Les processus de réaction-diffusion constituent des modèles simples pour décrire l’évolution de systèmes dynamiques hors équilibre, comme des réactions chimiques, ou l’évolution de populations en compétition. Ces modèles présentent en général un comportement critique caractéristique dúne classe dúniversalité, la plus répandue étant celle de la Percolation Dirigée. Les méthodes du Groupe de Renormalisation Non Perturbatif (GRNP) offrent un outil dánalyse efficace pour explorer ces problèmes. Après une petite revue du GRNP, nous revisitons la Percolation Dirigée, puis discutons en détail les processus dits de “Branching and Annihilating Random Walks”, pour lesquels lápproche non perturbative permet de déterminer le diagramme de phase, inaccessible par les méthodes perturbatives usuelles. Nous apportons en particulier une réponse au problème controversé de léxistence ou non dúne transition de phase en dimension supérieure à trois. Non-thermal yet disordered, strongly dissipative yet rigid, the mechanics of packings of grains has fascinated physicists and engineers at least since the time of Coulomb. This talk will focus on one of the classical problems in this field, the behavior of dense granular flows driven by gravity. I will give examples of such flows drawn from geophysics, and then introduce some of the ideas of Ralph Bagnold, who developed the concepts on which the modern study of granular flows are based. A systematic phenomenology of dense granular flows down inclines has recently been developed, based both on numerical work and on experiments. This phenomenology emphasizes the role of inelastic collapse in controlling the rheology of these flows, and hints at the structure of an ultimate theory of dense flows. Different aspects of protein folding are illustrated by simplified polymer models. Stressing the diversity of side chains (residues) leads one to view folding as the freezing transition of an heteropolymer. Technically, the most common approach to diversity is randomness, which is usually implemented in two body interactions (charges, polar character,..). On the other hand, the (almost) universal character of the protein backbone suggests that folding may also be viewed as the crystallization transition of an homopolymeric chain, the main ingredients of which are the peptide bond and chirality (proline and glycine notwithstanding). The model of a chiral dipolar chain leads to a unified picture of secondary structures, and to a possible connection of protein structures with ferroelectric domain theory.

LPTHE, Jussieu