Critical Scaling of Avalanches with Strain Rate in Athermal, Disordered Solids*

Molecular dynamics simulations are used to study critical behavior in slowly sheared disordered solids that are modeled as a bidisperse Lennard-Jones glass. The mean flow stress rises as strain rate to the power 1/β. Finite-size scaling is used to determine β and the exponent ν describing the divergence of the correlation length. The system length L varies from 55 to 1753 particle diameters in d=2 and 20 to 163 in d=3. Fluctuations in the stress and kinetic energy per particle scale as L^-d/2, implying that the largest avalanche scales as L^α with α < d/2. Temporal correlations are used to measure the dynamical exponent z relating the duration of an avalanche to its linear dimension. In contrast to lattice models, we find z>1, as required by causality. New scaling laws are derived for exponents describing the power law decay of the noise power spectrum with frequency and tested using finite-size scaling.