Avalanches in plastic deformation: maximum velocity statistics, finite temperature effects, and analysis of low time resolution data

In both crystalline and amorphous solids, plastic deformation consists of intermittent jumps called avalanches, whose sizes are power-law-distributed over a scaling regime. In this thesis, we study the statistics of a simple mean-field avalanche model, with emphasis on both theoretical calculations and application to the analysis of experimental data on material deformation. We establish a relationship between the simple mean-field model and a continuous time model called the ABBM model, originally proposed as a phenomenological model of Barkhausen noise in magnets. The relationship is formally valid for ductile materials without significant weakening, but the results of our calculations are expected to apply to the small avalanches even in materials with high weakening. We then use the ABBM model to calculate several exact results concerning a system's maximum velocity during an avalanche. We find that the scaling of the maximum velocity distribution agrees with experiments on crystal plasticity. Left over from our calculations are several experimental predictions ready to be tested. The maximum velocity is a robust experimental observable and it has several distinct advantages over the more commonly-considered avalanche durations, so we expect our predictions to be useful in future tests of avalanche statistics in experimental systems. Then, motivated by recent creep deformation experiments that find scale-invariant avalanches, we develop a scaling theory for thermally-activated avalanches in the simple avalanche model near the critical point and at low temperature. We highlight several generic predictions for how statistical observables scale with temperature. Finally, we use the simple avalanche model to study how experimental avalanche measurements are influenced by the time resolution of the data. Using both experimental data and simulation data from the model, we determine how measured quantities change with resolution. From these relationships, we develop methods to diagnose when the time resolution low enough that it changes the measured avalanche statistics. We also propose a new analysis method that allows us to extract accurate size statistics from low-resolution data, and show that it is successful both on simulation data and downsampled high-resolution experimental data