Related papers: Colored Sandpile
In this paper, we recall various features of non equilibrium granular systems. Clusters with specific properties are found depending on the packing density, going from loose (a granular gas) to sintered (though brittle) polycrystalline…
We investigate dynamics of deformable self-propelled particles with a repulsive interaction whose magnitude depends on the relative direction of elongation of a pair of particles. A collective motion of the particles appears in two…
We discuss biologically inspired, inherently non-equilibrium self-propelled particle models, in which the particles interact with their neighbours by choosing at each time step the local average direction of motion. We summarize some of the…
We consider the Abelian sandpile model on triangular and hexagonal lattices. We compute several height probabilities on the full plane and on half-planes, and discuss some properties of the universality of the model.
We study general aspects of active motion with fluctuations in the speed and the direction of motion in two dimensions. We consider the case in which fluctuations in the speed are not correlated to fluctuations in the direction of motion,…
We define two classes of colorings that have odd or even chirality on hexagonal lattices. This parity is an invariant in the dynamics of all loops, and explains why standard Monte-Carlo algorithms are nonergodic. We argue that adding the…
The well-known Edwards-Wilkinson equation with a flow term added exhibits a smoothing fixed point in addition to the normal EW fixed point. Based on this, we present a model of sandpiles involving a coupling between fixed and mobile grains,…
The aim of the current work is to investigate structural properties of the sandpile group of a special class of self-similar graphs. More precisely, we consider Abelian sandpiles on Sierpinski gasket graphs and for the choice of normal…
We present a comprehensive study of Vicsek-style self-propelled particle models in two and three space dimensions. The onset of collective motion in such stochastic models with only local alignment interactions is studied in detail and…
We obtain tilings with a singular point by applying conformal maps on regular tilings of the Euclidean plane, and determine its symmetries. The resulting tilings are then symmetrically colored by applying the same conformal maps on…
Two-component sandpile models are investigated numerically and theoretically. Monte Calro simulations are performed to show that probability distribution functions of avalanche size and lifetime obey power laws whose exponents are…
Discrete particle simulation methods have been used to study axial segregation in a horizontal rotating cylinder that is partially filled with a mixture of two different kinds of granular particles. Under suitable conditions segregation was…
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…
We consider a stochastic sandpile where the sand-grains of unstable sites are randomly distributed to the nearest neighbors. Increasing the value of the threshold condition the stochastic character of the distribution is lost and a…
Polarity fields are known to exhibit long distance patterns, in both physical and biological systems. The mechanisms behind such patterns are poorly understood. Here, we describe the dynamics of polarity fields using an original physical…
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…
We perform extensive numerical simulations of different versions of the sandpile model. We find that previous claims about universality classes are unfounded, since the method previously employed to analyze the data suffered a systematic…
Sandpile models are known to resist exact results. In this direction, space-time correlations between avalanches have proven to be especially difficult to access. One of the main obstacle to do so comes from taking memory effects in a…
We study collective dynamics of interacting deformable self-propelled particles whose migration velocity increases when the local density of particles is increased. Numerical simulations in two dimensions reveal that traveling bands similar…
A modular or distributive lattice is `diamond-colored' if its order diagram edges are colored in such a way that, within any diamond of edges, parallel edges have the same color. Such lattices arise naturally in combinatorial representation…