Related papers: Multi-Avalanche Correlations in Directed Sandpile …
Sand pile models are dynamical systems describing the evolution from $N$ stacked grains to a stable configuration. It uses local rules to depict grain moves and iterate it until reaching a fixed configuration from which no rule can be…
Bernoulli random walks, a simple avalanche model, and a special branching process are essesntially identical. The identity gives alternative insights into the properties of these basic model sytems.
We study the recently-introduced directed percolation depinning (DPD) model for interface roughening with quenched disorder for which the interface becomes pinned by a directed percolation (DP) cluster for $d = 1$, or a directed surface…
We study the critical behavior of a driven interface in a medium with random pinning forces by analyzing spatial and temporal correlations in a lattice model recently proposed by Sneppen [Phys. Rev. Lett. {\bf 69}, 3539 (1992)]. The static…
Charge multiplication through avalanche processes is commonly employed in the detection of single photons or charged particles in high-energy physics and beyond. In this report, we provide a detailed discussion of the properties of…
This paper presents a generalization of the sandpile model, called the parallel symmetric sandpile model, which inherits the rules of the symmetric sandpile model and implements them in parallel. In this new model, at each step the…
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 establish both experimentally and theoretically the relation between off the edge and internal avalanches in a sandpile model, a central issue in the interpretation of most experiments in these systems. In BTW simulations and also in the…
Topological defects dominate the deformation response of materials in processes ranging from quantum turbulence to crystal plasticity. We calculate the probability distribution function for the fluctuations in velocity $v$, using scaling…
We analyse by numerical simulations and scaling arguments the avalanche statistics of 1-dimensional elastic interfaces in random media driven at a single point. Both global and local avalanche sizes are power-law distributed, with universal…
Based on a theoretical model for opinion spreading on a network, through avalanches, the effect of external field is now considered, by using methods from non-equilibrium statistical mechanics. The original part contains the implementation…
A dissipative stochastic sandpile model is constructed and studied on small world networks in one and two dimensions with different shortcut densities $\phi$, where $\phi=0$ represents regular lattice and $\phi=1$ represents random network.…
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…
We investigate the sandpile model with Yukawa-type interactions, whose effective range is tuned by an external parameter $R$. Our results reveal that at specific values of $R$, the system exhibits giant avalanches that span the system,…
We characterize the distributions of size and duration of avalanches propagating in complex networks. By an avalanche we mean the sequence of events initiated by the externally stimulated `excitation' of a network node, which may, with some…
A class of $d$-dimensional reaction-diffusion models interpolating continuously between the diffusion-coagulation and the diffusion-annihilation models is introduced. Exact relations among the observables of different models are…
We consider a one-dimensional sandpile model which mimics an elastic string of particles driven through a strongly pinning periodic environment with phase disorder. The evolution towards depinning occurs by the triggering of avalanches in…
The statistical ensemble of avalanche intensities is considered to investigate diffusion in ultrametric space of hierarchically subordinated avalanches. The stationary intensity distribution and the steady-state current are obtained. The…
When sand flows out of a funnel onto a surface, a three dimensional pile that is stabilized by friction grows taller as it spreads. Here we investigate an idealized two dimensional analogue: spreading of a pile of monodisperse oil droplets…
We find that some equilibrium systems and their non-equilibrium counterparts actually show the same jerky response or avalanche behavior on many scales in response to slowly changing external conditions. In other words, their static and…