Predicting PDF tails of flux in plasma sheath region

Anderson, Johan; Kim, Eun Jin

doi:10.1088/0741-3335/52/1/012001

Cited by 10 publications

(10 citation statements)

References 30 publications

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“…The most widely encountered distribution in extreme value theory, the Gumbel distribution [79,80], has been frequently employed for climate modeling, including extreme rainfall and flooding [81][82][83][84][85], extreme winds [86], avalanches [87], and earthquakes [88]. The Gumbel distribution has also been found to reasonably characterize the density fluctuations within galaxies [89][90][91] and in certain areas of tokamaks [92][93][94], binding energies in liquids [95], as well as turbulent fluctuations [96,97]. The cumulative distribution function F for the Gumbel case has the well-known form:…”

Section: Results: Extreme-value Statistics Of Turbulent Particle Dispmentioning

confidence: 99%

Extreme-value statistics from Lagrangian convex hull analysis for homogeneous turbulent Boussinesq convection and MHD convection

et al. 2017

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We investigate the utility of the convex hull of many Lagrangian tracers to analyze transport properties of turbulent flows with different anisotropy. In direct numerical simulations of statistically homogeneous and stationary Navier-Stokes turbulence, neutral fluid Boussinesq convection, and MHD Boussinesq convection a comparison with Lagrangian pair dispersion shows that convex hull statistics capture the asymptotic dispersive behavior of a large group of passive tracer particles. Moreover, convex hull analysis provides additional information on the sub-ensemble of tracers that on average disperse most efficiently in the form of extreme value statistics and flow anisotropy via the geometric properties of the convex hulls. We use the convex hull surface geometry to examine the anisotropy that occurs in turbulent convection. Applying extreme value theory, we show that the maximal square extensions of convex hull vertices are well described by a classic extreme value distribution, the Gumbel distribution. During turbulent convection, intermittent convective plumes grow and accelerate the dispersion of Lagrangian tracers. Convex hull analysis yields information that supplements standard Lagrangian analysis of coherent turbulent structures and their influence on the global statistics of the flow.

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Section: Results: Extreme-value Statistics Of Turbulent Particle Dispmentioning

confidence: 99%

Extreme-value statistics from Lagrangian convex hull analysis for homogeneous turbulent Boussinesq convection and MHD convection

et al. 2017

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“…Gaussian statistics, however, has serious limitations in explaining emerging complex phenomena such as anomalous transport (super-or sub-diffusion), intermittency, selforganisation, or phase transition where a long-range correlation plays a key role [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. In fact, non-Gaussian PDFs often observed in these systems have stimulated active research on nonequilibrium statistics by considering nonlinear interaction, finite-correlated or Levy-flight noise, multiplicative noise, fractional calculus, etc.…”

Section: ∂V ∂Xmentioning

confidence: 99%

“…(e.g., see Refs. [4][5][6][7][8][9][10][11][12][13][14][15]17,[19][20][21][22][23]). The main aim of this paper to shed light on this issue by elucidating the effect of nonlinear interaction during the relaxation process of an initial PDF to a final stationary PDF as an example of nonequilibrium processes.…”

Section: ∂V ∂Xmentioning

confidence: 99%

“…For analytical computation of a time-dependent PDF, we consider a narrow initial PDF approximated by the δ function p(x,t = 0) = δ(x − x 0 ). In order to obtain a PDF at any later time, we utilize a path integral formulation by expressing the transition probability p(x f ,t f ; x 0 ,0) between initial x 0 at t = 0 and x f at later time t = t f [12][13][14][15][16]21,26,30,33] as follows:…”

Section: Analytical Predictionmentioning

confidence: 99%

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Time-dependent probability density function in cubic stochastic processes

Kim

Hollerbach

2016

Phys. Rev. E

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We report time-dependent probability density functions (PDFs) for a nonlinear stochastic process with a cubic force using analytical and computational studies. Analytically, a transition probability is formulated by using a path integral and is computed by the saddle-point solution (instanton method) and a new nonlinear transformation of time. The predicted PDF p(x,t) in general involves a time integral, and useful PDFs with explicit dependence on x and t are presented in certain limits (e.g., in the short and long time limits). Numerical simulations of the Fokker-Planck equation provide exact time evolution of the PDFs and confirm analytical predictions in the limit of weak noise. In particular, we show that transient PDFs behave drastically differently from the stationary PDFs in regard to the asymmetry (skewness) and kurtosis. Specifically, while stationary PDFs are symmetric with the kurtosis smaller than 3, transient PDFs are skewed with the kurtosis larger than 3; transient PDFs are much broader than stationary PDFs. We elucidate the effect of nonlinear interaction on the strong fluctuations and intermittency in the relaxation process.

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“…Here, n and m are the order of the highest non-linear interaction term and moments for which the PDFs are computed, respectively [23]. For arbitrary fluctuations, in the case of exponential non-linear interaction the PDF tails was found to be described by the Gumbel distribution which represents a frequency distribution of the extreme values of the ensemble [26]. However it is questionable that a Taylor expansion of the non-linear interaction term would be valid for an instanton driven process and thus a more rigorous study is needed.…”

Section: Introductionmentioning

confidence: 99%