difficulties caused by the Coulomb singularities. The VPAW method is applied to a periodic one-dimensional Schr\"odinger operator with Dirac potentials and analyzed in this setting. Eigenfunctions of this model have derivative jumps similar to the electronic cusps. The derivative jumps of eigenfunctions of the VPAW eigenvalue problem are significantly reduced. Hence, a smaller plane-wave cut-off is required for a given accuracy level. The study of the VPAW method is also carried out for 3D periodic Hamiltonians with Coulomb singularities yielding similar results. In the PAW method, the invertible transformation has infinite sums that are truncated in practice. The induced error is analyzed in the case of the periodic one-dimensional Schrödinger operator with Dirac potentials. Error bounds on the lowest eigenvalue are proved depending on the PAW parameters.

Neste trabalho, são caracterizadas as soluções do tipo ondas planas e modais de modelos matemáticos referentes à teoria de linhas de transmissão, com e sem perdas, e à teoria de vigas, modelo de Timoshenko e modelo não local de Eringen. Os modelos são formulados matricialmente, e as ondas em questão são determinadas em termos da base gerada pela resposta matricial fundamental de sistemas de equações diferenciais ordinárias de primeira, segunda e quarta ordem. A resposta matricial fundamental é utilizada numa forma fechada que envolve o acoplamento de um número finito de matrizes e uma função escalar geradora e suas derivadas. A função escalar geradora é bem comportada para mudanças em torno de frequências críticas e sua robustez é exibida através da técnica de Liouville. As ondas modais são decompostas em termos de uma parte que viaja para frente e uma parte que viaja para trás. Essa decomposição é utilizada para fornecer matrizes de reflexão e transmissão em descontinuidades e condições de contorno. No contexto das linhas de transmissão são consideradas uma junção de linhas com impedâncias características diferentes ou uma carga em uma extremidade da linha. Na teoria de Timoshenko são consideradas uma fissura ou condições de contorno em uma das extremidades. Exemplos numéricos com descontinuidade são considerados na viga. Na teoria de linhas de transmissão exemplos com multicondutores são considerados e observações são realizadas sobre a decomposição das ondas modais. No modelo não local de Eringen, para vigas bi-apoiadas é discutida a existência do segundo espectro de frequências. / Plane type solutions and modal waves of mathematical models, which refer to transmission lines theory, both lossless and lossy, and to beam theory, using both Timoshenko and nonlocal Eringen models, are being characterized in this work. The models are formulated in matrix form, and the waves are determined in terms of matrix basis generated by fundamental matrix response of systems of ordinary differential equations of first, second and fourth order. The fundamental matrix response is used in the closed-form, which involve the coupling between a number finite of matrices of a generating scalar function and its derivatives. The generating scalar function is well behaved for changes around critical frequencies and its robustness is exhibited through the Liouville technique. Modal waves are decomposed in forward and backward parts. This decomposition is used for providing reflection and transmission matrices when dealing with discontinuities and boundary conditions. In the context of transmission lines junction of lines with different characteristic impedances or a load at one end of the line are being considered. In Timoshenko’s theory the crack problem or boundary conditions at one end are also being considered. Numerical examples with discontinuities are considered in the context of beams. Numerical examples with discontinuities and boundary value problems were approached using modal wave decomposition. In transmission line theory examples with multiconductors are considered and observations are made about decomposition of the modal waves. In the nonlocal of Eringen model, for bi-supported beams, the existence of the second frequency spectrum is discussed.

Neste trabalho, são caracterizadas as soluções do tipo ondas planas e modais de modelos matemáticos referentes à teoria de linhas de transmissão, com e sem perdas, e à teoria de vigas, modelo de Timoshenko e modelo não local de Eringen. Os modelos são formulados matricialmente, e as ondas em questão são determinadas em termos da base gerada pela resposta matricial fundamental de sistemas de equações diferenciais ordinárias de primeira, segunda e quarta ordem. A resposta matricial fundamental é utilizada numa forma fechada que envolve o acoplamento de um número finito de matrizes e uma função escalar geradora e suas derivadas. A função escalar geradora é bem comportada para mudanças em torno de frequências críticas e sua robustez é exibida através da técnica de Liouville. As ondas modais são decompostas em termos de uma parte que viaja para frente e uma parte que viaja para trás. Essa decomposição é utilizada para fornecer matrizes de reflexão e transmissão em descontinuidades e condições de contorno. No contexto das linhas de transmissão são consideradas uma junção de linhas com impedâncias características diferentes ou uma carga em uma extremidade da linha. Na teoria de Timoshenko são consideradas uma fissura ou condições de contorno em uma das extremidades. Exemplos numéricos com descontinuidade são considerados na viga. Na teoria de linhas de transmissão exemplos com multicondutores são considerados e observações são realizadas sobre a decomposição das ondas modais. No modelo não local de Eringen, para vigas bi-apoiadas é discutida a existência do segundo espectro de frequências. / Plane type solutions and modal waves of mathematical models, which refer to transmission lines theory, both lossless and lossy, and to beam theory, using both Timoshenko and nonlocal Eringen models, are being characterized in this work. The models are formulated in matrix form, and the waves are determined in terms of matrix basis generated by fundamental matrix response of systems of ordinary differential equations of first, second and fourth order. The fundamental matrix response is used in the closed-form, which involve the coupling between a number finite of matrices of a generating scalar function and its derivatives. The generating scalar function is well behaved for changes around critical frequencies and its robustness is exhibited through the Liouville technique. Modal waves are decomposed in forward and backward parts. This decomposition is used for providing reflection and transmission matrices when dealing with discontinuities and boundary conditions. In the context of transmission lines junction of lines with different characteristic impedances or a load at one end of the line are being considered. In Timoshenko’s theory the crack problem or boundary conditions at one end are also being considered. Numerical examples with discontinuities are considered in the context of beams. Numerical examples with discontinuities and boundary value problems were approached using modal wave decomposition. In transmission line theory examples with multiconductors are considered and observations are made about decomposition of the modal waves. In the nonlocal of Eringen model, for bi-supported beams, the existence of the second frequency spectrum is discussed.