The main topics to be studied under this research project are non equilibrium phase transitions, self organized criticality and fractal systems, which represent one of the most challenging fields of modern's statistical physics and require the formu- lation of new theoretical concepts.
Certain non equilibrium systems experience, for critical parameter values, tran- sitions from disordered states to others with low entropy, i.e. a high degree of or- ganization (dissipative structures, spatio-temporal patterns, etc.). At the critical points, these systems are scale invariant, and can be classified in universality classes according to the symmetry and the nature of their singularities. We propose the analysis of some particular non equilibrium critical phenomena, in particular, the 'depinning' transition undergone by fluids invading random porous media. We will use standard renormalisation group techniques as well as the recently introduced fixed scale transformation method.
We will also study a second class of systems which exhibit self organis criti- cality, i.e. that are scale invariant for generic parameters values and without extra symmetries. Such systems have been conjectured to constitute the origin of the ubiquitous scale invariance observed in nature, but the necessary and sufficient con- ditions under which SOC appears are not yet well understood. In our project we intend to clarify the phenomenon of self-organization from a physical and mathe- matical point of view. The final task is the formulation of a general theory with predictive power for the understanding of the spontaneous generation of complex and fractal structures in nature.