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

Bhaumik, Himangsu; Santra, S. B.

doi:10.1103/physreve.88.062817

Cited by 13 publications

(27 citation statements)

References 77 publications

(94 reference statements)

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“…scale-free networks [36] or small-world networks [43]. More recently, the existence of two scaling regimes, one of mean-field-like and one of regular-lattice-like have also been reported [44,45]. We note that in all such studies definitive mean-field behavior has been observed for the value of shortcut link probability (long range connections) equal or greater than p ∼ 10 −1 .…”

Section: Discussionmentioning

confidence: 88%

Mean-field behavior as a result of noisy local dynamics in self-organized criticality: Neuroscience implications

Moosavi

Montakhab

2014

Phys. Rev. E

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Motivated by recent experiments in neuroscience which indicate that neuronal avalanches exhibit scale invariant behavior similar to self-organized critical systems, we study the role of noisy (nonconservative) local dynamics on the critical behavior of a sandpile model which can be taken to mimic the dynamics of neuronal avalanches. We find that despite the fact that noise breaks the strict local conservation required to attain criticality, our system exhibit true criticality for a wide range of noise in various dimensions, given that conservation is respected on the average. Although the system remains critical, exhibiting finite-size scaling, the value of critical exponents change depending on the intensity of local noise. Interestingly, for sufficiently strong noise level, the critical exponents approach and saturate at their mean-field values, consistent with empirical measurements of neuronal avalanches. This is confirmed for both two and three dimensional models. However, addition of noise does not affect the exponents at the upper critical dimension (D = 4). In addition to extensive finite-size scaling analysis of our systems, we also employ a useful time-series analysis method in order to establish true criticality of noisy systems. Finally, we discuss the implications of our work in neuroscience as well as some implications for general phenomena of criticality in non-equilibrium systems.

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Section: Discussionmentioning

confidence: 88%

Mean-field behavior as a result of noisy local dynamics in self-organized criticality: Neuroscience implications

Moosavi

Montakhab

2014

Phys. Rev. E

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“…x for x ≫ 1 [21]. Noting that for large enough αs F is a decreasing function, we see that the average shortest distance decreases with increasing α.…”

Section: The Btw Model On the Small World Networkmentioning

confidence: 68%

“…2a. It is worth mentioning that it is well-known in the literature that in the IR limit the BTW model on the random network phase (in which α 10) should have the same exponents as the mean field (MF) results [20,21,31,32]. Two points should be noted in this regard: Firstly we have not entered this phase.…”

Section: Three Dimensionsmentioning

confidence: 96%

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Statistical investigation of avalanches of three-dimensional small-world networks and their boundary and bulk cross-sections

Najafi

Dashti-Naserabadi

2018

Phys. Rev. E

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In many situations we are interested in the propagation of energy in some portions of a three-dimensional system with dilute long-range links. In this paper, a sandpile model is defined on the three-dimensional small-world network with real dissipative boundaries and the energy propagation is studied in three dimensions as well as the two-dimensional cross-sections. Two types of cross-sections are defined in the system, one in the bulk and another in the system boundary. The motivation of this is to make clear how the statistics of the avalanches in the bulk cross-section tend to the statistics of the dissipative avalanches, defined in the boundaries as the concentration of long-range links (α) increases. This trend is numerically shown to be a power law in a manner described in the paper. Two regimes of α are considered in this work. For sufficiently small αs the dominant behavior of the system is just like that of the regular BTW, whereas for the intermediate values the behavior is nontrivial with some exponents that are reported in the paper. It is shown that the spatial extent up to which the statistics is similar to the regular BTW model scales with α just like the dissipative BTW model with the dissipation factor (mass in the corresponding ghost model) m^{2}∼α for the three-dimensional system as well as its two-dimensional cross-sections.

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“…The probability of dissipation ǫ φ is taken as the inverse of the average number of steps n φ required for a random walker to reach the lattice boundary starting from any lattice point [27,19]. The dissipation factor ǫ φ = 1/ n φ for a given φ is then determined using the numerically estimated values of n φ .…”

Section: The Model: Dssm On Swnmentioning

confidence: 99%

Stochastic sandpile model on small-world networks: Scaling and crossover

Bhaumik

Santra

2018

Physica A: Statistical Mechanics and its Applications

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A dissipative stochastic sandpile model is constructed on one and two dimensional smallworld networks with different shortcut densities φ where φ = 0 and 1 represent a regular lattice and a random network respectively. In the small-world regime (2 −12 ≤ φ ≤ 0.1), the critical behaviour of the model is explored studying different geometrical properties of the avalanches as a function of avalanche size s. For both the dimensions, three regions of s, separated by two crossover sizes s 1 and s 2 (s 1 < s 2 ), are identified analyzing the scaling behaviour of average height and area of the toppling surface associated with an avalanche. It is found that avalanches of size s < s 1 are compact and follow Manna scaling on the regular lattice whereas the avalanches with size s > s 1 are sparse as they are on network and follow mean-field scaling. Coexistence of different scaling forms in the small-world regime leads to violation of usual finite-size scaling, in contrary to the fact that the model follows the same on the regular lattice as well as on the random network independently. Simultaneous appearance of multiple scaling forms are characterized by developing a coexistence scaling theory. As SWN evolves from regular lattice to random network, a crossover from diffusive to super-diffusive nature of sand transport is observed and scaling forms of such crossover is developed and verified.

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

Cited by 13 publications

References 77 publications

Mean-field behavior as a result of noisy local dynamics in self-organized criticality: Neuroscience implications

Mean-field behavior as a result of noisy local dynamics in self-organized criticality: Neuroscience implications

Statistical investigation of avalanches of three-dimensional small-world networks and their boundary and bulk cross-sections

Stochastic sandpile model on small-world networks: Scaling and crossover

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