Evolution of the average avalanche shape with the universality class

Abstract

A multitude of systems ranging from the Barkhausen effect in ferromagnetic materials to plastic deformation and earthquakes respond to slow external driving by exhibiting intermittent, scale-free avalanche dynamics or crackling noise. The avalanches are power-law distributed in size, and have a typical average shape: these are the two most important signatures of avalanching systems. Here we show how the average avalanche shape evolves with the universality class of the avalanche dynamics by employing a combination of scaling theory, extensive numerical simulations and data from crack propagation experiments. It follows a simple scaling form parameterized by two numbers, the scaling exponent relating the average avalanche size to its duration and a parameter characterizing the temporal asymmetry of the avalanches. The latter reflects a broken time-reversal symmetry in the avalanche dynamics, emerging from the local nature of the interaction kernel mediating the avalanche dynamics.

Microscopic aspects of magnetic lattice demagnetizing factors

“…The demagnetizing problem in magnetic systems is a natural setting for exploring this question since it is accessible and of intrinsic importance in experiments, and constitutes a paragon for exploring the thermodynamics of long-range interacting systems [1]. Demagnetizing effects are also important in superconductors, while analogs occur, for example, in electric systems [8] (depolarizing factor), in the problem of strain fields around inclusions [9], and in the treatment of avalanching systems in confined geometries [10][11][12].…”

Statistical features of magnetic noise in mixed-type impact fracture

“…The same temporal profile has been found very recently for crackling bursts generated at a slowly propagating crack front in heterogeneous materials. 14,15 It has been shown that the symmetry of the pulse shape carries information about the range of stress redistribution following local breaking events: long range interaction (mean field) results in symmetric profiles, while short range load sharing gives rise to a right handed asymmetry. 14,15 It follows that the right handed asymmetry of the pulse shapes in Fig.…”

Repulsion and Attraction between a Pair of Cracks in a Plastic Sheet

“…A large number of studies-both experimental and theoretical-have been devoted to the simplest model case of a single crack, growing in either brittle or viscoplastic materials [1][2][3][4][5][6][7][8]. Those works have shown that dynamical instabilities and/or heterogeneities may destabilize the crack dynamics, leading to strong deviations and roughness in the crack paths [6][7][8][9][10][11][12].…”