Criticality in sheared, disordered solids. II. Correlations in avalanche dynamics

TL;DR

This paper investigates the avalanche dynamics in sheared disordered solids, revealing a complex power spectrum with distinct regimes and developing a scaling theory validated by simulations, advancing understanding of critical behavior under shear.

Contribution

It introduces a new scaling theory for power spectra of avalanche activity in sheared disordered solids, validated by simulations, and identifies key exponents related to the yielding transition.

Findings

Power spectrum exhibits three regimes: power-law rise, white noise, power-law decay.

White-noise regime diminishes with increasing strain rate.

Derived scaling theory matches simulation data across regimes.

Abstract

Disordered solids respond to quasistatic shear with intermittent avalanches of plastic activity, an example of the crackling noise observed in many nonequilibrium critical systems. The temporal power spectrum of activity within disordered solids consists of three distinct domains: a novel power-law rise with frequency at low frequencies indicating anticorrelation, white-noise at intermediate frequencies, and a power-law decay at high frequencies. As the strain rate increases, the white-noise regime shrinks and ultimately disappears as the finite strain rate restricts the maximum size of an avalanche. A new strain-rate- and system-size-dependent scaling theory is derived for power spectra in both the quasistatic and finite-strain-rate regimes. This theory is validated using data from overdamped two- and three-dimensional molecular dynamics simulations. We identify important exponents in the yielding transition including the dynamic exponent $z$ which relates the size of an avalanche to its duration, the fractal dimension of avalanches, and the exponent characterizing the divergence in correlations with strain rate. Results are related to temporal correlations within a single avalanche and between multiple avalanches.