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

Yadav, Avinash Chand; Kumar, Naveen

doi:10.1209/0295-5075/ac4f09

Cited by 7 publications

(4 citation statements)

References 58 publications

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“…Informally, 1/f p noise is to white noise what anomalous diffusion is to regular diffusion. The scientific literature on 1/f p noise is vast [126][127][128][129][130][131][132][133][134][135][136][137][138], and recent studies on 1/f p noise include [139][140][141][142][143][144].…”

Section: Spectramentioning

confidence: 99%

Beta Brownian motion

Eliazar

2024

J. Phys. A: Math. Theor.

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Brownian Motion (BM) is the paradigmatic model of diffusion. Transcending from diffusion to anomalous diffusion, the prominent Gaussian generalizations of BM are Scaled BM (SBM) and Fractional BM (FBM). In the sub/super diffusivity regimes: SBM is characterized by aging/anti-aging, and FBM is characterized by anti-persistence/persistence. BM is neither aging/anti-aging, nor persistent/anti-persistent. Within the realm of diffusion, a recent Gaussian generalization of BM, Weird BM (WBM), was shown to display aging/anti-aging and persistence /anti-persistence. This paper introduces and explores the anomalous-diffusion counterpart of WBM, Beta BM (BBM), and shows that: the weird behaviors of WBM become even weirder when elevating to BBM. Indeed, BBM displays a rich assortment of anomalous behaviors, and an even richer assortment of combinations of anomalous behaviors. In particular, the BBM anomalous behaviors include aging/anti-aging and persistence/anti-persistence -- which BBM displays in both the sub and super diffusivity regimes. So, anomalous behaviors that are unattainable by the prominent models of SBM and FBM are well attainable by the BBM model.

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Section: Spectramentioning

confidence: 99%

Beta Brownian motion

Eliazar

2024

J. Phys. A: Math. Theor.

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“…As with anomalous diffusion: experimental evidence of 1/f noises started to appear in the nineteen-seventies [158][159][160]; 1/f noises are widely observed across the sciences [161]; the research of 1/f noises is vast and profound [162][163][164][165][166][167][168][169][170]; and, to date, the research of 1/f noises is bustling with activity [171][172][173][174][175][176] 8 . Also, there is a considerable scientific interest in the intersection of anomalous diffusion and 1/f noises, e.g.…”

Section: White Colored and 1/f Noisesmentioning

confidence: 99%

Regular and anomalous diffusion: I. Foundations

Eliazar

2024

J. Phys. A: Math. Theor.

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Diffusion is a generic term for random motions whose positions become more and more diffuse with time. Diffusion is of major importance in numerous areas of science and engineering, and the research of diffusion is vast and profound. This paper is the first in a stochastic `intro series' to the multidisciplinary field of diffusion. The paper sets off from a basic question: how to quantitatively measure diffusivity? Having answered the basic question, the paper carries on to a follow-up question regarding statistical behaviors of diffusion: what further knowledge can the diffusivity measure provide, and when can it do so? The answers to the follow-up question lead to an assortment of notions and topics including: persistence and anti-persistence; aging and anti-aging; spectral densities, white noise, and their generalizations; the Wiener-Khinchin theorem and its generalizations; and colored noises. Then, observing diffusion from a macro level, the paper culminates with: the universal emergence of power-law diffusivity; the three universal diffusion regimes -- one regular, and two anomalous; and the universal emergence of 1/f noise. The paper is entirely self-contained, and its prerequisites are undergraduate mathematics and statistics.

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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%

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

Cited by 7 publications

References 58 publications

Beta Brownian motion

Beta Brownian motion

Regular and anomalous diffusion: I. Foundations

Energy fluctuations in one dimensional Zhang sandpile model

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