Related papers: The abelian sandpile model on a random binary tree
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…
A dissipative stochastic sandpile model is constructed and studied on small world networks in one and two dimensions with different shortcut densities $\phi$, where $\phi=0$ represents regular lattice and $\phi=1$ represents random network.…
We study propagation of avalanches in a certain excitable network. The model is a particular case of the one introduced in [23], and is mathematically equivalent to an endemic variation of the Reed-Frost epidemic model introduced in [27].…
The Abelian sandpile model is the simplest analytically tractable model of self-organized criticality. This paper presents a brief review of known results about the model. The abelian group structure allows an exact calculation of many of…
We consider the model of random trees introduced by Devroye (1999), the so-called random split trees. The model encompasses many important randomized algorithms and data structures. We then perform supercritical Bernoulli bond-percolation…
Oscillatory sheared suspensions, when observed stroboscopically, exhibit a reversible-irreversible transition as a function of the strain amplitude, which is a kind of absorbing phase transition. So far studies of this transition focused on…
I discuss the size distribution ${\cal N}(S)$ of avalanches occurring at the yielding transition of mean field (i.e., Hebraud-Lequeux) models of amorphous solids. The size distribution follows a power law dependence of the form: ${\cal…
The stochastic sandpile model (SSM) is a generalisation of the standard Abelian sandpile model (ASM), in which topplings of unstable vertices are made random. When unstable, a vertex sends one grain to each of its neighbours independently…
Branching processes are widely used to model phenomena from networks to neuronal avalanching. In a large class of continuous-time branching processes, we study the temporal scaling of the moments of the instant population size, the survival…
Mean-field coupled lattice maps are used to approximate the physics of driven threshold systems with long range interactions. However, they are incapable of modeling specific features of the dynamic instability responsible for generating…
This paper considers a sandpile model subjected to a sinusoidal external drive with the time period $T$. We develop a theoretical model for the Green function in a large $T$ limit, which predicts that the avalanches are anisotropic and…
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 the sandpile model on multiplex networks with more than one type of edge and investigate its scaling and dynamical behaviors. We find that the introduction of multiplexity does not alter the scaling behavior of avalanche…
We define a new version of sandpile model which is very similar to Abelian Sandpile Model (ASM), but the height variables are continuous ones. With the toppling rule we define in our model, we show that the model can be mapped to ASM, so…
Recent experimental results on spike avalanches measured in the urethane-anesthetized rat cortex have revealed scaling relations that indicate a phase transition at a specific level of cortical firing rate variability. The scaling relations…
Time series resulting from wave decomposition show the existence of different correlation patterns for avalanche dynamics. For the d=2 Bak-Tang-Wiesenfeld model, long range correlations determine a modification of the wave size distribution…
Mean field slider block models have provided an important entry point for understanding the behavior of discrete driven threshold systems. We present a method of constructing these models with an arbitrary frictional weakening function.…
We present a new model for relaxations in piles of granular material. The relaxations are determined by a stochastic rule which models the effect of friction between the grains. We find power-law distributions for avalanche sizes and…
Topological defects dominate the deformation response of materials in processes ranging from quantum turbulence to crystal plasticity. We calculate the probability distribution function for the fluctuations in velocity $v$, using scaling…
We study scaling limits of exploding Abelian sandpiles using ideas from percolation and front propagation in random media. We establish sufficient conditions under which a limit shape exists and show via a family of counterexamples that…