Self-organization and complexity: a new age for theory, computation and experiment.

I first describe the notion of self-organization as a property of far-from-equilibrium nonlinear dissipative dynamical systems. Rather than describing such complex systems at a purely phenomenological level, however, I focus attention on the emergent nature of this complexity, by analysing a few examples of physical and physicochemical systems with simple underlying microscopic dynamics yet complex, self-organizing macroscopic properties. These include several mesoscopic models of fluid dynamics as well as a modern approach to nucleation and growth phenomena. Finally, I discuss how the advent of computational grids is set to provide a major boost to the study of such complex, self-organizing systems.