Linking space-time correlations for a class of self-organized critical systems

Kumar, Naveen; Singh, Suram; Yadav, Avinash Chand

doi:10.1103/physreve.104.064132

Cited by 9 publications

(6 citation statements)

References 41 publications

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“…The scaling approach for the 1/f noise is simple. Our scaling analysis suggests a very transparent link between the total and local mass fluctuations for the sandpile model, and it reveals a useful insight for space-time correlations in a class of other SOC systems [67]. Finally, it would be interesting to explore the class of examples showing the scaling feature that depends on the identification of a variable such as the loop length determining cutoff time.…”

Section: Influence Of Nonlinearity -mentioning

confidence: 74%

A cutoff time scaling of 1/f noise in a sandpile

Yadav¹,

Kumar²

2022

EPL

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We show that for fluctuations in a sandpile with $1/f^{\alpha}$ spectrum, the power may also exhibit a scaling with its cutoff time. Despite significant progress, this generic behaviour remains so far overlooked and poorly understood. An intriguing example is the power spectrum of a simple random walk (normal diffusive process) on a ring with $L$ sites, showing $L/f^{3/2}$ behaviour instead of $1/f^2$ (Brownian noise) in the frequency regime $1/L^2 \ll f \ll 1/2$. We address the intriguing problem by scaling method and discuss its relevance in the context of the sandpile system and a class of stochastic processes.

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Section: Influence Of Nonlinearity -mentioning

confidence: 74%

A cutoff time scaling of 1/f noise in a sandpile

Yadav¹,

Kumar²

2022

EPL

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“…The model explains the stick-slip phenomenon and is a simplified version of the spring block model introduced by Burridge and Knopoff [33]. Interestingly, a recent study [37] suggests that the train model does not belong to the universality class of the Oslo sandpile model. However, both model show the same critical exponents describing avalanche size distribution [32].…”

Section: Train Modelmentioning

confidence: 99%

Finite-size scaling of critical avalanches

Yadav,

Quadir,

Jafri

2022

Preprint

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We examine probability distribution for avalanche sizes observed in self-organized critical systems. While a power-law distribution with a cutoff because of finite system size is typical behavior, a systematic investigation reveals that it may decrease on increasing the system size at a fixed avalanche size. We implement the scaling method and identify scaling functions. The data collapse ensures a correct estimation of the critical exponents and distinguishes two exponents related to avalanche size and system size. Our simple analysis provides striking implications. While the exact value for avalanches size exponent remains elusive for the prototype sandpile on a square lattice, we suggest the exponent should be 1. The simulation results represent that the distribution shows a logarithmic system size dependence, consistent with the normalization condition. We also argue that for train or Oslo sandpile model with bulk drive, the avalanche size exponent is slightly less than 1 that is significantly different from the previous estimate 1.11.

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“…Then we can write Since Eq. ( 2) is a homogenous function of its arguments, we can apply the scaling method [26,27] to get…”

Section: Fluctuations In Locally Conservative Dynamicsmentioning

confidence: 99%

“…(10a) and (10b). The local energy fluctuations are Lorentzian spectra [26] with a cutoff time that grows exponentially as a function of distance from the driving end.…”

Section: The Local Energy: Z(x T)mentioning

confidence: 99%

Energy fluctuations in one dimensional Zhang sandpile model

Kumar,

Singh,

Yadav

2022

Preprint

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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.

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Linking space-time correlations for a class of self-organized critical systems

Cited by 9 publications

References 41 publications

A cutoff time scaling of 1/f noise in a sandpile

A cutoff time scaling of 1/f noise in a sandpile

Finite-size scaling of critical avalanches

Energy fluctuations in one dimensional Zhang sandpile model

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