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.
Highlights
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 average shape is to a high precision given by a function parameterized by the scaling exponent g characterizing the scaling of the average avalanche size as a function of the avalanche duration, and a parameter a describing the temporal asymmetry of the average avalanche shapes
We find that an inherent asymmetry in the average avalanche shapes is present in systems where the interaction kernel is not fully non-local, reflecting the underlying broken time-reversal symmetry of the avalanche dynamics
Summary
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. 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. We find that an inherent asymmetry in the average avalanche shapes is present in systems where the interaction kernel is not fully non-local, reflecting the underlying broken time-reversal symmetry of the avalanche dynamics We compare these results with experiments of planar crack front propagation, finding good agreement with the predictions of the scaling theory and the relevant depinning model
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