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Related papers: Self-similar Dynamics in Percolation and Sandpile

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The abelian sandpile serves as a model to study self-organized criticality, a phenomenon occurring in biological, physical and social processes. The identity of the abelian group is a fractal composed of self-similar patches, and its limit…

Mathematical Physics · Physics 2022-06-01 Moritz Lang , Mikhail Shkolnikov

In this paper, we investigate the impact of bond-dilution disorder on the critical behavior of the stochastic SIR model. Monte Carlo simulations were conducted using square lattices with first- and second-nearest neighbor interactions.…

Statistical Mechanics · Physics 2024-06-26 Carlos Handrey A. Ferraz , José Luiz S. Lima

Although the paradigm of criticality is centred around spatial correlations and their anomalous scaling, not many studies of Self-Organised Criticality (SOC) focus on spatial correlations. Often, integrated observables, such as avalanche…

Statistical Mechanics · Physics 2017-08-01 Gary Willis , Gunnar Pruessner

We have studied the damage spreading (defined in the text) in the 'sandpile' model of self organised criticality. We have studied the variations of the critical time (defined in the text) and the total no of sites damaged at critical time…

Condensed Matter · Physics 2007-05-23 Ajanta Bhowal

There is mounting empirical evidence that many communities of living organisms display key features which closely resemble those of physical systems at criticality. We here introduce a minimal model framework for the dynamics of a community…

Biological Physics · Physics 2020-02-17 Fabio Peruzzo , Mauro Mobilia , Sandro Azaele

The stability of powergrid is crucial since its disruption affects systems ranging from street lightings to hospital life-support systems. Nevertheless, large blackouts are inevitable if powergrids are in the state of self-organized…

Physics and Society · Physics 2018-10-18 Ho Fai Po , Chi Ho Yeung , An Zeng , K. Y. Michael Wong

We explore the connection between self-organized criticality and phase transitions in models with absorbing states. Sandpile models are found to exhibit criticality only when a pair of relevant parameters - dissipation epsilon and driving…

Statistical Mechanics · Physics 2009-10-30 Ronald Dickman , Alessandro Vespignani , Stefano Zapperi

We introduce a nonequilibrium percolation model which shows a self-organized critical (SOC) state and several periodic states. In the SOC state, the correlation length diverges slower than the system size, and the corresponding exponent…

Condensed Matter · Physics 2009-10-28 Siegfried Clar , Barbara Drossel , Franz Schwabl

A set of discrete individual points located in an embedding continuum space can be seen as percolating or non-percolating, depending on the radius of the discs/spheres associated with each of them. This problem is relevant in theoretical…

Statistical Mechanics · Physics 2022-07-21 Pablo Villegas , Tommaso Gili , Andrea Gabrielli , Guido Caldarelli

We have studied the damage spreading (defined in the text) in the 'sandpile' model of self organised criticality. We have studied the variations of the critical time (defined in the text) and the total number of sites damaged at critical…

Statistical Mechanics · Physics 2015-05-27 Ajanta Bhowal Acharyya

We study two driven dynamical systems with conserved energy. The two automata contain the basic dynamical rules of the Bak, Tang and Wiesenfeld sandpile model. In addition a global constraint on the energy contained in the lattice is…

Statistical Mechanics · Physics 2009-10-30 Alessandro Chessa , Enzo Marinari , Alessandro Vespignani

We study a one-dimensional fixed-energy version (that is, with no input or loss of particles), of Manna's stochastic sandpile model. The system has a continuous transition to an absorbing state at a critical value $\zeta_c$ of the particle…

Statistical Mechanics · Physics 2009-11-07 Ronald Dickman , Mikko Alava , Miguel A. Munoz , Jarkko Peltola , Alessandro Vespignani , Stefano Zapperi

We consider the Bernoulli percolation model in a finite box and we introduce an automatic control of the percolation probability, which is a function of the percolation configuration. For a suitable choice of this automatic control, the…

Probability · Mathematics 2022-01-21 Raphaël Cerf , Nicolas Forien

The Bak-Tang-Wiesenfeld (BTW) sandpile process is an archetypal, stylized model of complex systems with a critical point as an attractor of their dynamics. This phenomenon, called self-organized criticality (SOC), appears to occur…

Statistical Mechanics · Physics 2014-01-21 Pierre-André Noël , Charles D. Brummitt , Raissa M. D'Souza

Bak, Tang, and Wiesenfeld developed their theory of self-organized criticality in the late 1980s to explain why many real-life processes exhibit signs of critical behavior despite the absence of a tuning parameter. A decade later, Dickman,…

Probability · Mathematics 2024-07-11 Christopher Hoffman , Tobias Johnson , Matthew Junge

We show that deterministic systems with strong nonlinearities seem to be more appropriate to model sandpiles than stochastic systems or deterministic systems in which discontinuities are the only nonlinearity. In particular, we are able to…

Statistical Mechanics · Physics 2009-11-10 Maria de Sousa Vieira

We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the…

Statistical Mechanics · Physics 2009-11-07 Róbert Juhász , Ferenc Iglói

We introduce and study numerically a directed two-dimensional sandpile automaton with probabilistic toppling (probability parameter p) which provides a good laboratory to study both self-organized criticality and the far-from-equilibrium…

Condensed Matter · Physics 2009-10-28 S. Luebeck , B. Tadic , K. D. Usadel

In statistical and nonlinear systems, two qualitatively distinct parameter regions are typically identified: the regular region, characterized by smooth behavior of key quantities, and the critical region, where these quantities exhibit…

Statistical Mechanics · Physics 2025-04-01 V. I. Yukalov , E. P. Yukalova , D. Sornette

The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects dramatically different from those in cooperative systems on lattices. In the last few years,…

Statistical Mechanics · Physics 2009-11-13 S. N. Dorogovtsev , A. V. Goltsev , J. F. F. Mendes