Based on the synergetic approach, the theory of a single avalanche formation is presented for the simplest sandpile model. The stationary values of sand velocity, slope and avalanche intensity are derived as functions of control parameter (externally driven sandpile tilt). The statistical ensemble of avalanche intensities is considered to investigate diffusion in ultrametric space of hierarchic...

An Abelian sandpile model is considered on the Husimi lattice of triangles with an arbitrary coordination number q. Exact expressions for the distribution of height probabilities in the Self-Organized Critical state are derived.

Since its introduction by Bak,Tang and Wiesenfeld, the abelian sandpile dynamics has been studied extensively in finite volume. There are many problems posed by the existence of a sandpile dynamics in an infinite volume S: its invariant distribution should be the thermodynamic limit (does the latter exist?) of the invariant measure for the finite volume dynamics; the extension of the sand grain...

The Abelian sandpile growth model is a diffusion process for configurations of chips placed on vertices of the integer lattice Zd, in which sites with at least 2d chips topple, distributing 1 chip to each of their neighbors in the lattice, until no more topplings are possible. From an initial configuration consisting of n chips placed at a single vertex, the rescaled stable configuration seems ...

We prove a necessary and sufficient condition for an Abelian Sandpile Model (ASM) to be avalanche-finite, namely: all unstable states of the system can be brought back to stability in finite number of topplings. The method is also computationally feasible since it involves no greater than O (

The Fixed Energy Sandpile with the deterministic Bak-Tang-Wiesenfeld rule on the two-dimensional torus, is studied in order to characterize existence and growth rate of the basins of periodic avalanches. The link between discrete harmonicity and invariant quantities, or toppling invariants, is shown. For an important subclass, these invariants are proven to be related to discrete harmonic polyn...

The Gutenberg-Richter power law distribution for energy released at earthquakes can be understood as a consequence of the earth crust being in a self-organized critical state. A simple cellular automaton stick-slip type model yields D(E) • E -• with r = 1.0 and r = 1.35 in two and three dimensions, respectively. The size of earthquakes is unpredictable since the evolution of an earthquake depen...

let $g$ be a finite group with the identity $e$‎. ‎the subgroup intersection graph $gamma_{si}(g)$ of $g$ is the graph with vertex set $v(gamma_{si}(g)) = g-e$ and two distinct vertices $x$ and $y$ are adjacent in $gamma_{si}(g)$ if and only if $|leftlangle xrightrangle capleftlangle yrightrangle|>1$‎, ‎where $leftlangle xrightrangle $ is the cyclic subgroup of $g$ generated by $xin g$‎. ‎in th...

Given an א1-free abelian group G we characterize the class CG of all torsion abelian groups T satisfying Ext(G, T ) = 0 assuming the special continuum hypothesis CH. Moreover, in Gödel’s constructable universe we prove that this characterizes CG for arbitrary torsion-free abelian G. It follows that there exist some ugly א1-free abelian groups.

We generalize the Raychaudhuri equation for the evolution of a self gravitating fluid to include an Abelian and non-Abelian hybrid magneto fluid at a finite temperature. The aim is to utilize this equation for investigating the dynamics of astrophysical high temperature Abelian and non-Abelian plasmas.