Fractal dimension of superfluid turbulence: a random-walk toy model

Mongiovı̀, Maria Stella; Sciacca, Michele; Jou, David

doi:10.1685/journal.caim.471

Cited by 1 publication

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References 26 publications

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“…Intermittent turbulence is a concept often applied to describe and model complex physical behaviors that can be described as fractal. Intermittency of any physical phenomena such as turbulence in fluid flow or changes in heart rate changes the statistical properties of the scaling laws for the different moments of velocity, energy distribution, and diffusion behavior observed in intermittent systems (Jou, 1997 ; Mongiov et al, 2014 ). The occurrence of a short region of turbulence is a crucial event and the time distance between two consecutive turbulent events, assumed to be of negligible time duration, is given by an inverse power law (IPL) waiting time distribution density with an IPL index μ < 3 and related to fractal-like behavior that can manifest as 1/ f noise.…”

Section: Introductionmentioning

confidence: 99%

Diffusion Entropy vs. Multiscale and Rényi Entropy to Detect Progression of Autonomic Neuropathy

et al. 2021

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We review the literature to argue the importance of the occurrence of crucial events in the dynamics of physiological processes. Crucial events are interpreted as short time intervals of turbulence, and the time distance between two consecutive crucial events is a waiting time distribution density with an inverse power law (IPL) index μ, with μ < 3 generating non-stationary behavior. The non-stationary condition is characterized by two regimes of the IPL index: (a) perennial non-stationarity, with 1 < μ < 2 and (b) slow evolution toward the stationary regime, with 2 < μ < 3. Human heartbeats and brain dynamics belong to the latter regime, with healthy physiological processes tending to be closer to the border with the perennial non-stationary regime with μ = 2. The complexity of cognitive tasks is associated with the mental effort required to address a difficult task, which leads to an increase of μ with increasing task difficulty. On this basis we explore the conjecture that disease evolution leads the IPL index μ moving from the healthy condition μ = 2 toward the border with Gaussian statistics with μ = 3, as the disease progresses. Examining heart rate time series of patients affected by diabetes-induced autonomic neuropathy of varying severity, we find that the progression of cardiac autonomic neuropathy (CAN) indeed shifts μ from the border with perennial variability, μ = 2, to the border with Gaussian statistics, μ = 3 and provides a novel, sensitive index for assessing disease progression. We find that at the Gaussian border, the dynamical complexity of crucial events is replaced by Gaussian fluctuation with long-time memory.

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Section: Introductionmentioning

confidence: 99%