Related papers: Fine Structure of Avalanches in the Abelian Sandpi…
We introduce an external control to reduce the size of avalanches in some sandpile models exhibiting self organized criticality. This rather intuitive approach seems to be missing in the vast literature on such systems. The control action,…
This survey is an extended version of lectures given at the Cornell Probability Summer School 2013. The fundamental facts about the Abelian sandpile model on a finite graph and its connections to related models are presented. We discuss…
We introduce and study a new directed sandpile model with threshold dynamics and stochastic toppling rules. We show that particle conservation law and the directed percolation-like local evolution of avalanches lead to the formation of a…
The roughness properties of two-dimensional fracture surfaces as created by the slow failure of random fuse networks are considered and compared to yield surfaces of perfect plasticity with similar disorder. By studying systems up to a…
We investigate the sandpile model on the two--dimensional Sierpinski gasket fractal. We find that the model displays novel critical behavior, and we analyze the distribution functions of avalanche sizes, lifetimes and topplings and…
Experimental observation of a new mechanism of sandpile formation is reported. As a steady stream of dry sand is poured onto a horizontal surface, a pile forms which has a thin river of sand on one side flowing from the apex of the pile to…
We study the coarsening dynamics of a two dimensional system via lattice Boltzmann numerical simulations. The system under consideration is a biphasic system consisting of domains of a dispersed phase closely packed together in a continuous…
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…
Mean-field coupled lattice maps are used to approximate the physics of driven threshold systems with long range interactions. However, they are incapable of modeling specific features of the dynamic instability responsible for generating…
We introduce a natural Boltzmann measure over polyominoes induced by boundary avalanches in the Abelian Sandpile Model. Through the study of a suitable associated process, we give an argument suggesting that the probability distribution of…
Crackling dynamics is characterized by a release of incoming energy through intermittent avalanches. The shape, i.e. the internal temporal structure of these avalanches, gives insightful information about the physical processes involved. It…
The relaxation in complex systems is in general nonexponential. After an initial rapid decay the system relax slowly following a long time tail. In the present paper a sandpile modelation of the relaxation in complex systems is analysed.…
We study avalanches in a model for a planar crack propagating in a disordered medium. Due to long-range interactions, avalanches are formed by a set of spatially disconnected local clusters, the sizes of which are distributed according to a…
We have studied one-dimensional cellular automata with updating rules depending stochastically on the difference of the heights of neighbouring cells. The probability for toppling depends on a parameter lambda which goes to one with…
Multi-phase materials, such as composite materials, exhibit multiple competing failure mechanisms during the growth of a macroscopic defect. For the simulation of the overall fracture process in such materials, we develop a two-phase spring…
We report arrays of monodisperse water-in-oil microdroplets printed onto a substrate in a form of a compact linear chain -- a 1D-crystal -- pinned at one end. The chain spontaneously collapses under capillary forces via a sequence of…
We study the abelian sandpile model on a random binary tree. Using a transfer matrix approach introduced by Dhar & Majumdar, we prove exponential decay of correlations, and in a small supercritical region (i.e., where the branching process…
We investigate the effect of the amount of disorder on the statistics of breaking bursts during the quasi-static fracture of heterogeneous materials. We consider a fiber bundle model where the strength of single fibers is sampled from a…
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…
We present a directed unloading sand box type avalanche model, driven by slowly lowering the retaining wall at the bottom of the slope. The avalanche propagation in the two dimensional surface is related to the space-time configurations of…