Diffusion in mesoscopic lattice models of amorphous plasticity

TL;DR

This study investigates particle diffusion in a meso-scale lattice model of amorphous materials under shear, revealing size-dependent diffusion regimes and resolving discrepancies with particle-based models.

Contribution

It demonstrates the size scaling of diffusion coefficients at different times and shows the impact of interaction kernel details on long-term behavior, addressing a longstanding puzzle.

Findings

Short-time diffusion coefficient scales as D ~ L^{1.05}.

Long-time diffusion coefficient scales as D ~ L^{1.6}.

Near-field interaction details significantly affect long-term diffusion behavior.

Abstract

We present results on tagged particle diffusion in a meso-scale lattice model for sheared amorphous material in athermal quasi-static conditions. We find a short time diffusive regime and a long time diffusive regime whose diffusion coefficients depend on system size in dramatically different ways. At short time, we find that the diffusion coefficient, $D$, scales roughly linearly with system length, $D\sim L^{1.05}$. This short time behavior is consistent with particle-based simulations. The long-time diffusion coefficient scales like $D\sim L^{1.6}$, close to previous studies which found $D\sim L^{1.5}$. Furthermore, we show that the near-field details of the interaction kernel do not affect the short time behavior, but qualitatively and dramatically affect the long time behavior, potentially causing a saturation of the mean-squared displacement at long times. Our finding of a $D\sim L^{1.05}$ short time scaling resolves a long standing puzzle about the disagreement between the diffusion coefficient measured in particle-based models and meso-scale lattice models of amorphous plasticity.