Avalanche dynamics and related power law statistics are ubiquitous in nature, arising in phenomena like earthquakes, forest fires and solar flares. Very interestingly, an analogous behavior is associated with many condensed matter systems, like ferromagnets and martensites. Bearing it in mind, we study the prototypical 3D RFIM at T=0. We find a finite correlation between waiting intervals between avalanches and the previous avalanche size. This correlation is not found in other models for avalanches, such as the standard BTW model, but it is experimentally found in earthquakes and in forest fires. Our study suggests that this effect occurs in critical points which are at the end of an athermal first-order transition line separating two behaviors: one with high activity from another with low activity.
The sequence of deformation bursts during plastic deformation exhibits scale-free features. In addition to the burst or avalanche sizes and the rate of avalanches the process is characterized by correlations in the series which become manifest in the resulting shape of the stress-strain curve. We analyze such features of plastic deformation with 2D and 3D simulations of discrete dislocation dynamics models and we show, that only with severe plastic deformation the ensuing memory effects become negligible. The role of past deformation history and dislocation pinning by disorder are studied. In …
We study the correlations between avalanches in the depinning dynamics of elastic interfaces driven on a random substrate. In the mean field theory (the Brownian force model), it is known that the avalanches are uncorrelated. Here we obtain a simple field theory which describes the first deviations from this uncorrelated behavior in a $ε=d_c-d$ expansion below the upper critical dimension $d_c$ of the model. We apply it to calculate the correlations between (i) avalanche sizes (ii) avalanche dynamics in two successive avalanches, or more generally, in two avalanches separated by a uniform disp…
Power-law-shaped avalanche-size distributions are widely used to probe for critical behavior in many different systems, particularly in neural networks. The definition of avalanche is ambiguous. Usually, theoretical avalanches are defined as the activity between a stimulus and the relaxation to an inactive absorbing state. On the other hand, experimental neuronal avalanches are defined by the activity between consecutive silent states. We claim that the latter definition may be extended to some theoretical models to characterize their power-law avalanches and critical behavior. We study a syst…
Combining X-ray tomography with simultaneous shear force measurement, we investigate shear-induced granular avalanches using spherical particles with different surface roughness. We find that systems consisting of particles with large surface roughness display quasi-periodic avalanches interrupted by crackling-like small ones. In contrast, systems consisting of particles with small roughness display no detectable avalanches. The stress drop of quasi-periodic avalanche shows a linear relation with the correlation length of particle non-affine displacement, suggesting that roughness enhances int…
The interplay between the critical fluctuations and the sample geometry is investigated numerically using thin random-field ferromagnets exhibiting the field-driven magnetisation reversal on the hysteresis loop. The system is studied along the theoretical critical line in the plane of random-field disorder and thickness. The thickness is varied to consider samples of various geometry between a two-dimensional plane and a complete three-dimensional lattice with an open boundary in the direction of the growing thickness. We perform a multi-fractal analysis of the Barkhausen noise signals and sca…
The non-equilibrium random-field Ising model is well studied, yet there are outstanding questions. In two dimensions, power law scaling approaches fail and the critical disorder is difficult to pin down. Additionally, the presence of faceting on the square lattice creates avalanches that are lattice dependent at small scales. We propose two methods which we find solve these issues. First, we perform large scale simulations on a Voronoi lattice to mitigate the effects of faceting. Secondly, the invariant arguments of the universal scaling functions necessary to perform scaling collapses can be …
Simulations with more than $10^{12}$ spins are used to study the motion of a domain wall driven through a three-dimensional random-field Ising magnet (RFIM) by an external field $H$. The interface advances in a series of avalanches whose size diverges at a critical external field $H_c$. Finite-size scaling is applied to determine critical exponents and test scaling relations. Growth is intrinsically anisotropic with the height of an avalanche normal to the interface $\ell_\perp$ scaling as the width along the interface $\ell_\|$ to a power $χ=0.85 \pm 0.01$. The total interface roughness is co…
Cortical neural circuits display highly irregular spiking in individual neurons but variably sized collective firing, oscillations and critical avalanches at the population level, all of which have functional importance for information processing. Theoretically, the balance of excitation and inhibition inputs is thought to account for spiking irregularity and critical avalanches may originate from an underlying phase transition. However, the theoretical reconciliation of these multilevel dynamic aspects in neural circuits remains an open question. Herein, we study excitation-inhibition (E-I) b…
Many experimental results, both in-vivo and in-vitro, support the idea that the brain cortex operates near a critical point, and at the same time works as a reservoir of precise spatio-temporal patterns. However the mechanism at the basis of these observations is still not clear. In this paper we introduce a model which combines both these features, showing that scale-free avalanches are the signature of a system posed near the spinodal line of a first order transition, with many spatio-temporal patterns stored as dynamical metastable attractors. Specifically, we studied a network of leaky int…
Experiments in various neural systems found avalanches: bursts of activity with characteristics typical for critical dynamics. A possible explanation for their occurrence is an underlying network that self-organizes into a critical state. We propose a simple spiking model for developing neural networks, showing how these may "grow into" criticality. Avalanches generated by our model correspond to clusters of widely applied Hawkes processes. We analytically derive the cluster size and duration distributions and find that they agree with those of experimentally observed neuronal avalanches.
