| In this dissertation, I study avalanche phenomena in the framework of self-organized criticality (SOC) and non-equilibrium phase transitions. In particular, I analyze the physical mechanism responsible for avalanches in different experimental systems: the fracturing of disordered materials and the Barkhausen effect in ferromagnets. The methods used range from computer simulations to analytical tools such as mean-field theory, scaling arguments and the renormalization group.;First, to understand the general conditions for avalanche propagation, I discuss several SOC models and compare them with other non-equilibrium models with steady states. A unifying theoretical framework for all these models is presented using dynamic mean-field theory, the theory of branching processes and the renormalization group. I introduce a novel renormalization group method especially suited to the study of critical properties of non-equilibrium systems. The method acts directly on the master equation and overcomes the difficulties present when applying the usual renormalization group to non-equilibrium systems. Applications to specific models are then presented.;Next, I study the avalanche response in network models of fracture. I present a mean-field theory that combines effective medium theory and scaling arguments. The exponents predicted by the theory agree with computer simulations of the two dimensional random fuse model. I discuss the relations between fracture and first-order transitions as well as spinodal points. I also introduce a new scalar model for microfractures, similar to the fuse model, that displays a plastic steady-state.;Finally, I construct an equation of motion for the dynamics of a ferromagnetic domain wall, including the effect of magnetostatic, dipolar and exchange interactions, and quenched disorder. I study the depinning transition of the domain wall using a functional renormalization group and show that mean-field theory holds above three dimensions. Using scaling relations, I obtain the critical exponents which describe Barkhausen jump distributions. These results are confirmed by computer simulations and are in excellent agreement with experiments in soft ferromagnetic materials. I show that the model provides a microscopic justification for previously introduced phenomenological models of domain wall motion. |
