Structural evolution of amorphous systems during avalanches*

Under applied shear strain, granular and amorphous materials deform. At zero temperature, the deformation can be separated into elastic branches where the particles do not change neighbors and rearrangements where they do. Some rearrangement events are small and localized, while others involve large or system-spanning avalanches. Using numerical simulations of soft spheres, we find that avalanches can be decomposed into a series of localized excitations, and we develop an extension of persistent homology to isolate these excitations. Next, we develop a method to study the linear response of unstable systems during an avalanche, by extending existing tools for identifying structural defects using the Hessian and study how the population of structural defects evolves during an avalanche. We find that localized excitations in the avalanche correlate strongly with localized excitations in the linear spectrum, and investigate how these excitations are created and coupled during the avalanche. These data should help to constrain elastoplastic models for glasses and granular matter.