Diss. : Fakultät fün Sozial-und Verhaltenswissenschaften : Tübingen : 1982. - Bibliogr. p. 266-273. -

Diplomarbeit--Sozialwissenschaftliche Fakultät--Universität Konstanz, 1989.

In this thesis we use various techniques to investigate the occurrence of trapped modes in the presence of thin obstacles. Physically trapped modes are oscillations of finite energy in a fluid which is unbounded in at least one direction. These oscillations mainly occur locally to some structure and decay to zero at large distances away from it. Trapped modes are important as they have been found to exist in a wide range of physical situations. We consider a number of problems in two and three dimensions including waveguides containing bodies and arrays of identical structures. A modified residue calculus technique, a variational technique and a method based on the truncation of matched eigenfunction expansions are used to solve the problems, with numerous results presented.

Usando teoria de perturbação, fizemos uma análise detalhada da divergência infravermelha em 4ª ordem do processo de aniquilação do par elétron-pósitron. Mostramos que o teorema de Bloch-Nordsieck garante o cancelamento destas divergências em QED. Em seguida, consideramos um processo em QCD com duas partículas coloridas no estado inicial, somando sobre as cores destas duas partículas. O processo escolhido foi o de aniquilação do par quark-anti-quark. O processo em 4ª ordem de perturbação e mostramos neste caso que o Teorema de Block-Nordsieck não se verifica. Este resultado é consequência do fato desta teoria ter um caráter não-abeliano. O não-cancelamento das divergências infravermelhas significa que a natureza do estado ligado é fundamental para o uso consistente da teoria de perturbação na QCD. / Using pertubation theory, we made a detailed analysis of the infrared divergencies to the 4th order for the phocess of annihilation of the pair electron-positron. We showed that the Bloch-Nordsieck theorem guarantees the cancellation of these divergencies in QED. Then we considered a process in QED involving two coloured particles in the initial state, summing over the colours of these particles. The process chosen was the annihilation of the pair quark-anti-quark. We calculated the process to the 4ª order in perturbation theory, and showed that in this case the Bloch-Nordsieck theorem in not verified. This result is a consequence of the fact that this theory has a non-abelian caracter. The non-cancellation of the infrared divergencies signifies that the nature of the bound-state is fundamental for the consistent use of perturbation theory in QCD.

Wannierfunctions are a superposition of the Blochorbitals in a Brillouin zone belonging to a manifold of energy bands. These Wannier functions have several uses regarding the analysis of the crystal on a local level. Since the Bloch orbital has a gauge indeterminacy and the Wannier functions therefore is strongly non-unique, the natural choice is the maximally localized Wannier funcition. These can be calculated from the standard Bloch orbital using unitary transformation by a steepest descent algorithm as proposed by Nicola Marzari and David Vanderbilt. Here the argument for this algorithm is discussed and explained.

La propagation des ondes ultrasonores à travers des cristaux phononiques CP à deux dimensions 2D constitués de diffuseurs solides dans des matrices solide et fluide est ici étudiée, ainsi que la caractérisation de ces milieux et leur application à l’imagerie acoustique. Les techniques expérimentales utilisées permettent une mesure complète des champs transmis à travers les cristaux. Les études sont menées dans des bandes fréquentielles autorisant les effets de réfraction négative indispensables à l’obtention d’une résolution inférieure à la limite de diffraction (super-résolution). De manière à compléter les analyses, différents outils théoriques sont exploités Décomposition en Ondes Planes et Eléments Finis, notamment.La première partie du document concerne la réalisation et la caractérisation de cristaux phononiques possédant des propriétés nécessaires à la réalisation de systèmes d’imagerie acoustique réfraction négative, contours équi-fréquences circulaires, accord d’indice, accord d’impédance. Cette première étude est menée sur un cristal à matrice solide, elle met en relief la possibilité de générer différents modes de Bloch au cours de la propagation. L’accord d’indice avec l’eau n’étant cependant pas obtenu, la seconde partie porte sur la réfraction négative et la focalisation des ondes à travers un CP à matrice fluide. Les propriétés du CP déterminées, le dernier chapitre s’attache à évaluer les performances des systèmes d’imagerie développés : dynamique et résolution. / This investigation deals with wave propagation in two dimensional phononic crystals (PC) made of solid scatterers embedded in solid or fluid matrices. After characterizing such composite materials, their application to acoustic imaging is brought to the forth. The ultrasonic techniques used in the experiments allow the complete measurement of the acoustic transmitted fields and the investigations concern frequency bandwidth able to exhibit negative refraction allowing Oie super-resolution effects. In order to complete the analysis, different theoretical tools are used: Plane Wave Expansion (PWE) and Finite Elements Method (FEM).The first part of this work deals with the realization and characterization of PC to be introduced into acoustic imaging devices (lenses) based on negative refraction. Special attention is given to characteristics such as circular equi-frequency contours, or index and impedance matching. However, during the acoustic wave propagation in a solid PC immersed in water, the presence of different Bloch modes contributing to the transmission of ultrasound is revealed and the index matching was not possible to obtain. Therefore the second part of the manuscript deals with negative refraction and waves focusing through a PC filled with a fluid. After determining the crystal properties, last chapter is devoted to the evaluation of the performances of acoustic imaging systems based on phononic lens.

Usando teoria de perturbação, fizemos uma análise detalhada da divergência infravermelha em 4ª ordem do processo de aniquilação do par elétron-pósitron. Mostramos que o teorema de Bloch-Nordsieck garante o cancelamento destas divergências em QED. Em seguida, consideramos um processo em QCD com duas partículas coloridas no estado inicial, somando sobre as cores destas duas partículas. O processo escolhido foi o de aniquilação do par quark-anti-quark. O processo em 4ª ordem de perturbação e mostramos neste caso que o Teorema de Block-Nordsieck não se verifica. Este resultado é consequência do fato desta teoria ter um caráter não-abeliano. O não-cancelamento das divergências infravermelhas significa que a natureza do estado ligado é fundamental para o uso consistente da teoria de perturbação na QCD. / Using pertubation theory, we made a detailed analysis of the infrared divergencies to the 4th order for the phocess of annihilation of the pair electron-positron. We showed that the Bloch-Nordsieck theorem guarantees the cancellation of these divergencies in QED. Then we considered a process in QED involving two coloured particles in the initial state, summing over the colours of these particles. The process chosen was the annihilation of the pair quark-anti-quark. We calculated the process to the 4ª order in perturbation theory, and showed that in this case the Bloch-Nordsieck theorem in not verified. This result is a consequence of the fact that this theory has a non-abelian caracter. The non-cancellation of the infrared divergencies signifies that the nature of the bound-state is fundamental for the consistent use of perturbation theory in QCD.

Universiẗat, Diss., 2004--Mainz.

Texte remanié de: Diss.--Philos.--Tübingen, 1984. Titre de soutenance : Marxismus und Freiheit : Versuch einer Bestimmung moeglicher Verhaeltnisse auf der Grundlage der Philosophie Ernst Blochs. / Bibliogr. p. 239-245.

Th. doct.--Philo.--Rome--Pontificia universitatis Lateranensis, 1987.