We give a rather self-contained introduction to the rare pion to dielectron decay which in nontrivial leading order is given by a QED triangle loop. We work within the dispersive framework where the imaginary part of the amplitude is obtained via the Cutkosky rules. We derive these rules in detail. Using the twofold Mellin-Barnes representation for the pion transition form factor, we derive a simple expression for the branching ratio B(π0 <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Crightarrow" /> e+e-) which we then test for various models. In particular a more recent form factor derived from a Lagrangian for light pseudoscalars and vector mesons inspired by effective field theories. Comparison with the KTeV experiment at Fermilab is made and we find that we are more than 3σ below the KTeV experiment for some of the form factors. This is in agreement with other theoretical models, such as the Vector Meson Dominance model and the quark-loop model within the constituent-quark framework. But we also find that we can be in agreement with KTeV if we explore some freedom of the form factor not fixed by the low-energy Lagrangian.

Dans le cadre de la discrétion acoustique des navires militaires, cette thèse contribue à la modélisation de structures amorties par des matériaux viscoélastiques, sous forme de couches contraintes. Afin de pouvoir optimiser et dimensionner la structure et le matériau amortissant, il est souhaitable de disposer d'un outil numérique prédictif et efficace. Dans un premier temps, une stratégie de caractérisation et de modélisation du comportement de matériaux viscoélastiques est proposée. Elle inclue une méthode de recalage de résultats de mesures par DMA basée sur le respect des relations de Kramers-Kronig, permettant ainsi de construire des courbes maîtresses du matériau en accord avec le principe de causalité. Dans un deuxième temps, un code de calcul par éléments finis est développé, puis des essais de vibration sur structures sandwich sont réalisés afin de valider la modélisation par éléments finis de structures munies de matériaux viscoélastiques. Dans le cas d'une fine couche viscoélastique insérée dans une structure maillée par des éléments volumiques, deux éléments d'interface sont développés : ils permettent de tester simplement plusieurs configurations. Enfin, dans un troisième temps, deux catégories de méthodes de réduction adaptées au calcul de la réponse fréquentielle de structures fortement amorties par des matériaux viscoélastiques sont étudiées : les méthodes de projection sur bases modales et la méthode de reconstruction par approximants de Padé. Dans le cadre d'études paramétriques pour l'optimisation des performances acoustiques des traitements viscoélastiques contraints, les avantages des méthodes développées sont mis avant à travers deux cas d'application. / In the context of acoustic discretion of naval ships, this thesis contributes to the modelling of viscoelastically damped structures by means of thin constrained layers. In order to optimize and design the structure and the damping material, a predictive and efficient numerical tool is desirable. Firstly, a characterization and modelling strategy of the behaviour of viscoelastic materials is proposed. A shifting procedure of DMA measurements based on the fulfillment of the Kramers-Kronig relations is developed in order to build master curves of the material which are consistent with the causality principle. Secondly, a finite element code is developed, and vibration experiments are realized in order to validate the finite element modelling of structures with viscoelastic materials. In the case of thin constrained viscoelastic layers applied to a structure meshed using brick elements, two interface finite elements are developed, which facilitate parametric studies. Finally, two families of reduction methods adapted to the calculation of the frequency response of structures highly damped by viscoelastic materials are studied: modal projection methods and Padé approximants reconstruction method. The advantages of the proposed methods, in the frame of parametric studies for the optimization of the acoustic performances of constrained viscoelastic layers, are highlighted through two applications.

Abnormal electromagnetic wave propagation characterized by negative group velocity and consequently negative group delay (NGD) has been observed in certain materials as well as in artificially built structures. Within finite frequency intervals where an NGD phenomenon is observed, higher frequency components of the applied waveform are propagated with phase advancement, not delay, relative to the lower frequency components. These media have found use in many applications that require positive delay compensation and an engineered phase characteristic, such as eliminating phase variation with frequency in phase shifters, beam-squint minimization in phased array antenna systems, size reduction of feed-forward amplifiers and others. The three principal questions this thesis addresses are: can a generic formulation for artificial NGD structures based on electric circuit resonators be developed; is it possible to derive a quantitative functional relationship (asymptotic limit) between the maximum achievable NGD and the identified trade-off quantity (out-of-band gain); and, can a microwave circuit exhibiting a fully loss-compensated NGD propagation in both directions be designed and implemented? A generic frequency-domain formulation of artificial NGD structures based on electric circuit resonators is developed and characterized by three parameters, namely center frequency, bandwidth and the out-of-band gain. The developed formulation is validated through several topologies reported in the literature. The trade-off relationship between the achievable NGD on one hand, and the out-of-band gain on the other, is identified. The out-of-band gain is shown to be proportional to transient amplitudes when waveforms with defined “turn on/off” times are propagated through an NGD medium. An asymptotic limit for achievable NGD as a function of the out-of-band gain is derived for multi-stage resonator-based NGD circuits as well as for an optimally engineered linear causal NGD medium. Passive NGD media exhibit loss which can be compensated for via active elements. However, active elements are unilateral in nature and therefore do not allow propagation in both directions. A bilateral gain-compensated circuit is designed and implemented, which overcomes this problem by employing a dual-amplifier configuration while preserving the overall circuit stability.

Abnormal electromagnetic wave propagation characterized by negative group velocity and consequently negative group delay (NGD) has been observed in certain materials as well as in artificially built structures. Within finite frequency intervals where an NGD phenomenon is observed, higher frequency components of the applied waveform are propagated with phase advancement, not delay, relative to the lower frequency components. These media have found use in many applications that require positive delay compensation and an engineered phase characteristic, such as eliminating phase variation with frequency in phase shifters, beam-squint minimization in phased array antenna systems, size reduction of feed-forward amplifiers and others. The three principal questions this thesis addresses are: can a generic formulation for artificial NGD structures based on electric circuit resonators be developed; is it possible to derive a quantitative functional relationship (asymptotic limit) between the maximum achievable NGD and the identified trade-off quantity (out-of-band gain); and, can a microwave circuit exhibiting a fully loss-compensated NGD propagation in both directions be designed and implemented? A generic frequency-domain formulation of artificial NGD structures based on electric circuit resonators is developed and characterized by three parameters, namely center frequency, bandwidth and the out-of-band gain. The developed formulation is validated through several topologies reported in the literature. The trade-off relationship between the achievable NGD on one hand, and the out-of-band gain on the other, is identified. The out-of-band gain is shown to be proportional to transient amplitudes when waveforms with defined “turn on/off” times are propagated through an NGD medium. An asymptotic limit for achievable NGD as a function of the out-of-band gain is derived for multi-stage resonator-based NGD circuits as well as for an optimally engineered linear causal NGD medium. Passive NGD media exhibit loss which can be compensated for via active elements. However, active elements are unilateral in nature and therefore do not allow propagation in both directions. A bilateral gain-compensated circuit is designed and implemented, which overcomes this problem by employing a dual-amplifier configuration while preserving the overall circuit stability.