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A theoretical interpretation of numerically generated probability density functions (PDFs) of intermittent plasma transport events in unforced zonal flows is provided within the Charney-Hasegawa-Mima (CHM) model. The governing equation is…
Mathematical models based on probability density functions (PDF) have been extensively used in hydrology and subsurface flow problems, to describe the uncertainty in porous media properties (e.g., permeability modelled as random field).…
A theory of the probability distribution function (PDF) tails of the blob density in plasma edge turbulence is provided. A simplified model of the fast convective radial transport is used. The theoretically predicted PDF tails corroborate…
Random processes play a crucial role in scientific research, often characterized by distribution functions or probability density functions (PDFs). These PDFs serve as essential approximations of the actual and frequently undisclosed…
This Letter provides a theoretical interpretation of numerically generated probability density functions (PDFs) of intermittent plasma transport events. Specifically, nonlinear gyrokinetic simulations of ion-temperature-gradient turbulence…
Atmospheric wind speeds and their fluctuations at different locations (onshore and offshore) are examined. One of the most striking features is the marked intermittency of probability density functions (PDF) of velocity differences -- no…
We show that the parton distribution functions (PDF) described by the statistical model have very interesting physical properties which help to understand the structure of partons. The role of the quark helicity components is emphasized as…
Supersonic turbulence occurs in many environments, particularly in astrophysics. In the crucial case of isothermal turbulence, the probability density function (PDF) of the logarithmic density, $s$, is well measured, but a theoretical…
The statistical properties of the $E \times B$ flux in different types of plasma turbulence simulations are investigated using probability density distribution functions (PDF). The physics included in the models ranges from two dimensional…
By means of the multifractal analysis (MFA), the expressions of the probability density functions (PDFs) are unified in a compact analytical formula which is valid for various quantities in turbulence. It is shown that the formula can…
Dispersion of a passive scalar from concentrated sources in fully developed turbulent channel flow is studied with the probability density function (PDF) method. The joint PDF of velocity, turbulent frequency and scalar concentration is…
We discuss the statistical properties of parton distributions within the framework of the NNPDF methodology. We present various tests of statistical consistency, in particular that the distribution of results does not depend on the…
Chance-constrained optimization has emerged as a promising framework for managing uncertainties in power systems. This work advances its application to the DC Optimal Power Flow (DC-OPF) model, developing a novel approach to uncertainty…
We present a non-perturbative calculation of the 1-point probability distribution function (PDF) for the spherically-averaged matter density field. The PDF is represented as a path integral and is evaluated using the saddle-point method. It…
Uncertainty propagation in nonlinear dynamic systems remains an outstanding problem in scientific computing and control. Numerous approaches have been developed, but are limited in their capability to tackle problems with more than a few…
In a recent letter, Christian Beck described a theoretical link between a family of stochastic differential equations and the probability density functions (PDF) derived from the formalism of nonextensive statistical mechanics. He applied…
Traditionally, single realizations of the turbulent state have been the object of study in shear flow turbulence. When a statistical quantity was needed it was obtained from a spatial, temporal or ensemble average of sample realizations of…
Experimental results for the evolution of the probability distribution function (PDF) of a scalar mixed by a turbulence flow in a channel are presented. The sequence of PDF from an initial skewed distribution to a sharp Gaussian is found to…
Perturbation Theory (PT) applied to a cosmological density field with Gaussian initial fluctuations suggests a specific hierarchy for the correlation functions when the variance is small. In particular quantitative predictions have been…
We develop a new computational framework to solve the partial differential equations (PDEs) governing the flow of the joint probability density functions (PDFs) in continuous-time stochastic nonlinear systems. The need for computing the…