Higher order spectra and universal shape functions in avalanche models

We study non-equilibrium critical phenomena in disordered systems that crackle. Crackling refers to jumps or "avalanches" over many orders of magnitude that are induced by a slow external driving force or field. We study two kinds of crackling noise produced by disordered systems: Barkhausen noise, that is produced by magnetic material magnetized by a changing external field, and earthquakes, that are produced by the contact of two shifting tectonic plates. Both systems exhibit critical behavior; critical exponents and universal scaling functions associated with the crackling noise are studies in both systems. Theoretical results are obtained from simulation and compared with experiment and observation. Universal scaling functions allow a sharper test of theoretical models against experiment. While agreement in critical exponents is observed between theory and experiment, differences are found between universal scaling functions. Also, a simple mean field earthquake model that produces aftershocks is proposed. We also introduce a second approach to test theoretical models against experiment. In this approach, Barkhausen noise is analyzed with higher order spectral transformations, in both mean field theory, simulation, and experiment. Novel exponents are found through our analysis and key differences are found between simulation and experiment.