Estudamos duas classes de teorias de campos com métrica indefinida: os modelos sigma não linear não-compactos e as teorias quárticas da gravitação. Mostramos que a prova da unitariedade para os modelos sigma de simetria não compacta é a mesma que para os modelos compactos nas regiões fisicamente relevantes. Além disso, analisamos a possibilidade de ocorrer geração dinâmica de massa nos modelos sigma sob influência de temperatura finita, em várias dimensões. No que se refere às teorias quárticas da gravitação, calculamos o valor esperado no vácuo da função de dois pontos com inserção da relação de Gauss-Bonnet. Encontramos que a identidade clássica não é preservada quando empregamos a regularização dimensional, mesmo num espaço sem singularidades. Isto revela o surgimento de anomalias gravitacionais / Two classes of field theories with indefinite metric are studied: noncompact nonlinear sigma models and higher-derivative quantum gravity. We show that the proof of unitarity for noncompact sigma models is the same as the one for compact models in the physically relevant regions. Moreover, we analyze the possibility of dynamical mass generation at finite temperature in various space-time dimensions. Concerning to the higher-derivative quantum gravity, we calculate the vacuum expectation value of the two-point function with the insertion of Gauss-Bonnet Relation. In the quantum context, we also show, using dimensional regularization, that the Gauss-Bonnet relation is not satisfied due to gravitational anomalies.

Estudamos duas classes de teorias de campos com métrica indefinida: os modelos sigma não linear não-compactos e as teorias quárticas da gravitação. Mostramos que a prova da unitariedade para os modelos sigma de simetria não compacta é a mesma que para os modelos compactos nas regiões fisicamente relevantes. Além disso, analisamos a possibilidade de ocorrer geração dinâmica de massa nos modelos sigma sob influência de temperatura finita, em várias dimensões. No que se refere às teorias quárticas da gravitação, calculamos o valor esperado no vácuo da função de dois pontos com inserção da relação de Gauss-Bonnet. Encontramos que a identidade clássica não é preservada quando empregamos a regularização dimensional, mesmo num espaço sem singularidades. Isto revela o surgimento de anomalias gravitacionais / Two classes of field theories with indefinite metric are studied: noncompact nonlinear sigma models and higher-derivative quantum gravity. We show that the proof of unitarity for noncompact sigma models is the same as the one for compact models in the physically relevant regions. Moreover, we analyze the possibility of dynamical mass generation at finite temperature in various space-time dimensions. Concerning to the higher-derivative quantum gravity, we calculate the vacuum expectation value of the two-point function with the insertion of Gauss-Bonnet Relation. In the quantum context, we also show, using dimensional regularization, that the Gauss-Bonnet relation is not satisfied due to gravitational anomalies.

La densification extrême des cartes électroniques, couplée à une compacité toujours plus accrue entraîne des contraintes thermiques exacerbées, ceci constitue un verrou technologique à l’évolution des systèmes électroniques.Ce document traite de la modélisation thermique des composants électroniques, et de leur interaction avec des systèmes électroniques en général.Dans une première partie, le concept de modèles compacts, qui est une représentation partielle d’un composant électronique qui s’affranchit de sa géométrie, est abordé. Les différents concepts de modèles numériques sont expliqués et comparés en fonction de leur niveau de précision par rapport à une représentation détaillée d’un composant électronique.Dans une deuxième partie, la modélisation analytique des composants électroniques est développée, pour les composants mono-puces puis multi-puces. Le modèle analytique établi est basé sur la résolution 3-D de l’équation de la chaleur par les séries de Fourier dans un domaine multi-couche et avec des sources de chaleur volumique. Le modèle analytique est également comparé à une modélisation numérique dans le but de quantifier l’avantage de ce type de modélisation.Le concept de modèles compacts temporels est validé expérimentalement dans la troisième partie de ce document. Les modèles compacts explicités dans la première partie sont confrontés à des essais expérimentaux en régime transitoire. Ces essais démontrent que les modèles compacts temporels permettent d’obtenir un écart de température inférieur à 10%, ceci quelle que soit la configuration des véhicules de test thermique.Une quatrième partie s’attache sur un nouveau concept de modèles simplifiés dans le cas où la géométrie des composants électroniques n’est pas connue. Ce type de modélisation se base sur le modèle analytique de la seconde partie. Il est démontré que celui permet d’obtenir un écart inférieur à 10% avec le modèle numérique détaillé, quel que soit le niveau de complexité du composant.Enfin, la dernière partie aborde la potentielle utilisation des modèles compacts développés pour améliorer la conception d’une carte électronique industrielle. Pour cela, la modélisation compacte de cartes électroniques avec composants enterrés a été explorée. Cette approche s’appuie sur le développement analytique effectuée dans la seconde partie des travaux exposés avec pour objectif d’accentuer la capacité à modéliser les cartes possédant de multiples couches. Une méthode intelligente de calcul des diverses couches d’une la carte électronique a été établie. Celle-ci offre la possibilité d’explorer rapidement diverses options d’une conception tout en préservant un niveau de précision important. / The extreme densification of electronic boards, coupled with their size reduction leads to critical thermal stress, resulting in technology barriers to the evolution of electronic systems.This document is about the thermal modelling of electronic components, and their interaction with electronic systems in general.In the first chapter, the concept of compact models, which is a partial representation of an electronic component without its geometry complexity, is addressed. The different types of compact models are explained and discussed in function of their accuracy towards detailed models of electronic components.In a second chapter, the analytical modelling of electronic components is developed, for mono and multi chips packages. The analytical model is based on the resolution of 3-D heat equation by the use of Fourier series for multi-layer domain and volumetric heat sources. The analytical model is therefore compared to numerical models with the goal to quantify the cons and pros of this representation.The concept of dynamical compact models is validated experimentally in a third chapter. The compact models of first chapter are confronted to experimental data in dynamic state. This comparison shows that the developed dynamical compact models have a deviation lower than 10% with experimental results, whatever the configuration of the thermal test vehicles.A fourth chapter introduces a new concept of simplified models, in the case of a lack of information about the geometry of electronic components. This new modelling concept is based on the analytical development of second chapter. It is shown that a discrepancy of less than 10% with detailed numerical models can be achieved, whatever the complexity level of electronic components.Finally, the last chapter deals with a potential way to exploit the developed thermal models for performing industrial board design. Thus, the compact modelling of electronic multilayer boards with buried components in its core layers is investigated.This approach is based on the analytical model of second chapter in order to deal with thin multi-layer electronic boards. A concept of a smart decomposition of the board layers is introduced, which allows a fast design exploration while preserving a high accuracy level.