Avalanches in the Random Organization Model with long-range interactions

Abstract

Oscillatory sheared suspensions, when observed stroboscopically, exhibit a reversible-irreversible transition as a function of the strain amplitude, which is a kind of absorbing phase transition. So far studies of this transition focused on global quantities, e.g. quantifying the irreversibility on one side of the transition or the time to reach a reversible state on the other side. Here, motivated by the kin depinning transition, we focus on the intermittent dynamics near the transition. We perform simulations of a modified Random Organization Model (ROM), a minimal particle model which we recently adapted to take into account the generic presence of long-range interactions mediated by the fluid, taking the power-law-decay exponent $\alpha$ as an additional control parameter of the model. We show that at the absorbing phase transition, this model displays power-law-distributed avalanches. We characterize the avalanche statistics in terms of avalanche size, duration and number of particles involved, and we determine the associated exponents. By varying the exponent $\alpha$, the fractal dimension of avalanches crosses space dimension $d$, inducing a qualitative change of the spatial structure of avalanches, from compact avalanches when interactions have a short range, to sparse avalanches when interactions are long-ranged. Finally, we characterize the clusters within the avalanches, which we also find power-law distributed.