La théorie de couplage de mode (MCT) est l'une des méthodes les plus utilisées pour étudier les transitions vitreuses dans les fluides classiques. Ses prédictions sont en général en accord semi quantitatif avec les simulations. Sa mise en oeuvre nécessite la détermination de la structure statique, généralement par résolution des équations d'Orsntein-Zernike avec une fermeture adéquate. Partant de fermetures utilisant des fonctions « bridges » déduites de la fonctionnelle de référence du mélange de sphères dures, notre travail a consisté d'abord à étudier l'influence de la qualité de cette structure statique sur les prédictions relatives aux états non ergodiques dans des mélanges binaires dissymétriques. Nous avons ensuite considéré les résultats de la théorie du couplage de modes dans sa version naïf (NMCT ) et complète, afin d'analyser les mécanismes d'arrêt, les comparer au fluide effectif et aux approches stochastiques (équations de Langevin généralisées). Enfin, nous proposons une version pragmatique de cette méthode qui fournit des prédictions en meilleur accord quantitatif avec les résultats des simulations pour une variété de potentiels d'interaction / The mode coupling theory (MCT) is one of the most widely used methods for studying the glass transition in classical fluids. Its predictions are usually in semi-quantitative agreement with simulation. Its implementation requires the determination of the static structure usually from the Ornstein-Zernike equations with a suitable closure. Starting from closures that use bridge functions deduced from the hard-sphere reference functional, our work consisted first in studying the influence of the quality of this static structure on the predictions concerning the non-ergodic states in asymmetric binary mixtures. We next considered the results of the mode coupling theory in its naive and full versions, in order to analyze the arrest mechanisms and compare them to the effective fluid and the stochastic approaches (generalized Langevin equations). Finally, we propose a pragmatic version of this method that provides predictions in better quantitative agreement with simulations for a variety of interaction potentials

Gamma-ray burst light curves are notoriously irregular, yet a significant number consists of a single fast-rising, exponentially decaying pulse. These are called single-peaked light curves. The goal of this thesis is to analyse a sample of 2710 GRBs collected by the Fermi space telescope by identifying single-peaked bursts and comparing their properties to those of the multi-peaked bursts. Furthermore, the validity of the relativistic shock breakout theory as an explanation for single-peaked, low-luminosity GRBs is investigated using a closure relation. For this investigation, the Fermi sample wascomplemented by low-luminosity GRBs observed by other instruments. A criterion for selecting single-peaked bursts was successfully developed, yielding 48% long and 79% short, single-peaked GRBs. Significant differences between the populations were found in multiple properties. In general, single-peaked GRBs appear to be weaker and more slowly varying than multi-peaked ones; however, a larger sample of GRBs with redshift measurements is needed to draw conclusions about possible intrinsic differences in energy connected to the progenitor systems. The investigation of low-luminosity GRBs’ compliance with the shock breakout closure relation showed that 64% of the low-luminosity GRBs were within a factor 5 of fulfilling the relation as opposed to only 24% of high-luminosity GRBs. It was further shown that only a small number (< 5%) of Fermi GRBs without redshift measurements could be low-luminosity shock breakout GRBs according to this theory. In conclusion, while the shock breakout closure relation does hold for a greater proportion of low-luminosity GRBs than high-luminosity GRBs, there is still a large number of low-luminosity GRBs left unexplained by this theory. / Gammablixtljuskurvor är ökänt oregelbundna men en betydande andel består av en enda snabbt stigande och exponentiellt avtagande puls. Dessa kallas singelpeakade ljuskurvor. Målet med detta examensarbete är att analysera de 2710 gammablixtar som Fermirymdteleskopet har observerat genom att identifiera singelpeakade blixtar och jämföra deras egenskaper med multipeakade blixtars. Dessutom undersöks den relativistiska shockbreakoutteorin som förklaringsmodell för singelpeakade lågluminositetsgammablixtar. I denna undersökning kompletterades fermiblixtarna med lågluminositetsblixtar från andra instrument. Ett kriterium för identifikation av singelpeakade gammablixtar utvecklades och detta resulterade i 48% långa och 70% korta, singelpeakade gammablixtar. Flertalet egenskaper uppvisade signifikanta skillnader mellan populationerna. I allmänhet verkar singelpeakade gammablixtar vara svagare och variera långsammare än multipeakade. Dock behövs en större population av gammablixtar med uppmätta rödskift för att med säkerhet kunna avgöra om singelpeakade blixtar verkligen släpper ut mindre energi. Undersökningen av huruvida lågluminositetsgammablixtar kan förklaras med shockbreakoutteorin visade att 64% av lågluminositetsblixtarna uppfyllde kravet upp till en faktor fem medan bara 24% av högluminositetsblixtarna gjorde det. Vidare visades att endast ett litet antal (<5%) av fermiblixtarna utan uppmätta rödskift skulle kunna vara lågluminositetsshockbreakoutblixtar enligt denna teori. Även om shockbreakoutteorin kan förklara en större andel av lågluminositetsblixtarna än högluminositetsblixtarna återstår ett stort antal oförklarade lågluminositetsblixtar.