Related papers: One-Dimensional Directed Sandpile Models and the A…
A general n-state directed `sandpile' model is introduced. The stationary properties of the n-state model are derived for n < infty, and analytical arguments based on a central limit theorem show that the model belongs to the universality…
We perform large scale numerical simulations of a directed version of the two-state stochastic sandpile model. Numerical results show that this stochastic model defines a new universality class with respect to the Abelian directed sandpile.…
We introduce a sandpile model where, at each unstable site, all grains are transferred randomly to downstream neighbors. The model is local and conservative, but not Abelian. This does not appear to change the universality class for the…
The avalanche statistics in a stochastic sandpile model where toppling takes place with a probability p is investigated. The limiting case p=1 corresponds to the Bak-Tang-Wiesenfeld (BTW) model with deterministic toppling rule. Based on the…
We study sandpile models with stochastic toppling rules and having sticky grains so that with a non-zero probability no toppling occurs, even if the local height of pile exceeds the threshold value. Dissipation is introduced by adding a…
Quantifying the universality of avalanche observables beyond critical exponents is of current great interest in theory and experiments. Here, we improve the characterization of the spatio-temporal process inside avalanches in the…
We perform large-scale simulations of directed sandpile models with both deterministic and stochastic toppling rules. Our results show the existence of two distinct universality classes. We also provide numerical simulations of directed…
Multiple avalanches, initiated by simultaneously toppling neighbouring sites, are studied in three different directed sandpile models. It is argued that, while the single avalanche exponents are different for the three models, a suitably…
Directed sandpile models with different toppling rules are studied by means of numerical simulations in two dimensions, with the purpose of determining the different universality classes. It is concluded that the random-threshold directed…
The degree of predictability of large avalanche events in the directed sandpile model is studied. A waiting time based prediction strategy which exploits the local anticorrelation of large events is discussed. With this strategy we show…
We show that in a broad class of directed abelian sandpile models that had been expected to have the same exponents as the Dhar-Ramaswamy model, the avalanche exponent depends upon the details of the interaction, calling into question the…
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 study a directed stochastic sandpile model of Self-Organized Criticality, which exhibits recurrent, multiple topplings, putting it in a separate universality class from the exactly solved model of Dhar and Ramaswamy. We show that in the…
The Brownian force model (BFM) is the mean-field model for the avalanches of an elastic interface slowly driven in a random medium. It describes the spatio-temporal statistics of the velocity field, and, to some extent is analytically…
We provide a comprehensive view on the role of Abelian symmetry and stochasticity in the universality class of directed sandpile models, in context of the underlying spatial correlations of metastable patterns and scars. It is argued that…
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…
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…
We study the Brownian force model (BFM), a solvable model of avalanche statistics for an interface, in a general discrete setting. The BFM describes the overdamped motion of elastically coupled particles driven by a parabolic well in…
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,…
In most driven-dissipative sandpile models, the dynamics of the system reaches a critical stationary state. This state displays organization features such as a power-law avalanche spectrum and hyperuniformity, but these features often…