Consequences of Anomalous Diffusion in Disordered Systems Under Cyclic Forcing

TL;DR

This study uses numerical simulations to analyze how 2D disordered granular systems transition from subdiffusive to diffusive behavior under cyclic shear, revealing scale-invariant cage dynamics and introducing a modified MSD for local displacement analysis.

Contribution

It introduces a modified mean-squared displacement that accounts for local neighborhood motion and connects observed behaviors to stochastic models of anomalous diffusion.

Findings

Crossover from subdiffusive to diffusive regimes depending on shear amplitude

Displacement distributions align with models of anomalous diffusion

Evidence of scale-invariant cage dynamics in granular systems

Abstract

We use numerical simulations to study the behavior of 2D frictionless disk systems under cyclic shear as a function of reversal amplitude \gamma_r. Our studies focus on mean bulk and disk dynamics. These measurements suggest a crossover from a subdiffusive, \gamma_r dependent regime to a regime where the grain motions are diffusive, with properties dependent only on total shear strain. We discuss model stochastic processes that are consistent with these observations. Finally, we introduce a modified Mean-Squared Displacement (mMSD) which takes into account the motion of the neighborhood of nearby grains and yields new insights into local displacement fluctuations. We find that scaling properties of the displacement distributions are consistent with well studied stochastic models of anomalous diffusion and suggest scale-invariant cage dynamics.