Shocks and avalanches: From glasses to turbulence – SAGT

The aim of the project is to develop promising emerging connections between disordered systems, non-equilibrium phase transitions and statistical turbulence. A common denominator in these traditionally separated domains is the crucial role played by singularities, such as shocks and avalanches, in their statics and dynamics. In some cases mathematical mappings exist, in other cases relations are conjectured. In all cases the relations have not been fully exploited. In the context of elastic disordered systems we have developed powerful field-theoretical methods, such as the functional renormalization group (FRG), and innovative numerical algorithms. These have recently proven essential in characterizing shocks and the statistics of avalanches. Our plan is to carry such approaches to the other fields mentioned above, to bring together the different communities, and generate a considerable cross-fertilization. In parallel, our goal is to strengthen the conceptual understanding of disordered systems using field theory and numerics in a complementary way. We plan to explore the consequences of conformal invariance for two-dimensional critical interfaces and fermion models in quenched disorder, with applications to graphene. We aim at finding a coherent picture between the present approaches to glassy systems, using concepts and tools of extremal value statistics. This will allow to study freezing phenomena which are at the boundary between these methods, and currently of interest beyond physics in mathematics and finance. We plan to develop the FRG approach in areas where it is not yet understood, to study plasticity and chaos, systems of lines where ergodicity is not guaranteed, hysteresis and broadly distributed disorder. An important part of our project is a direct collaboration with three experimental groups to test the theory in experiments on wetting, magnetic domains and crack propagation. One aim is to directly measure the renormalized disorder correlator, i.e. the central object of the field theory. Another is to develop the theory around outstanding questions raised by experiments, such as activated dynamics. This ambitious and coherent project is proposed by a small team of researchers with complementary expertise in field theory and numerics: Alberto Rosso (``mention SFP jeune chercheur 2002'', CNRS, recently promoted CR1), Kay Wiese (hired by CNRS as CR1 in 2004, physics prize of the Academy of Sciences in Goettingen), and Pierre Le Doussal (DR1 and Silver Medal of CNRS 2003). They do not presently have the means to develop their research and sustain their worldwide collaborations, despite the novelty of their approach and its numerous applications.