Estimation of the Radionuclide Transport by Applying the Mean, the Standard Deviation and the Skewness of Permeability

1996 ◽  
Vol 465 ◽  
Author(s):  
Y. Niibori ◽  
O. Tochiyama ◽  
T. Chida
Keyword(s):  
Standard Deviation ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Lognormal Distribution ◽  
Heterogeneous Media ◽  
Arithmetic Mean ◽  
Bernoulli Trials ◽  
The Mean ◽  
Independent Parameters

ABSTRACTA new method for estimating the mass transport by using the stochastic values (the arithmetic mean, the standard deviation and the skewness) of permeability is presented. Generally, detail of permeability distribution cannot be obtained except for moments of the distribution. Also, measurement results of permeability for the rock matrix including cracks or fast flowpaths do not always follow the log-normal distribution frequently applied. In such a situation, we must evaluate the characteristic permeabilities for the whole or some regions of the disposal site including the accessible environment.The authors have investigated the characteristic permeability on the basis of some probability density functions of permeability, applying the Monte Carlo method and FEM. It was found that its value does not depend on type of probability density function of permeability, but on the arithmetic mean, the standard deviation and the skewness of permeability [1].This paper describes the use of the stochastic values of permeability for estimating the rate of radioactivity release to the accessible environment, applying the advection-dispersion model to two-dimensional, heterogeneous media. When a discrete probability density function (referred to as ‘the Bernoulli trials’) and the lognormal distribution have common values for the arithmetic mean, the standard deviation and the skewness of permeability, the calculated transport rates (described as the pseudo impulse responses) show good agreements for Peclet number around 10 and the dimensionless standard deviation around 1. Further, it is found that the transport rates apparently depends not only on the arithmetic mean and the standard deviation, but also on the skewness of permeability. When the value of skewness dose not follow the lognormal distribution which has only two independent parameters (the mean and the standard deviation), we can replicate the three moments estimated from an observed distribution of permeability, by using the Bernoulli trials having three independent parameters.

scholarly journals The Probability Distribution of Sea Surface Wind Speeds. Part I: Theory and SeaWinds Observations

2006 ◽  
Vol 19 (4) ◽  
pp. 497-520 ◽  
Author(s):  
Adam Hugh Monahan
Keyword(s):  
Standard Deviation ◽  
Probability Density Function ◽  
Probability Distribution ◽  
Probability Density ◽  
Density Function ◽  
Surface Wind ◽  
Sea Surface ◽  
Wind Speeds ◽  
Sea Surface Wind ◽  
The Mean

Abstract The probability distribution of sea surface wind speeds, w, is considered. Daily SeaWinds scatterometer observations are used for the characterization of the moments of sea surface winds on a global scale. These observations confirm the results of earlier studies, which found that the two-parameter Weibull distribution provides a good (but not perfect) approximation to the probability density function of w. In particular, the observed and Weibull probability distributions share the feature that the skewness of w is a concave upward function of the ratio of the mean of w to its standard deviation. The skewness of w is positive where the ratio is relatively small (such as over the extratropical Northern Hemisphere), the skewness is close to zero where the ratio is intermediate (such as the Southern Ocean), and the skewness is negative where the ratio is relatively large (such as the equatorward flank of the subtropical highs). An analytic expression for the probability density function of w, derived from a simple stochastic model of the atmospheric boundary layer, is shown to be in good qualitative agreement with the observed relationships between the moments of w. Empirical expressions for the probability distribution of w in terms of the mean and standard deviation of the vector wind are derived using Gram–Charlier expansions of the joint distribution of the sea surface wind vector components. The significance of these distributions for improvements to calculations of averaged air–sea fluxes in diagnostic and modeling studies is discussed.

Effects of the Fractional Laplacian Order on the Nonlocal Elastic Rod Response

2017 ◽  
Vol 3 (3) ◽  
Author(s):  
Giuseppina Autuori ◽  
Federico Cluni ◽  
Vittorio Gusella ◽  
Patrizia Pucci
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Coefficient Of Variation ◽  
Fractional Laplacian ◽  
Numerical Procedure ◽  
Elastic Rod ◽  
The Mean ◽  
Distributed Forces ◽  
Nonlinear Fashion

In this paper, we yield with a nonlocal elastic rod problem, widely studied in the last decades. The main purpose of the paper is to investigate the effects of the statistic variability of the fractional operator order s on the displacements u of the rod. The rod is supposed to be subjected to external distributed forces, and the displacement field u is obtained by means of numerical procedure. The attention is particularly focused on the parameter s, which influences the response in a nonlinear fashion. The effects of the uncertainty of s on the response at different locations of the rod are investigated by the Monte Carlo simulations. The results obtained highlight the importance of s in the probabilistic feature of the response. In particular, it is found that for a small coefficient of variation of s, the probability density function of the response has a unique well-identifiable mode. On the other hand, for a high coefficient of variation of s, the probability density function of the response decreases monotonically. Finally, the coefficient of variation and, to a small extent, the mean of the response tend to increase as the coefficient of variation of s increases.

scholarly journals Comparison Of Three Numerical Methods For Estimating Weibull Parameters Using Weibull Distribution Model In Nigeria

2020 ◽  
Vol 27 (2) ◽  
pp. 8-15
Author(s):  
J.A. Oyewole ◽  
F.O. Aweda ◽  
D. Oni
Keyword(s):  
Standard Deviation ◽  
Wind Speed ◽  
Probability Density Function ◽  
Weibull Distribution ◽  
Probability Density ◽  
Density Function ◽  
Accurate Estimation ◽  
Weibull Parameters ◽  
Factor Method ◽  
Deviation Method

There is a crucial need in Nigeria to enhance the development of wind technology in order to boost our energy supply. Adequate knowledge about the wind speed distribution becomes very essential in the establishment of Wind Energy Conversion Systems (WECS). Weibull Probability Density Function (PDF) with two parameters is widely accepted and is commonly used for modelling, characterizing and predicting wind resource and wind power, as well as assessing optimum performance of WECS. Therefore, it is paramount to precisely estimate the scale and shape parameters for all regions or sites of interest. Here, wind data from year 2000 to 2010 for four different locations (Port Harcourt, Ikeja, Kano and Jos) were analysed and the Weibull parameters was determined. The three methods employed are Mean Standard Deviation Method (MSDM), Energy Pattern Factor Method (EPFM) and Method of Moments (MOM) for estimating Weibull parameters. The method that gave the most accurate estimation of the wind speed was MSDM method, while Energy Pattern Factor Method (EPFM) is the most reliable and consistent method for estimating probability density function of wind. Keywords: Weibull Distribution, Method of Moment, Mean Standard Deviation Method, Energy Pattern Method

scholarly journals A new subgrid-scale representation of hydrometeor fields using a multivariate PDF

2016 ◽  
Author(s):  
Brian M. Griffin ◽  
Vincent E. Larson
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Vertical Velocity ◽  
Lognormal Distribution ◽  
Large Eddy Simulations ◽  
Subgrid Scale ◽  
Microphysical Process ◽  
Large Eddy ◽  
Probability Density Function Pdf

Abstract. The subgrid-scale representation of hydrometeor fields is important for calculating microphysical process rates. In order to represent subgrid-scale variability, the Cloud Layers Unified By Binormals (CLUBB) parameterization uses a multivariate Probability Density Function (PDF). In addition to vertical velocity, temperature, and moisture fields, the PDF includes hydrometeor fields. Previously, each hydrometeor field was assumed to follow a multivariate single lognormal distribution. Now, in order to better represent the distribution of hydrometeors, two new multivariate PDFs are formulated and introduced. The new PDFs represent hydrometeors using either a delta-lognormal or a delta-double-lognormal shape. The two new PDF distributions, plus the previous single lognormal shape, are compared to histograms of data taken from Large-Eddy Simulations (LES) of a precipitating cumulus case, a drizzling stratocumulus case, and a deep convective case. Finally, the warm microphysical process rates produced by the different hydrometeor PDFs are compared to the same process rates produced by the LES.

scholarly journals A Phenomenological Epidemic Model Based On the Spatio-Temporal Evolution of a Gaussian Probability Density Function

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2000
Author(s):  
Domingo Benítez ◽  
Gustavo Montero ◽  
Eduardo Rodríguez ◽  
David Greiner ◽  
Albert Oliver ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Epidemic Model ◽  
Temporal Evolution ◽  
Growth Models ◽  
Model Fit ◽  
Gaussian Probability Density Function ◽  
Spatio Temporal

A novel phenomenological epidemic model is proposed to characterize the state of infectious diseases and predict their behaviors. This model is given by a new stochastic partial differential equation that is derived from foundations of statistical physics. The analytical solution of this equation describes the spatio-temporal evolution of a Gaussian probability density function. Our proposal can be applied to several epidemic variables such as infected, deaths, or admitted-to-the-Intensive Care Unit (ICU). To measure model performance, we quantify the error of the model fit to real time-series datasets and generate forecasts for all the phases of the COVID-19, Ebola, and Zika epidemics. All parameters and model uncertainties are numerically quantified. The new model is compared with other phenomenological models such as Logistic Grow, Original, and Generalized Richards Growth models. When the models are used to describe epidemic trajectories that register infected individuals, this comparison shows that the median RMSE error and standard deviation of the residuals of the new model fit to the data are lower than the best of these growing models by, on average, 19.6% and 35.7%, respectively. Using three forecasting experiments for the COVID-19 outbreak, the median RMSE error and standard deviation of residuals are improved by the performance of our model, on average by 31.0% and 27.9%, respectively, concerning the best performance of the growth models.

A New Microcontact Model Developed for Variable Fractal Dimension, Topothesy, Density of Asperity, and Probability Density Function of Asperity Heights

2006 ◽  
Vol 74 (4) ◽  
pp. 603-613 ◽  
Author(s):  
Jeng Luen Liou ◽  
Jen Fin Lin
Keyword(s):  
Fractal Dimension ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Gaussian Distribution ◽  
Fractal Theory ◽  
Radius Of Curvature ◽  
The Mean ◽  
Contact Surfaces ◽  
Non Gaussian

In the present study, the fractal theory is applied to modify the conventional model (the Greenwood and Williamson model) established in the statistical form for the microcontacts of two contact surfaces. The mean radius of curvature (R) and the density of asperities (η) are no longer taken as constants, but taken as variables as functions of the related parameters including the fractal dimension (D), the topothesy (G), and the mean separation of two contact surfaces. The fractal dimension and the topothesy varied by differing the mean separation of two contact surfaces are completely obtained from the theoretical model. Then the mean radius of curvature and the density of asperities are also varied by differing the mean separation. A numerical scheme is thus developed to determine the convergent values of the fractal dimension and topothesy corresponding to a given mean separation. The topographies of a surface obtained from the theoretical prediction of different separations show the probability density function of asperity heights to be no longer the Gaussian distribution. Both the fractal dimension and the topothesy are elevated by increasing the mean separation. The density of asperities is reduced by decreasing the mean separation. The contact load and the total contact area results predicted by variable D, G*, and η as well as non-Gaussian distribution are always higher than those forecast with constant D, G*, η, and Gaussian distribution.

Bifurcation Analysis of an Energy Harvesting System with Fractional Order Damping Driven by Colored Noise

2021 ◽  
Vol 31 (15) ◽  
Author(s):  
Yong-Ge Yang ◽  
Ya-Hui Sun ◽  
Wei Xu
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Fractional Order ◽  
Colored Noise ◽  
Energy Harvester ◽  
Advanced Materials ◽  
Vibration Energy ◽  
Vibration Energy Harvester ◽  
The Mean

Vibration energy harvester, which can convert mechanical energy to electrical energy so as to achieve self-powered micro-electromechanical systems (MEMS), has received extensive attention. In order to improve the efficiency of vibration energy harvesters, many approaches, including the use of advanced materials and stochastic loading, have been adopted. As the viscoelastic property of advanced materials can be well described by fractional calculus, it is necessary to further discuss the dynamical behavior of the fractional-order vibration energy harvester. In this paper, the stochastic P-bifurcation of a fractional-order vibration energy harvester subjected to colored noise is investigated. Variable transformation is utilized to obtain the approximate equivalent system. Probability density function for the amplitude of the system response is derived via the stochastic averaging method. Numerical results are presented to verify the proposed method. Critical conditions for stochastic P-bifurcation are provided according to the change of the peak number for the probability density function. Then bifurcation diagrams in the parameter planes are analyzed. The influences of parameters in the system on the mean harvested power are discussed. It is found that the mean harvested power increases with the enhancement of the noise intensity, while it decreases with the increase of the fractional order and the correlation time.

scholarly journals A new subgrid-scale representation of hydrometeor fields using a multivariate PDF

2016 ◽  
Vol 9 (6) ◽  
pp. 2031-2053 ◽  
Author(s):  
Brian M. Griffin ◽  
Vincent E. Larson
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Vertical Velocity ◽  
Lognormal Distribution ◽  
Large Eddy Simulations ◽  
Subgrid Scale ◽  
Microphysical Process ◽  
Large Eddy ◽  
Probability Density Function Pdf

Abstract. The subgrid-scale representation of hydrometeor fields is important for calculating microphysical process rates. In order to represent subgrid-scale variability, the Cloud Layers Unified By Binormals (CLUBB) parameterization uses a multivariate probability density function (PDF). In addition to vertical velocity, temperature, and moisture fields, the PDF includes hydrometeor fields. Previously, hydrometeor fields were assumed to follow a multivariate single lognormal distribution. Now, in order to better represent the distribution of hydrometeors, two new multivariate PDFs are formulated and introduced.The new PDFs represent hydrometeors using either a delta-lognormal or a delta-double-lognormal shape. The two new PDF distributions, plus the previous single lognormal shape, are compared to histograms of data taken from large-eddy simulations (LESs) of a precipitating cumulus case, a drizzling stratocumulus case, and a deep convective case. Finally, the warm microphysical process rates produced by the different hydrometeor PDFs are compared to the same process rates produced by the LES.

scholarly journals Mixing and combustion at low heat release in large eddy simulations of a reacting shear layer

2021 ◽  
Author(s):  
J. X. Huang ◽  
W. A. McMullan
Keyword(s):  
Probability Density Function ◽  
Heat Release ◽  
Shear Layer ◽  
Probability Density ◽  
Density Function ◽  
Temperature Rise ◽  
Mixing Layer ◽  
Large Eddy ◽  
Inflow Condition ◽  
The Mean

AbstractIn this paper, the mixing and combustion at low-heat release in a turbulent mixing layer are studied numerically using large eddy simulation. The primary aim of this paper is to successfully replicate the flow physics observed in experiments of low-heat release reacting mixing layers, where a duty cycle of hot structures and cool braid regions was observed. The nature of the imposed inflow condition shows a dramatic influence on the mechanisms governing entrainment, and mixing, in the shear layer. An inflow condition perturbed by Gaussian white noise produces a shear layer which entrains fluid through a nibbling mechanism, which has a marching scalar probability density function where the most probable scalar value varies across the layer, and where the mean-temperature rise is substantially over-predicted. A more sophisticated inflow condition produced by a recycling and rescaling method results in a shear layer which entrains fluid through an engulfment mechanism, which has a non-marching scalar probability density function where a preferred scalar concentration is present across the thickness of the layer, and where the mean-temperature rise is predicted to a good degree of accuracy. The latter simulation type replicates all of the flow physics observed in the experiment. Extensive testing of subgrid-scale models, and simple combustion models, shows that the WALE model coupled with the Steady Laminar Flamelet model produces reliable predictions of mixing layer diffusion flames undergoing with fast chemistry.

Sign in / Sign up

Export Citation Format

Share Document