Related papers: On the robustness of scale invariance in SOC model…
A simple random-neighbor SOC model that combines properties of the Bak-Sneppen and the relaxation oscillators (slip-stick) models is introduced. The analysis in terms of branching processes is transparent and gives insight about the…
We analyze a random neighbor version of the OFC stick-slip model. We find that the mean avalanche size is finite as soon as dissipation exists in the bulk but that this size grows exponentially fast when dissipation tends to zero.
The talk presented at ICMP 97 focused on the scaling limits of critical percolation models, and some other systems whose salient features can be described by collections of random lines. In the scaling limit we keep track of features seen…
This paper applies the theory of continuous phase transitions of statistical mechanics to a slider-block model. The slider-block model is chosen as a representative of systems with avalanches. Similar behavior can be observed in a…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
We consider the breakdown of conformal and scale invariance in random systems with strongly random critical points. Extending previous results on one-dimensional systems, we provide an example of a three-dimensional system which has a…
We report on the computer study of a lattice system that relaxes from a metastable state. Under appropriate nonequilibrium randomness, relaxation occurs by avalanches, i.e., the model evolution is discontinuous and displays many scales in a…
An analysis of moments and spectra shows that, while the distribution of avalanche areas obeys finite size scaling, that of toppling numbers is universally characterized by a full, nonlinear multifractal spectrum. Rare, large avalanches…
Recent observation for scale invariant neural avalanches in the brain have been discussed in details in the scientific literature. We point out, that these results do not necessarily imply that the properties of the underlying neural…
The "Self-organized criticality" (SOC), introduced in 1987 by Bak, Tang and Wiesenfeld, was an attempt to explain the 1/f noise, but it rapidly evolved towards a more ambitious scope: explaining scale invariant avalanches. In two decades,…
The depinning transition critical point is manifested as power-law distributed avalanches exhibited by slowly driven elastic interfaces in quenched random media. Here we show that since avalanches with different starting heights relative to…
In real-world applications, observations are often constrained to a small fraction of a system. Such spatial subsampling can be caused by the inaccessibility or the sheer size of the system, and cannot be overcome by longer sampling.…
Avalanches, or Avalanche-like, events are often observed in the dynamical behaviour of many complex systems which span from solar flaring to the Earth's crust dynamics and from traffic flows to financial markets. Self-organized criticality…
An analysis of stick-slip behavior and convergence of trajectories in the feedback-controlled motion systems with discontinuous Coulomb friction is provided. A closed-form parameter-dependent stiction region, around an invariant equilibrium…
An extremal model for the plasticity of amorphous materials is studied in a simple two-dimensional anti-plane geometry. The steady-state is analyzed through numerical simulations. Long-range spatial and temporal correlations in local slip…
As the variety of systems displaying scale invariant characteristics are matched only by their number, it is becoming increasingly important to understand their fundamental and universal elements. Much work has attempted to apply 2nd order…
Plastic deformation of crystals proceeds through a sequence of intermittent slip avalanches with scale-free (power-law) size distribution. On macroscopic scales, however, plastic flow is known to be smooth and homogeneous. In the present…
The major difficulty in developing theories for anomalous scaling in hydrodynamic turbulence is the lack of a small parameter. In this Letter we introduce a shell model of turbulence that exhibits anomalous scaling with a tunable small…
Understanding quantum phase transitions in highly excited Hamiltonian eigenstates is currently far from being complete. It is particularly important to establish tools for their characterization in time domain. Here we argue that a scaled…
We study the sandpile model on three-dimensional spanning Ising clusters with the temperature $T$ treated as the control parameter. By analyzing the three dimensional avalanches and their two-dimensional projections (which show…