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Driving rate dependence of avalanche statistics and shapes at the yielding transition

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In the past decades, a widespread consensus has emerged about the heterogeneous response of yield stress material subjected to shear. However, the characterization of the transition towards the plastic flow regime remains an open issue. Especially the correct mean-field description of the transition shows to be controversial.

In sheared yield stress materials, the common picture is that local plastic rearrangements, the so-called shear transformations, lead to an elastic response of the surrounding medium. Due to the long range nature of the elastic kernel it is tempting to believe that mean-field considerations are meaningful to describe the resulting dynamics in the slow driving limit, close to the yielding transition. Nevertheless, the specific form of the elastic kernel prevents usual analytical assumptions to be applied, and the question about a mean-field or non mean-field criticality is still open.

The combined study of avalanche size and duration distributions together with the particular shape of avalanches has played an essential role in our understanding of the universal aspects of crackling noise and depinning dynamics. In this work we provide numerical predictions for similar quantities in the case of the yielding transition, with a clear indication of a complex non mean field behavior. Interestingly, mean field predictions are recovered only in the stronger driving limit, where the dynamics are effectively randomized. This work has been published in Physical Review Letters.