scholarly journals Emergence of skewed non-Gaussian distributions of velocity increments in isotropic turbulence

2019 ◽  
Vol 4 (6) ◽  
Author(s):  
W. Sosa-Correa ◽  
R. M. Pereira ◽  
A. M. S. Macêdo ◽  
E. P. Raposo ◽  
D. S. P. Salazar ◽  
...  
Keyword(s):  
Isotropic Turbulence ◽  
Gaussian Distributions ◽  
Velocity Increments ◽  
Non Gaussian

Lagrangian statistics from direct numerical simulations of isotropic turbulence

1989 ◽  
Vol 207 ◽  
pp. 531-586 ◽  
Author(s):  
P. K. Yeung ◽  
S. B. Pope
Keyword(s):  
Numerical Simulations ◽  
Isotropic Turbulence ◽  
Reynolds Numbers ◽  
Small Time ◽  
Direct Numerical Simulations ◽  
Time Lags ◽  
Lagrangian Statistics ◽  
Lagrangian Velocity ◽  
Velocity Increments ◽  
Non Gaussian

A comprehensive study is reported of the Lagrangian statistics of velocity, acceleration, dissipation and related quantities, in isotropic turbulence. High-resolution direct numerical simulations are performed on 643 and 1283 grids, resulting in Taylor-scale Reynolds numbers Rλ in the range 38-93. The low-wavenumber modes of the velocity field are forced so that the turbulence is statistically stationary. Using an accurate numerical scheme, of order 4000 fluid particles are tracked through the computed flow field, and hence time series of Lagrangian velocity and velocity gradients are obtained.The results reported include: velocity and acceleration autocorrelations and spectra; probability density functions (p.d.f.'s) and moments of Lagrangian velocity increments; and p.d.f.'s, correlation functions and spectra of dissipation and other velocity-gradient invariants. It is found that the acceleration variance (normalized by the Kolmogorov scales) increases as R½λ - a much stronger dependence than predicted by the refined Kolmogorov hypotheses. At small time lags, the Lagrangian velocity increments are distinctly non-Gaussian with, for example, flatness factors in excess of 10. The enstrophy (vorticity squared) is found to be more intermittent than dissipation, having a standard-deviation-to-mean ratio of about 1.5 (compared to 1.0 for dissipation). The acceleration vector rotates on a timescale about twice the Kolmogorov scale, while the timescales of acceleration magnitude, dissipation and enstrophy appear to scale with the Lagrangian velocity timescale.

scholarly journals DETERMINING SOURCE CUMULANTS IN FEMTOSCOPY WITH GRAM–CHARLIER AND EDGEWORTH SERIES

2011 ◽  
Vol 26 (24) ◽  
pp. 1771-1782 ◽  
Author(s):  
H. C. EGGERS ◽  
M. B. DE KOCK ◽  
J. SCHMIEGEL
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Fourth Order ◽  
Momentum Space ◽  
Crucial Role ◽  
Gaussian Distributions ◽  
Edgeworth Series ◽  
The Central Limit Theorem ◽  
Non Gaussian

Lowest-order cumulants provide important information on the shape of the emission source in femtoscopy. For the simple case of noninteracting identical particles, we show how the fourth-order source cumulant can be determined from measured cumulants in momentum space. The textbook Gram–Charlier series is found to be highly inaccurate, while the related Edgeworth series provides increasingly accurate estimates. Ordering of terms compatible with the Central Limit Theorem appears to play a crucial role even for non-Gaussian distributions.

Control charts for non-Gaussian distributions

2007 ◽  
Author(s):  
Florina Babus ◽  
Abdessamad Kobi ◽  
Th. Tiplica ◽  
Ioan Bacivarov ◽  
Angelica Bacivarov
Keyword(s):  
Control Charts ◽  
Gaussian Distributions ◽  
Non Gaussian

Reliability-Based Design Optimization With Confidence Level for Non-Gaussian Distributions Using Bootstrap Method

2011 ◽  
Vol 133 (9) ◽  
Author(s):  
Yoojeong Noh ◽  
Kyung K. Choi ◽  
Ikjin Lee ◽  
David Gorsich ◽  
David Lamb
Keyword(s):  
Statistical Model ◽  
Design Optimization ◽  
Confidence Intervals ◽  
Confidence Level ◽  
Bootstrap Method ◽  
Random Variables ◽  
Reliability Based Design Optimization ◽  
Gaussian Distributions ◽  
Reliability Based Design ◽  
Non Gaussian

For reliability-based design optimization (RBDO), generating an input statistical model with confidence level has been recently proposed to offset inaccurate estimation of the input statistical model with Gaussian distributions. For this, the confidence intervals for the mean and standard deviation are calculated using Gaussian distributions of the input random variables. However, if the input random variables are non-Gaussian, use of Gaussian distributions of the input variables will provide inaccurate confidence intervals, and thus yield an undesirable confidence level of the reliability-based optimum design meeting the target reliability βt. In this paper, an RBDO method using a bootstrap method, which accurately calculates the confidence intervals for the input parameters for non-Gaussian distributions, is proposed to obtain a desirable confidence level of the output performance for non-Gaussian distributions. The proposed method is examined by testing a numerical example and M1A1 Abrams tank roadarm problem.

Stable non-Gaussian distributions in scientometrics

1985 ◽  
Vol 7 (3-6) ◽  
pp. 459-470 ◽  
Author(s):  
A. I. Yablonsky
Keyword(s):  
Gaussian Distributions ◽  
Non Gaussian
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