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In the prototype sandpile model of self-organized criticality time series obtained by decomposing avalanches into waves of toppling show intermittent fluctuations. The q-th moments of wave size differences possess local multiscaling and…

Statistical Mechanics · Physics 2009-11-07 Mario De Menech , Attilio L. Stella

The Abelian sandpile model was the first example of a self-organized critical system studied by Bak, Tang and Wiesenfeld. The dynamics of the sandpiles occur when the grains topple over a graph. In this study, we allow the graph to evolve…

Combinatorics · Mathematics 2024-07-24 Carlos A. Alfaro , Juan Pablo Serrano , Ralihe R. Villagrán

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…

Statistical Mechanics · Physics 2009-10-31 Maya Paczuski , Kevin E. Bassler

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…

Soft Condensed Matter · Physics 2009-10-31 S. S. Manna , A. D. Chakrabarti , R. Cafiero

A stochastic theory for the toppling activity in sandpile models is developed, based on a simple mean-field assumption about the toppling process. The theory describes the process as an anti-persistent Gaussian walk, where the diffusion…

Statistical Finance · Quantitative Finance 2009-11-13 Martin Rypdal , Kristoffer Rypdal

In the stochastic sandpile model on a graph, particles interact pairwise as follows: if two particles occupy the same vertex, they must each take an independent random walk step with some probability $0<p<1$ of not moving. These…

Probability · Mathematics 2022-04-27 Andrew Melchionna

A popular theory of self-organized criticality relates the critical behavior of driven dissipative systems to that of systems with conservation. In particular, this theory predicts that the stationary density of the abelian sandpile model…

Probability · Mathematics 2010-09-22 Anne Fey , Lionel Levine , David B. Wilson

We study a restricted-height version of the one-dimensional Oslo sandpile with conserved density, using periodic boundary conditions. Each site has a limiting height which can be either two or three. When a site reaches its limiting height…

Statistical Mechanics · Physics 2015-11-09 Vanuildo Silva de Carvalho , Alvaro de Almeida Caparica , Ronald Dickman

We prove a necessary and sufficient condition for an Abelian Sandpile Model (ASM) to be avalanche-finite, namely: all unstable states of the system can be brought back to stability in finite number of topplings. The method is also…

adap-org · Physics 2015-06-24 S. W. Chan , H. F. Chau

Vicsek fractal graphs are an important class of infinite graphs with self similar properties, polynomial growth and treelike features, on which several dynamical processes such as random walks or Abelian sandpiles can be rigorously analyzed…

Probability · Mathematics 2024-08-22 Nico Heizmann , Robin Kaiser , Ecaterina Sava-Huss

We discuss various critical densities in sandpile models. The stationary density is the average expected height in the stationary state of a finite-volume model; the transition density is the critical point in the infinite-volume…

Mathematical Physics · Physics 2012-11-21 Anne Fey , Ronald Meester

Given an initial distribution of sand in an Abelian sandpile, what final state does it relax to after all possible avalanches have taken place? In d >= 3, we show that this problem is P-complete, so that explicit simulation of the system is…

Condensed Matter · Physics 2015-06-25 Cristopher Moore , Martin Nilsson

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…

Statistical Mechanics · Physics 2011-03-01 N. M. Bogoliubov , A. G. Pronko , J. Timonen

With a toppling rule which generates metastable sites, we explore the properties of a gradient-driven sandpile that is minimally perturbed at one boundary. In two dimensions we find that the transport of grains takes place along deep…

Statistical Mechanics · Physics 2009-11-07 Lucian Anton , Hendrik B. Geyer

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…

Statistical Mechanics · Physics 2009-11-10 Kavita Jain

We study a synchronous dispersion process in which $M$ particles are initially placed at a distinguished origin vertex of a graph $G$. At each time step, at each vertex $v$ occupied by more than one particle at the beginning of this step,…

Discrete Mathematics · Computer Science 2018-01-17 Colin Cooper , Andrew McDowell , Tomasz Radzik , Nicolas Rivera , Takeharu Shiraga

Capillary forces significantly affect the stability of sandpiles. We analyze the stability of sandpiles with such forces, and find that the critical angle is unchanged in the limit of an infinitely large system; however, this angle is…

Soft Condensed Matter · Physics 2009-10-31 Thomas C. Halsey , Alex J. Levine

We derive a general formulation of the self-organized branching process by considering sandpile dynamics in an evolving population characterized by "birth" (excitation) and "death" (de-excitation) of active sites ($z=1$). New active sites…

Adaptation and Self-Organizing Systems · Physics 2007-05-23 D. E. Juanico , C. Monterola , C. Saloma

Dust at the midplane of a circumstellar disk can become gravitationally unstable and fragment into planetesimals if the local dust-to-gas density ratio mu is sufficiently high. We simulate how dust settles in passive disks and ask how high…

Earth and Planetary Astrophysics · Physics 2015-05-20 Aaron T. Lee , Eugene Chiang , Xylar Asay-Davis , Joe Barranco

A growing random graph is constructed by successively sampling without replacement an element from the pool of virtual vertices and edges. At start of the process the pool contains $N$ virtual vertices and no edges. Each time a vertex is…

Probability · Mathematics 2024-02-29 Michael Farber , Alexander Gnedin , Wajid Mannan