Related papers: Generic Sandpile Models Have Directed Percolation …
We perform a computational study of a variant of the ``train'' model for earthquakes [PRA 46, 6288 (1992)], where we assume a static friction that is a stochastic function of position rather than being velocity dependent. The model consists…
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…
Emergence is a concept that is easy to exhibit, but very hard to formally handle. This paper is about cubic sand grains moving around on nicely packed columns in one dimension (the physical sandpile is two dimensional, but the support of…
We study an inhomogeneous sandpile model in which two different toppling rules are defined. For any site only one rule is applied corresponding to either the Bak, Tang and Wiesenfeld model {[}P.Bak, C. Tang, and K. Wiesenfeld, Phys. Rev.…
A directed avalanche model with a control parameter is introduced to describe the transition between cohesive and noncohesive granular material. The underlying dynamics of the process can be mapped to interface growth model. In that…
A dynamical transition separating intermittent and continuous flow is observed in a sandpile model, with scaling functions relating the transport behaviors between both regimes. The width of the active zone diverges with system size in the…
A simple, discrete, parametric model is proposed to describe conditional (correlated) deposition of particles on a surface and formation of a connecting (percolating) cluster. The surface changes spontaneously its properties (phase…
Due to intermittency and conservation, the Abelian sandpile in 2D obeys multifractal, rather than finite size scaling. In the thermodynamic limit, a vanishingly small fraction of large avalanches dominates the statistics and a constant gap…
The triggering of avalanches is investigated using discrete element simulations for a process of random extraction of spheres. A monolayer, formed by identical spheres in a hexagonal configuration, is placed on a tilted plane surrounded by…
We study probability distributions of waves of topplings in the Bak-Tang-Wiesenfeld model on hypercubic lattices for dimensions D>=2. Waves represent relaxation processes which do not contain multiple toppling events. We investigate bulk…
We introduce a non-standard model for percolation on the integer lattice $\mathbb Z^2$. Randomly assign to each vertex $a \in \mathbb Z^2$ a potential, denoted $\phi_a$, chosen independently and uniformly from the interval $[0, 1]$. For…
Similar evolutionary variational inequalities appear as convenient formulations for continuous quasistationary models for sandpile growth, formation of a network of lakes and rivers, magnetization of type-II superconductors, and…
We introduce a one-dimensional sandpile model which incorporates particle inertia. The inertial dynamics are governed by a new parameter which, as it passes through a threshold value, alters the toppling dynamics in such a way that the…
We introduce perhaps the simplest models of graph evolution with choice that demonstrate discontinuous percolation transitions and can be analyzed via mathematical evolution equations. These models are local, in the sense that at each step…
We introduce a new model of a stochastic sandpile on a graph $G$ containing a sink. When unstable, a site sends one grain to each of its neighbours independently with probability $p \in (0,1]$. For $p=1$, this coincides with the standard…
The dynamics of complex systems in nature often occurs in terms of punctuations, or avalanches, rather than following a smooth, gradual path. A comprehensive theory of avalanche dynamics in models of growth, interface depinning, and…
Stochastic sandpiles self-organize to a critical point with scaling behavior different from directed percolation (DP) and characterized by the presence of an additional conservation law. This is usually called C-DP or Manna universality…
We generalize the directed percolation (DP) model by relaxing the strict directionality of DP such that propagation can occur in either direction but with anisotropic probabilities. We denote the probabilities as $p_{\downarrow}= p \cdot…
We present the results of a percolation-like model that has been restricted compared to standard percolation models in the sense that we do not allow finite sized clusters to break up once they have formed. We calculate the critical…
We consider directed percolation with an absorbing boundary in 1+1 and 2+1 dimensions. The distribution of cluster lifetimes and sizes depend on the boundary. The new scaling exponents can be related to the exponents characterizing standard…