Spatial Clustering of Depinning Avalanches in Presence of Long-Range Interactions

Yielding transition of a two dimensional glass former under athermal cyclic shear deformation

“…Further, we perform a careful investigation of avalanches above yielding, by distinguishing the number of all particles participating in a plastic rearrangement, for which we use the term avalanche, vs. spatially connected clusters of rearranging particles. We further investigate the distribution of the number of clusters that participate in an avalanche, to understand the clustering properties of avalanches recently discussed in [54]. These analyses confirm earlier conclusions for three dimensional glasses [23], and provide additional insights into the nature of avalanches in the two dimensional model we investigate.…”

“…The scaling function g, shown in Fig. 9, is peaked around the mean value n cl S , as also seen in [54]. The full distribution of n cl can be obtained as…”

“…The distribution of cluster sizes for a given S exhibits a power law form up to the maximum size of S, as also noted in [54] (The distributions, however, are noisy within the statistics we have and thus we do not rely on them directly in the discussion below, but instead on average quantities as described later.) We thus assume n(s|S) = As τ , and the condition Eq.…”

“…We compute the cluster statistics of the active particles, considering two active particles (or type A, B) to be in the same cluster if they are separated by less than a distance r min AB , the first minimum of the relevant partial pair correlation function (r min AB = 1.03, 1.40, 1.70 for SS,LL, and SL pairs respectively). The distribution of the investigated quantities, namely the avalanche size (S), cluster size (s), and the number of clusters in an avalanche, n cl , are expected to exhibit power law regimes [54], characterised by exponents identified below:…”

“…We discuss the relationship between τ a , τ c and κ, following the arguments in Ref. [54] for models of crack propagation, in the presence of long range interactions [74], and as discussed for three dimensional glasses in Ref. [55].…”