Characteristics of deterministic and stochastic sandpile models in a rotational sandpile model

Abstract

Rotational constraint representing a local external bias generally has a nontrivial effect on the critical behavior of lattice statistical models in equilibrium critical phenomena. In order to study the effect of rotational bias in an out-of-equilibrium situation like self-organized criticality, a two state "quasideterministic" rotational sandpile model is developed here imposing rotational constraint on the flow of sand grains. An extended set of critical exponents are estimated to characterize the avalanche properties at the nonequilibrium steady state of the model. The probability distribution functions are found to obey usual finite size scaling supported by negative time autocorrelation between the toppling waves. The model exhibits characteristics of both deterministic and stochastic sandpile models.

Critical properties of a dissipative sandpile model on small-world networks

“…The exponent γ xy (φ) can also be obtained in terms of the distribution exponents τ x (φ) and τ y (φ) as given in [39],…”

Rotational sandpile models: A finite size scaling study

“…[6]. Different toppling conditions on RSM lead to different rotational models, namely RSM1 and RSM2.…”

“…Beside the seminal Bak, Tang and Wiesenfeld (BTW) sandpile model [3], varieties of sandpile models were then constructed and their critical properties were studied by incorporating different toppling rule as well as external bias to the original BTW model. For example, Manna's stochastic model (MSM) [4], directed sandpile model [5], rotational sandpile model (RSM) [6] and many others can be found in Ref. [7].…”

“…Santra). [8,9,6]. Microscopic measurements include probability distribution of toppling number of individual sites, two point correlation in toppling surface and loop fractal dimension [10].…”

Crossover from rotational to stochastic sandpile universality in the random rotational sandpile model

“…In the RSM, an internal stochasticity appears due to a superposition of toppling waves from different directions during time evolution. Eventually, that induces all the features of a stochastic sandpile model, such as toppling imbalance, negative time auto correlation, and existence of finitesize scaling (FSS) into the RSM [13][14][15][16]. The RSM is thus a stochastic model, but it belongs to a completely different universality class than the Manna class of the SSM.…”