Sandpile model on the Sierpinski gasket fractal.

@article{KutnjakUrbanc1996SandpileMO,
  title={Sandpile model on the Sierpinski gasket fractal.},
  author={Kutnjak-Urbanc and Zapperi and Milosevic and Stanley},
  journal={Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics},
  year={1996},
  volume={54 1},
  pages={
          272-277
        }
}
  • Kutnjak-Urbanc, Zapperi, +1 author Stanley
  • Published 6 April 1995
  • Physics, Medicine
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
We investigate the sandpile model on the two-dimensional Sierpinski gasket fractal. We find that the model displays interesting critical behavior, and we analyze the distribution functions of avalanche sizes, lifetimes, and topplings and calculate the associated critical exponents t51.5160.04, a51.6360.04, and m51.3660.04. The avalanche size distribution shows power-law behavior modulated by logarithmic oscillations which can be related to the discrete scale invariance of the underlying lattice… 
Sandpiles on a Sierpinski gasket
We perform extensive simulations of the sandpile model on a Sierpinski gasket. Critical exponents for waves and avalanches are determined. We extend the existing theory of waves to the present case.
Coevolutionary extremal dynamics on gasket fractal
Abstract We considered a Bak–Sneppen model on a Sierpinski gasket fractal. We calculated the avalanche size distribution and the distribution of distances between subsequent minimal sites. To observe
Waves in the sandpile model on fractal lattices
The scaling properties of waves of topplings of the sandpile model on a fractal lattice are investigated. The exponent describing the asymptotics of the distribution of last waves in an avalanche is
Abelian Manna model on two fractal lattices.
TLDR
It is shown that the scaling law D(2-τ)=d(w) generalizes the corresponding scaling law on regular lattices, in particular hypercubes, where d(w)=2.0 and the critical exponent D forms a plane in three-dimensional parameter space.
Laplacian growth and sandpiles on the Sierpiński gasket: limit shape universality and exact solutions
We establish quantitative spherical shape theorems for rotor-router aggregation and abelian sandpile growth on the graphical Sierpinski gasket ($SG$) when particles are launched from the corner
Ballistic deposition on deterministic fractals: observation of discrete scale invariance.
TLDR
It is argued that the interplay between the spatial discrete scale invariance of the fractal substrate and the dynamics of the physical process occurring in those media is a quite general phenomenon that leads to the observation of logarithmic-periodic modulations of physical observables.
Log-periodic oscillations for diffusion on self-similar finitely ramified structures.
TLDR
This work gives a simple explanation of the origin of this modulation for diffusion on a substrate with two properties: self-similarity and finite ramification order, which can be understood on the basis of a hierarchical set of diffusion constants.
Predictability and Scaling in a BTW Sandpile on a Self-similar Lattice
This paper explores the predictability of a Bak–Tang–Wiesenfeld isotropic sandpile on a self-similar lattice, introducing an algorithm which predicts the occurrence of target events when the stress
The abelian sandpile model on randomly rooted graphs and self-similar groups
The Abelian sandpile model is an archetypical model of the physical phenomenon of self-organized criticality. It is also well studied in combinatorics under the name of chip-firing games on graphs.
Theoretical studies of self-organized criticality
These notes are intended to provide a pedagogical introduction to the abelian sandpile model of self-organized criticality, and its related models. The abelian group, the algebra of particle addition
...
1
2
3
4
...