Related papers: Correlation, crossover and broken scaling in the A…
Although the paradigm of criticality is centred around spatial correlations and their anomalous scaling, not many studies of Self-Organised Criticality (SOC) focus on spatial correlations. Often, integrated observables, such as avalanche…
The average avalanche size can be calculated exactly in a number of models of self-organised criticality (SOC). While the calculation is straight-forward in one dimension, it is more involved in higher dimensions and further complicated by…
We investigate a random--neighbours version of the two dimensional non-conserving earthquake model of Olami, Feder and Christensen [Phys. Rev. Lett. {\bf 68}, 1244 (1992)]. We show both analytically and numerically that criticality can be…
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…
The Abelian Manna model of self-organized criticality is studied on various three-dimensional and fractal lattices. The exponents for avalanche size, duration and area distribution of the model are obtained by using a high-accuracy moment…
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…
The aim of this study is to investigate a wave dynamics and size scaling of avalanches which were created by the mathematical model {[}J. \v{C}ern\'ak Phys. Rev. E \textbf{65}, 046141 (2002)]. Numerical simulations were carried out on a two…
We perform a high-accuracy moment analysis of the avalanche size, duration and area distribution of the Abelian Manna model on eight two-dimensional and four one-dimensional lattices. The results provide strong support to establish…
A spatial avalanche model is introduced, in which avalanches increase stability in the regions where they occur. Instability is driven globally by a driving process that contains shocks. The system is typically subcritical, but the shocks…
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…
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 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…
Numerous systems ranging from deformation of materials to earthquakes exhibit bursty dynamics, which consist of a sequence of events with a broad event size distribution. Very often these events are observed to be temporally correlated or…
The Abelian Sandpile Model (ASM) is a paradigm of self-organized criticality (SOC) which is related to $c=-2$ conformal field theory. The conformal fields corresponding to some height clusters have been suggested before. Here we derive the…
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,…
A globally driven self-organized critical model of earthquakes with conservative dynamics has been studied. An open but moving boundary condition has been used so that the origin (epicenter) of every avalanche (earthquake) is at the center…
We discuss sensitivity to initial conditions in a model for avalanches in granular media displaying self-organized criticality. We show that damage, due to a small perturbation in initial conditions, does not spread. The damage persists in…
In disordered elastic systems, driven by displacing a parabolic confining potential adiabatically slowly, all advance of the system is in bursts, termed avalanches. Avalanches have a finite extension in time, which is much smaller than the…
The avalanche properties of models that exhibit 'self-organized criticality' (SOC) are still mostly awaiting theoretical explanations. A recent mapping (Europhys. Lett.~53, 569) of many sandpile models to interface depinning is presented…
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,…