Global Oscillations in Depinning Models with Aging

TL;DR

This paper introduces an aging mechanism into depinning models, leading to global oscillations and avalanches, with distinct behaviors in mean field and two-dimensional systems.

Contribution

It extends the depinning paradigm by incorporating aging, revealing new oscillatory regimes and phase diagrams in both mean field and 2D systems.

Findings

Mean field models exhibit king avalanches and global instabilities.

Two-dimensional systems show persistent stress oscillations without system-size avalanches.

Avalanche activity alternates with stress oscillations in 2D systems.

Abstract

We propose a model that extends the standard depinning paradigm by incorporating an aging mechanism into the local pinning force. This favors oscillations between a stuck state of large pinning, and a slipping state of smaller pinning. We show that for mean field interactions between sites this mechanism can lead to the appearance of ``king avalanches" and global instabilities, producing a global oscillatory stick-slip stress regime. We construct the phase diagram for this mean field case and identify regions of smooth dynamics, pure stick-slip, and bistability. Crucially, when considering two-dimensional systems with short-range interactions we find that states of global stress oscillation persist, but in contrast to the mean field case, no system-size avalanches appear. Instead, we observe alternating temporal intervals of larger and lower avalanche activity that correlate with the stress oscillations.