Related papers: Asymptotics of the single-source stochastic sandpi…
We consider patterns generated by adding large number of sand grains at a single site in an abelian sandpile model with a periodic initial configuration, and relaxing. The patterns show proportionate growth. We study the robustness of these…
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…
We introduce a family of abelian sandpile models with two parameters $n, m \in {\bf N}$ defined on finite lattices on $d$-dimensional torus. Sites with $2dn+m$ or more grains of sand are unstable and topple, and in each toppling $m$ grains…
The two dimensional directed sandpile with dissipation is transformed into a (1+1) dimensional problem with discrete space and continuous `time'. The master equation for the conditional probability that K grains preserve their initial order…
The evolution of a pile of granular material is investigated by molecular dynamics using a new model including nonsphericity of the particles instead of introducing static friction terms. The angle of repose of the piles as well as the…
We study the sandpile model in infinite volume on $\mathbb{Z}^d$. In particular, we are interested in the question whether or not initial configurations, chosen according to a stationary measure $\mu$, are $\mu$-almost surely stabilizable.…
We study fixed density sandpiles in which the number of particles transferred to a neighbor on relaxing an active site is determined stochastically by a parameter $p$. Using an argument, the critical density at which an active-absorbing…
We define two general classes of nonabelian sandpile models on directed trees (or arborescences) as models of nonequilibrium statistical phenomena. These models have the property that sand grains can enter only through specified reservoirs,…
We numerically study the directed version of the fixed energy sandpile. On a closed square lattice, the dynamical evolution of a fixed density of sand grains is studied. The activity of the system shows a continuous phase transition around…
We use techniques from the theory of electrical networks to give nearly tight bounds for the transience class of the Abelian sandpile model on the two-dimensional grid up to polylogarithmic factors. The Abelian sandpile model is a discrete…
We introduce and study a non-conserving sandpile model, the autonomously adapting sandpile (AAS) model, for which a site topples whenever it has two or more grains, distributing three or two grains randomly on its neighboring sites,…
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 study the temporal evolution of avalanches in the fiber bundle model of disordered solids, when the model is gradually driven towards the critical breakdown point. We use two types of loading protocols: (i) the quasi-static loading, and…
Uniform spherical beads were used to explore the behavior of a granular system near its critical angle of repose on a conical bead pile. We found two tuning parameters that could take the system to a critical point where a simple power-law…
We show that tilting a model sandpile that has dynamic disorder leads to bistability and hysteresis at the angle of repose. Also the distribution of {\it local slopes} shows an interesting dependence on the amount of tilt - weakly tilted…
A directed dissipative sandpile model is studied in the two-dimension. Numerical results indicate that the long time steady states of this model are critical when grains are dropped only at the top or, everywhere. The critical behaviour is…
We derive the first four terms in a series for the order paramater (the stationary activity density rho) in the supercritical regime of a one-dimensional stochastic sandpile; in the two-dimensional case the first three terms are reported.…
The theory of a flux steady-state (avalanche) formation is presented for the simplest model of a real sand pile within the framework of Lorenz approach. The stationary values of sand velocity and sand pile slope are derived as functions of…
We solve a one-dimensional sandpile problem analytically in a thick flow regime when the pile evolution may be described by a set of linear equations. We demonstrate that, if an income flow is constant, a space periodicity takes place while…
A symmetric version of the well-known SPM model for sandpiles is introduced. We prove that the new model has fixed point dynamics. Although there might be several fixed points, a precise description of the fixed points is given. Moreover,…