Connecting the microdynamics to the emergent macrovariables: Self-organized criticality and absorbing phase transitions in the deterministic lattice gas

Giometto, Andrea

doi:10.1103/physreve.85.011128

Cited by 8 publications

(5 citation statements)

References 22 publications

(29 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We on the other hand, observe a gradual change of exponents to their mean-field values. Therefore, our results provide evidence for a critical sandpile model with stochastic undirected dynamics which does not belong to the Manna universality class, requiring us to reconsider the controversial concept of universality in sandpile models [51,52]. We close by noting that the mean-field behavior observed in our model is due to an effective range of "interaction" which increases with increasing noise, which underlies the mean-field universality class.…”

Section: Resultsmentioning

confidence: 56%

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

Moosavi

Montakhab

2014

Phys. Rev. E

View full text Add to dashboard Cite

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.

show abstract

Section: Resultsmentioning

confidence: 56%

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

Moosavi

Montakhab

2014

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…Simulations of this model exhibit 1/f spectra and the dissipation take place on fractal-like structures. However, recently it was realized that the model does not display self-organization to criticality (Giometto and Jensen 2012), but requires tuning to reach the critical point of the (conserved directed percolation) absorbing state phase transition. It is probably fair to say that despite its long history (van der Ziel 1950) 1/f -noise is no longer a motivation for SOC, possibly because of the confusion about its actual meaning (1/f versus 1/f α ) and also the possibility, at least in contemporary computer models, to characterize correlations directly in the time domain rather than indirectly via the power spectrum.…”

Section: Paradigmatic Versus Good Modelsmentioning

confidence: 99%

25 Years of Self-organized Criticality: Concepts and Controversies

et al. 2015

View full text Add to dashboard Cite

Introduced by the late Per Bak and his colleagues, self-organized criticality (SOC) has been one of the most stimulating concepts to come out of statistical mechanics and condensed matter theory in the last few decades, and has played a significant role in the development of complexity science. SOC, and more generally fractals and power laws, have attracted much comment, ranging from the very positive to the polemical. The other papers (Aschwanden et al. in Space Sci. Rev., 2014, this issue; McAteer et al. in Space Sci. Rev., 2015, this issue; Sharma et al. in Space Sci. Rev. 2015, in preparation) in this special issue showcase the considerable body of observations in solar, magnetospheric and fusion plasma inspired by the SOC idea, and expose the fertile role the new paradigm has played in approaches to modeling and understanding multiscale plasma instabilities. This very broad impact, and the necessary process of adapting a scientific hypothesis to the conditions of a given physical system, has meant that SOC as studied in these fields has sometimes differed significantly from the definition originally given by its creators. In Bak's own field of theoretical physics there are significant observational and theoretical open questions, even 25 years on (Pruessner 2012). One aim of the present review is to address the dichotomy between the great reception SOC has received in some areas, and its shortcomings, as they became manifest in the controversies it triggered. Our article tries to clear up what we think are misunderstandings of SOC in fields more remote from its origins in statistical mechanics, condensed matter and dynamical systems by revisiting Bak, Tang and Wiesenfeld's original papers

show abstract

“…Christensen et al [20] showed 1/f noise in a SOC system with locally non-conservative dynamics. For deterministic lattice gases [21,22], the density-fluctuations show 1/f power-spectrum.…”

Section: Introductionmentioning

confidence: 99%

Energy fluctuations in one dimensional Zhang sandpile model

Kumar,

Singh,

Yadav

2022

Preprint

View full text Add to dashboard Cite

We consider the Zhang sandpile model in one-dimension (1D) with locally conservative (or dissipative) dynamics and examine its total energy fluctuations at the external drive time scale. The bulk-driven system leads to Lorentzian spectra, with a cutoff time T growing linearly with the system size L. The fluctuations show 1/f α behavior with α ∼ 1 for the boundary drive, and the cutoff time varies non-linearly. For conservative local dynamics, the cutoff time shows a power-law growth T ∼ L λ that differs from an exponential form ∼ exp(µL) observed for the nonconservative case. We suggest that the local dissipation is not a necessary ingredient of the system in 1D to get the 1/f noise, and the cutoff time can reveal the distinct nature of the local dynamics. We also discuss the energy fluctuations for locally nonconservative dynamics with random dissipation.

show abstract

Connecting the microdynamics to the emergent macrovariables: Self-organized criticality and absorbing phase transitions in the deterministic lattice gas

Cited by 8 publications

References 22 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

25 Years of Self-organized Criticality: Concepts and Controversies

Energy fluctuations in one dimensional Zhang sandpile model

Contact Info

Product

Resources

About