Magnetospheric Multiscale Observations of Markov Turbulence on Kinetic Scales

Macek, Wiesław M.; Wójcik, Dariusz; Burch, J. L.

doi:10.3847/1538-4357/aca0a0

Cited by 6 publications

(1 citation statement)

References 27 publications

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“…The KM coefficients have been used in several areas, such as atmospheric turbulence, medicine, finance, oil prices, and neurophysics (see [15][16][17] and references therein for more information). They have also been used in palaeomagnetism studies [18], optics [19], climatology [20], astrophysics [21,22], and geomagnetism [23]. In addition, packages have been developed in R [24] and Python [25] for estimation.…”

Section: Introductionmentioning

confidence: 99%

Data-driven reconstruction of wind speed randomness in an urban area

Walle,

Soto,

Saldaña

et al. 2024

Preprint

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This study proposes two diffusion models to analyze the wind speed variability in an urban area. The analysis is based on annual time series data collected from fourteen weather stations. A basic criterion has been suggested to categorize these stations based on the variance of the stochastic process for the stationary case. This criterion can be used in studies of air pollution, wind energy, and other related fields where the geographical classification of weather stations is not feasible. The Kramers-Moyal (KM) coefficients and kernel-based regression (KBR) have been utilized to estimate the drift and diffusion terms. The numerical solution of the proposed Langevin equation was used to calculate the statistical properties of the process, taking into account the variance values for station classification. The results show that only two Langevin models are required instead of the original fourteen, based on the variance values. This demonstrates that it is feasible to establish models using basic statistical properties of time series when geographical classification is not possible.

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Section: Introductionmentioning

confidence: 99%

Data-driven reconstruction of wind speed randomness in an urban area

Walle,

Soto,

Saldaña

et al. 2024

Preprint

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Derivation of a generalized Kappa distribution from the scaling properties of solar wind magnetic field fluctuations at kinetic scales

Belardinelli,

Benella,

Stumpo

et al. 2024

A&A

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Context. Kinetic-scale dynamics in weakly collisional space plasmas usually exhibits a self-similar statistics of magnetic field fluctuations. This implies the existence of an invariant probability density function (master curve). Aims. We provide an analytical derivation of the master curve by assuming that perpendicular fluctuations can be modeled through a scale-dependent Langevin equation. Methods. In our model, magnetic field fluctuations are the stochastic variable, and their scale-to-scale evolution is assumed to be a Langevin process. We propose a formal derivation of the master curve describing the statistics of the fluctuations at kinetic scales. The model predictions were tested on independent data samples of the fast solar wind measured near the Sun by Parker Solar Probe and near the Earth by Cluster. Results. The master curve is a generalization of the Kappa distribution with two parameters: One parameter regulates the tails, and the other controls the asymmetry. The model predictions match the spacecraft observations up to 5σ and even beyond in the case of perpendicular magnetic field fluctuations.

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Statistical analysis of stochastic magnetic fluctuations in space plasma based on theMMSmission

Macek,

Wójcik

2023

Monthly Notices of the Royal Astronomical Society

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Based on the Magnetospheric Multiscale (MMS) mission we look at magnetic field fluctuations in the Earth’s magnetosheath. We apply the statistical analysis using a Fokker–Planck equation to investigate processes responsible for stochastic fluctuations in space plasmas. As already known, turbulence in the inertial range of hydromagnetic scales exhibits Markovian features. We have extended the statistical approach to much smaller scales in space, where kinetic theory should be applied. Here we study in detail and compare the characteristics of magnetic fluctuations behind the bow shock, inside the magnetosheath, and near the magnetopause. It appears that the first Kramers–Moyal coefficient is linear and the second term is a quadratic function of magnetic increments, which describe drift and diffusion, correspondingly, in the entire magnetosheath. This should correspond to a generalization of Ornstein–Uhlenbeck process. We demonstrate that the second-order approximation of the Fokker–Planck equation leads to non-Gaussian kappa distributions of the probability density functions. In all cases in the magnetosheath, the approximate power-law distributions are recovered. For some moderate scales, we have the kappa distributions described by various peaked shapes with heavy tails. In particular, for large values of the kappa parameter this shape is reduced to the normal Gaussian distribution. It is worth noting that for smaller kinetic scales the rescaled distributions exhibit a universal global scale invariance, consistently with the stationary solution of the Fokker–Planck equation. These results, especially on kinetic scales, could be important for a better understanding of the physical mechanism governing turbulent systems in space and astrophysical plasmas.

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Magnetospheric Multiscale Observations of Markov Turbulence on Kinetic Scales

Cited by 6 publications

References 27 publications

Data-driven reconstruction of wind speed randomness in an urban area

Data-driven reconstruction of wind speed randomness in an urban area

Derivation of a generalized Kappa distribution from the scaling properties of solar wind magnetic field fluctuations at kinetic scales

Statistical analysis of stochastic magnetic fluctuations in space plasma based on theMMSmission

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