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 an absorbing phase transition, separating diffusive states on the irreversible side from absorbing states on the reversible side. So far studies of this transition focused on global quantities, e.g., quantifying the irreversibility on the one side of the transition or the time to reach a reversible state on the other side. Here, inspired by depinning-type transitions, we focus on intermittent dynamics close to 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 to be power-law distributed.

Spacetime plots of avalanches of irreversible events (in red) in presence of mediated mechanical noise. Left: long-ranged mechanical noise leads to sparse avalanches. Right: short-ranged mechanical noise leads to compact avalanches.