Related papers: Pattern formation in fast-growing sandpiles

After the introduction of sandpile model a number of different variants have been studied. In most of these models sand particles are indistinguishable. Here we have painted the sand particles using a few distinct colors, and restrict them…

We investigate a non-equilibrium one-dimensional model known as the raise and peel model describing a growing surface which grows locally and has non-local desorption. For specific values of adsorption ($u_a$) and desorption($u_d$) rates…

We report on extensive numerical simulations on the Bak-Sneppen model in high dimensions. We uncover a very rich behavior as a function of dimensionality. For d>2 the avalanche cluster becomes fractal and for d \ge 4 the process becomes…

A dissipative stochastic sandpile model is constructed on one and two dimensional small-world networks with different shortcut densities $\phi$ where $\phi=0$ and $1$ represent a regular lattice and a random network respectively. In the…

We consider a model of interface growth in two dimensions, given by a height function on the sites of the one--dimensional integer lattice. According to the discrete time update rule, the height above the site $x$ increases to the height…

We study erratically moving spatial structures that are found in a driven interface in a random medium at the depinning threshold. We introduce a bond-disordered variant of the Sneppen model and study the effect of extremal dynamics on the…

In landscape-scale experiments at the edge of the Gobi desert, we show that various dune types develop simultaneously under natural wind conditions. Using 4 years of high-resolution topographic data, we demonstrate that, depending on sand…

We continue to study a model of disordered interface growth in two dimensions. The interface is given by a height function on the sites of the one--dimensional integer lattice and grows in discrete time: (1) the height above the site $x$…

We insert some asymmetries in the continuous Abelian sandpile models, such as directedness and ellipticity. We analyze probability distribution of different heights and also find the field theory corresponding to the models. Also we find…

Pattern formation and evolution in unsynchronizable complex networks are investigated. Due to the asymmetric topology, the synchronous patterns formed in complex networks are irregular and nonstationary. For coupling strength immediately…

We study the growing patterns in the rotor-router model formed by adding $N$ walkers at the center of a $L \times L$ two-dimensional square lattice, starting with a periodic background of arrows, and relaxing to a stable configuration. The…

Sand pile models are dynamical systems emphasizing the phenomenon of Self Organized Criticality (SOC). From N stacked grains, iterating evolution rules leads to some critical configuration where a small disturbance has deep consequences on…

This paper is about cubic sand grains moving around on nicely packed columns in one dimension (the physical sand pile is two dimensional, but the support of sand columns is one dimensional). The Kadanoff Sand Pile Model is a discrete…

The phenomenon of sediment pattern formation in a channel flow is numerically investigated by performing simulations which resolve all the relevant scales of the problem. The numerical approach employed and the flow configuration considered…

In the single-source sandpile model, a number $N$ grains of sand are positioned at a central vertex on the 2-dimensional grid $\mathbb{Z}^2$. We study the stabilisation of this configuration for a stochastic sandpile model based on a…

We present a detailed analysis of large scale simulations of avalanches in the 2D Abelian sandpile model. We compare statistical properties of two different decompositions of avalanches into clusters of topplings and waves of topplings.…

We consider the Bak-Tang-Wiesenfeld sandpile model on square lattices in different dimensions (D>=6). A finite size scaling analysis of the avalanche probability distributions yields the values of the distribution exponents, the dynamical…

Vegetation in semi-arid environments self-organizes into striking spatial patterns -- bands, spots, labyrinths, and gaps -- with characteristic wavelengths on the order of tens to hundreds of meters. Existing reaction-diffusion models…

We reveal the fractal nature of patterns arising in random sequential adsorption of particles with continuum power-law size distribution, $P(R)\sim R^{\alpha-1}$, $R \le R_{\rm max}$. We find that the patterns become more and more ordered…

We revisit the calculation of height correlations in the two-dimensional Abelian sandpile model by taking advantage of a technique developed recently by Kenyon and Wilson. The formalism requires to equip the usual graph Laplacian,…