Spatiotemporal Organization of Correlated Local Activity within Global Avalanches in Slowly Driven Interfaces

Abstract

We study the jerky response of slowly driven fronts in disordered media, just above the depinning transition. We focus on how spatially disconnected clusters of internally correlated activity lead to large-scale velocity fluctuations in the form of global avalanches and identify three different ways in which local activity clusters may organize within a global avalanche, depending on the distance to criticality. Our analysis provides new scaling relations between the power-law exponents of the statistical distributions of sizes and durations of local bursts and global avalanches. Fluid fronts of imbibition in heterogeneous media are taken as a case study to validate these scaling relations.

Avalanches and extreme value statistics in interfacial crackling dynamics

“…Moreover, it is important to note that the values of those exponents characterizing the scaling behaviour of the global avalanches are different when considering local crack front bursts [12,48]. Our new experimental results clearly confirm that high local velocity clusters and global avalanches measured on crackling time series are different observables with different statistical properties, as already reported in numerical simulations [46,48], and in imbibition experiments [23,55,56]. Finally, we can also remark that those scaling exponents are also different from those reported for a three-dimensional crack front propagating in a bulk artificial rock [59].…”

“…Nevertheless, this phenomenology is not limited to the physical processes of deformation and rupture of disordered materials. Indeed, such intermittent avalanche dynamics can be observed for very different heterogeneous systems, slowly driven in out-of-equilibrium conditions, with, for instance, the magnetic response of a disordered ferromagnet, also known as 'Barkhausen noise' [17,18], the motion of vortex lines in superconductors [19], the fluid imbibition in porous and fractured media [20][21][22][23], the motion of contact lines over substrates with wetting heterogeneities [24], but also the yielding of amorphous materials [25][26][27] and single crystals [28][29][30] or even in the biological activity of neuronal networks [31,32] and cell migration [33].…”

Spin activity correlations in driven disordered systems

“…Thus, studies [24,25] include newly introduced concept of an instantaneous correlation length followed by some novel scaling forms that have been proposed for spatial and temporal correlation functions of the velocity field estimated from the results obtained in crack propagation experiments and numerical simulations [26]. Also, there was a study of dynamical correlations near dislocation jamming (yielding transition) [27] enhanced with the further analyses of the spatio-temporal organization of correlated local activity within global avalanches in slowly driven interfaces [28].…”

Surface super-roughening driven by spatiotemporally correlated noise

“…This leads to the existence of an independent local roughness exponent α loc that characterizes the local interface fluctuations and differs from the global roughness exponent α obtained by, for instance, the global width. This phenomenon is referred to as anomalous roughening and has received much attention in the last few years because its commonness in experiments [9][10][11][12][13][14][15][16][17][18][19][20][21]. Current theoretical knowledge has firmly established [22] that, indeed, the existence of power-law scaling of the correlation functions (i.e., scale invariance) does not determine a unique dynamic scaling form of the correlation functions.…”

“…This leads to the existence of an independent local roughness exponent α loc that characterizes the local interface fluctuations and diers from the global roughness exponent α obtained by, for instance, the global width. This phenomenon is referred to as anomalous roughening and has received much attention in the last few years because its commonness in experiments [10][11][12][13][14][15][16][17][18][19][20][21][22].…”