Related papers: Avalanche Behavior in an Absorbing State Oslo Mode…
Long-range frustrating interactions, even if their strength is infinitesimal, can give rise to a dramatic proliferations of ground or near-ground states. As a consequence, the ordering temperature can exhibit a discontinuous drop as a…
We study the zero temperature random field Ising model as a model for noise and avalanches in hysteretic systems. Tuning the amount of disorder in the system, we find an ordinary critical point with avalanches on all length scales. Using a…
Motivated by the fact that empirical time series of earthquakes exhibit long-range correlations in space and time and the Gutenberg-Richter distribution of magnitudes, we propose a simple fault model that can account for these types of…
Kinetic equations, which explicitly take into account the branching nature of sandpile avalanches, are derived. The dynamics of the sandpile model is described by the generating functions of a branching process. Having used the results…
We show that deterministic systems with strong nonlinearities seem to be more appropriate to model sandpiles than stochastic systems or deterministic systems in which discontinuities are the only nonlinearity. In particular, we are able to…
Two-component sandpile models are investigated numerically and theoretically. Monte Calro simulations are performed to show that probability distribution functions of avalanche size and lifetime obey power laws whose exponents are…
A random neighbor extremal stick-slip model is introduced. In the thermodynamic limit, the distribution of states has a simple analytical form and the mean avalanche size, as a function of the coupling parameter, is exactly calculable. The…
We study extreme events of avalanche activities in finite-size two-dimensional self-organized critical (SOC) models, specifically the stochastic Manna model (SMM) and the Bak-Tang-Weisenfeld (BTW) sandpile model. Employing the approach of…
Scale-free behavior as well as oscillations are frequently observed in the activity of many natural systems. One important example is the cortical tissues of mammalian brain where both phenomena are simultaneously observed. Rhythmic…
We discuss avalanche and finite size fluctuations in a mesoscopic model to describe the shear plasticity of amorphous materials. Plastic deformation is assumed to occur through series of local reorganizations. Yield stress criteria are…
We perform large scale simulations of a two dimensional lattice model for amorphous plasticity with random local yield stresses and long-range quadrupolar elastic interactions. We show that as the external stress increases towards the…
We study the scaling properties of avalanche activity in the two-dimensional Abelian sandpile model. Instead of the conventional avalanche size distribution, we analyze the site activity distribution, which measures how often a site…
In a semi-infinite geometry, a 1D, M-component model of biological evolution realizes microscopically an inhomogeneous branching process for $M \to \infty$. This implies in particular a size distribution exponent $\tau'=7/4$ for avalanches…
Scale-invariant avalanches -- with events of all sizes following power-law distributions -- are considered critical. Above the upper critical dimension of four, the mean-field solution with a robust $3/2$ size exponent describes the…
Self organisation provides an elegant explanation for how complex structures emerge and persist throughout nature. Surprisingly often, these structures exhibit remarkably similar scale-invariant properties. While this is sometimes captured…
We report avalanche criticality of thermal relaxation in glassy systems after a rapid quench by molecular simulation. Our analysis of the energy landscape and the scaling reveals that particle rearrangement is critical. The critical…
The hypothesis of critical failure relates the presence of an ultimate stability point in the structural constitutive equation of materials to a divergence of characteristic scales in the microscopic dynamics responsible for deformation.…
We study the statistical properties of the yielding transition in model amorphous solids in the limit of slow, athermal deformation. Plastic flow occurs via alternating phases of elastic loading punctuated by rapid dissipative events in the…
We introduce a toy model displaying the avalanche dynamics of failure in scale-free networks. In the model, the network growth is based on the Barab\'asi and Albert model and each node is assigned a capacity or tolerance, which is constant…
The notion of Self-organized criticality (SOC) had been conceived to interpret the spontaneous emergence of long range correlations in nature. Since then many different models had been introduced to study SOC. All of them have few common…