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Study of the probability density functions from a large-eddy simulation for a stably stratified boundary layer

BOUNDARY-LAYER METEOROLOGY 2006年第2期118卷 401-420页

作者： Jimenez, M. A. Cuxart, J. Univ Illes Balears Dept Fis Grp Meteorol E-07071 Palma de Mallorca Spain

Turbulence in a non-strongly stably stratified large-eddy simulation (LES) case is studied through probability density functions (PDFs) to obtain additional information than that provided by classical LES averages. The PDFs are computed for one hour within the steady-state regime at three different levels: near the surface, in the middle and at the top of the boundary layer, for the wind components and the temperature. The physical significance of these PDFs from LES is discussed and they are compared to those obtained from observations. The analysis of the eddy structures within the stably stratified boundary layer is made through the combined study of the fields, the spectra and the statistical moments obtained from the PDFs and joint PDFs. The homogeneity of the fields is inspected through a comparison of the ensemble to the temporal and the spatial PDFs, showing that the ergodic theorem is not fulfilled. To this end, the sensitivity of the PDF moments to the LES resolution is explored.

关键词： ergodicity gaussianity large-eddy simulations probability density functions stably stratified boundary layer

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Phase transitions to superionic Li₂Te and Li₂Se - A high-temperature neutron powder diffraction study, atom displacements, probability density functions and atom potentials

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SOLID STATE IONICS 2018年 325卷 90-101页

作者： Schneider, Julius Schroeder, Thorsten Hoelzel, Markus Kluge, Oliver Schmahl, Wolfgang W. Oeckler, Oliver Ludwig Maximilian Univ Munich Crystallog Sect Dept Geo & Environm Sci Theresienstr 41 D-80333 Munich Germany Tech Univ Munich Heinz Maier Leibnitz Zentrum MLZ D-85748 Garching Germany Univ Leipzig Inst Inorgan Chem Johannisallee 29 D-04103 Leipzig Germany Univ Leipzig Inst Mineral Crystallog & Mat Sci Scharnhorststr 20 D-04275 Leipzig Germany

Despite much research on Li ion batteries at ambient temperature, Li-ion conductors at high temperature have received less attention. In the series of ionic Li2X compounds (X = O, S, Se, Te), superionic phase transitions have been reported for Li2O and Li2S. The lower transition temperature of Li2S, supposedly caused by the larger anion size of S, inspired the investigation of the superionic behavior of Li2Se and Li2Te. Their thermal expansion and thermally excited spatial distribution of Li cations and Se/Te anions was monitored by neutron diffraction up to 800 degrees C for Li2Te and up to 1000 degrees C for Li2Se. Both compounds exhibit positive thermal expansion with changing coefficient of expansivity at the superionic transition temperatures. No deviation from cubic metrics or abrupt changes of the cell volume were observed. Rietveld refinements of the fluorite-type structures (space group Fm (3) over barm) employing Gaussian spatial distribution functions reveal discontinuities in the slope of the increasing mean square displacement parameters as a function of temperature. At similar to 600 degrees C (Li2Te) and similar to 780 degrees C (Li2Se), the mean square displacements of Li atoms increase abruptly, indicating a superionic transition. For the Te/Se anions, similar discontinuities occur at slightly lower temperatures. Difference Fourier syntheses reveal strongly anisotropic Li spatial distribution density around the 8c (1/4 1/4 1/4) positions of cubic site symmetry m (3) over barm. Moving the maximum of the density distribution to adjacent 32f (xxx) (site symmetry.3 m) positions introduces four virtual split atoms. In addition to the small displacement x along <111>, denoting the mean positions of the split atoms, anisotropic spatial distributions may then be refined. Whereas x deviates from 1/4 as an almost linear function of temperature, the abrupt changes in the increase of mean square amplitudes of thermal displacements with temperature are retained.

关键词： Superionic phase transitions Lithium chalcogenides High-temperature neutron powder diffraction Atom displacement parameters probability density functions

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Flammability limits and probability density functions in simulated solid-fuel ramjet combustors

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JOURNAL OF PROPULSION AND POWER 1997年第5期13卷 643-650页

作者： Liou, TM Lien, WY Hwang, PW National Tsing Hua Univ. Hsinchu Taiwan

A numerical analysis was performed to study turbulent reacting flows in solid-fuel ramjet combustors. The time-dependent axisymmetric compressible conservation equations were solved with a subgrid-scale turbulence model. The combustion profess considered was a one-step, irreversible, and infinitely fast chemical reaction. The numerical code used the finite volume technique, which involved alternating in time the second-order, explicit MacCormack's and modified Godunov's schemes. Computed temperature profiles are compared with existing experimental data and the previous calculations, incorporating the k-epsilon turbulence model and two-layer near-wail treatment. The superiority of the present predictions is demonstrated. Flammability limits in solid-fuel ramjet combustors have been determined using the characteristic exhaust velocity, Moreover, a compact correlation relating the minimum step height to the combustor diameter, air mass now rate, and equivalence ratio for sustained combustion is provided for practical design reference. probability density function (PDF) profiles of temperature and mixture fraction are also analyzed to understand the thermal structure of turbulent flames, and to provide information for examining the applicability of the conserved-scalar approach incorporated PDF models to turbulent-reacting flows.

关键词： probability density functions Solid Fuel Ramjet Combustor Turbulence Models Combustion Process Exhaust Velocity Conservation Equations Numerical Analysis Turbulent Boundary Layer Turbulence Kinetic Energy Combustion Chambers

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COMPUTER-PROGRAM FOR GRAPHICAL AND ITERATIVE FITTING OF probability density functions TO BIOLOGICAL DATA

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COMPUTER PROGRAMS IN BIOMEDICINE 1975年第1期5卷 11-38页

作者： BRASSARD, JR CORREIA, MJ LANDOLT, JP UNIV TEXAS MED BRANCHDEPT OTOLARYNGOLGALVESTONTX 77550 DEF & CIVIL INST ENVIRONM MED POB 2000DOWNSVIEW M3M 3B9ONTARIOCANADA

A tutorially-assisted, interactive program, written for a Digital Equipment Corporation LAB-11 minicomputer (PDP-11/20), is described which allows a user to fit (with or without automatic estimation of initial parameter values), by a method of nonlinear least squares, any one of seven different types of probability density functions (p.d.f.'s) to an empirical frequency distribution; the latter of which may be input to the program or formed by the program whenever it is furnished a series of times between events. The iteratively-obtained, “best fit” p.d.f. is displayed on a two color, point-plot display against the background of a point-plot histogram. By selecting any one of nine output modes, the user is allowed: (1) to view histograms successively on the point-plot display, (2) to generate selected p.d.f.'s, (3) to “force” p.d.f.'s having known parameters through the histogram data, (4) to obtain Chi-square ( χ 2 ) and Kolmogorov-Smirnov estimates of the goodness of fit to the data, and (5) to apply a special test [Williams and Kloot, 1953] in order to determine whether the least squares estimates of two candidate models are statistically different. The resident driver program and the four overlayable program segments are written in standard FORTRAN IV; except for two plot routines, which are written in PDP-11 assembly language.

关键词： Biostatistics probability density functions Least Squares Minicomputer Interactive program Nonlinear curve fitting Parameter estimation Neuromathematical techniques

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Development of design flood hydrographs using probability density functions

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HYDROLOGICAL PROCESSES 2010年第4期24卷 415-428页

作者： Pramanik, Niranjan Panda, Rabindra K. Sen, Drubajyoti Indian Inst Technol Agr & Food Engn Dept Kharagpur 721302 W Bengal India Indian Inst Technol Dept Civil Engn Kharagpur 721302 W Bengal India

probability density functions (PDFs) are used to fit the shape of hydrographs and have been popularly used for the development of synthetic unit hydrographs by many hydrologists. Nevertheless, modelling the shapes of continuous stream flow hydrographs, which are probabilistic in nature, is rare. In the present study, a novel approach was followed to model the shape of stream flow hydrographs using PDF and subsequently to develop design flood hydrographs for various return periods. Four continuous PDFs, namely, two parameter Beta, Weibull, Gamma and Lognormal, were employed to fit the shape of the hydrographs of 22 years at a site of Brahmani River in eastern India. The shapes of the observed and PDF fitted hydrographs were compared and root mean square errors, error of peak discharge (EQ(P)) and error of time to peak (ETP) were computed. The best-fitted shape and scale parameters of all PDFs were subjected to frequency analysis and the quartiles corresponding to 20-, 50-, 100- and 200-year were estimated. The estimated parameters of each return period were used to develop the flood hydrographs for 20-, 50-, 100-and 200-year return periods. The peak discharges of the developed design flood hydrographs were compared with the design discharges estimated from the frequency analysis of 22 years of annual peak discharges at that site. Lognormal-produced peak discharge was very close to the estimated design discharge in case of 20-year flood hydrograph. On the other hand, peak discharge obtained using the Weibull PDF had close agreement with the estimated design discharge obtained from frequency analysis in case of 50-, 100-and 200-year return periods. The ranking of the PDFs based on estimation of peak of design flood hydrograph for 50-, 100-and 200-year return periods was found to have the following order: Weibull > Beta > Lognormal > Gamma. Copyright (C) 2009 John Wiley & Sons, Ltd.

关键词： design flood hydrograph probability density functions frequency analysis

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A database of saturated hydraulic conductivity of fine-grained soils: probability density functions

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GEORISK-ASSESSMENT AND MANAGEMENT OF RISK FOR ENGINEERED SYSTEMS AND GEOHAZARDS 2019年第4期13卷 255-261页

作者： Feng, Shuyin Vardanega, Paul J. Univ Bristol Dept Civil Engn Univ Walk Bristol BS8 1TR Avon England

Saturated hydraulic conductivity is a key soil mechanics parameter which has widespread use in many geotechnical applications. In order to set up stochastic analyses, geotechnical modellers require databases to calibrate the parameter ranges and distributions employed. This letter uses a recently compiled database of saturated hydraulic conductivity measurements called FG/KSAT-1358 and reports on the fitting of various probability density functions to the data of void ratio, liquid limit, water content ratio and the negative natural logarithm of k(sat). It is shown that the best fit distribution is the lognormal for void ratio, while the loglogistic distribution is most favoured for liquid limit and water content ratio, and the best fit distribution for -ln[k(sat)(m/s)] is the logistic function. The data of -ln[k(sat)(m/s)] is then subdivided according to liquid limit level, silt or clay classification, type of hydraulic conductivity test used and sample preparation/condition. When some subdivisions of the database are analysed, the best fit distribution is more variable with GEV and logistic being the most favoured for most of the studied subsets.

关键词： Saturated hydraulic conductivity probability density functions Akaike information criterion corrected Akaike information criterion

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INSTAT: a program for computing non-ideal probability density functions of |E|

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JOURNAL OF APPLIED CRYSTALLOGRAPHY 2013年第5期46卷 1521-1522页

作者： Shmueli, Uri Tel Aviv Univ Sch Chem IL-69978 Tel Aviv Israel

The purpose of this program is to evaluate probability density functions (p.d.f.s) of the magnitude of the normalized structure factor vertical bar E vertical bar for the space groups of the triclinic, monoclinic and orthorhombic systems, and for any chemical composition of the asymmetric unit, assuming that the atoms are located in general positions. The p.d.f.s are computed by the Fourier and Fourier-Bessel methods [see e.g. Shmueli (2012). J. Appl. Cryst. 45, 389-392]. The p.d.f.s evaluated are scaled together with the histogram of observed vertical bar E vertical bar values and discrepancy criteria are computed. In addition to the above non-ideal p.d.f.s, the ideal p.d.f.s [Wilson (1949). J. Appl. Cryst. 2, 318-321] are also computed and prepared for comparison with an experimental histogram. (C) 2013 International Union of Crystallography Printed in Singapore - all rights reserved

关键词： probability density functions INSTAT computer programs

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Wind energy forecasting by fitting predicted probability density functions of wind speed measurements

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INTERNATIONAL JOURNAL OF ENERGY AND ENVIRONMENTAL ENGINEERING 2022年第2期13卷 573-585页

作者： Abdul Majid, Amir J. Univ Sci & Technol Fujairah Coll Engn & Technol POB 2202 Al Fujairah U Arab Emirates

The aim of this work is to forecast wind energy by fitting the wind speed logged data, that have been measured over a year period (Nov. 2019-Mar. 2021), on a unique probability density function selected among a number of similar probability functions, as it is not always possible to select one distribution function that fits all wind speed regimes. The wind speed and direction data were measured at Fujairah site, which are affected by long-term fluctuation of +/- 10% of wind speed, and short-term fluctuation of more than +/- 20%. Based on the foregoing measurements, five different probability density functions can be fitted, namely Weibull, Rayleigh, Gamma, Lognormal and Exponential, with their associated parameters. A procedural algorithm is proposed for wind speed forecasting with best selected fitting distribution function, using a procedural forecast-check method, in which forecasting is performed with time on the most suitable distribution function that fits the foregoing data, depending on minimum errors accumulated from preceded measurements. Different error estimation methods are applied. The algorithm of selecting different distribution functions with time, makes energy prediction more accurate depending on the fluctuation of wind speed. A detailed probabilistic analysis is carried out to predict probable wind speed, and hence wind energy, based on variations of the parameters of the selected fitting distribution function.

关键词： Energy forecasting Error estimation Curve fitting probability density functions Procedural algorithm Speed prediction

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ON THE PARAMETER SPACE DERIVED FROM THE JOINT probability density-functions AND THE PROPERTY OF ITS SCALAR CURVATURE

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JOURNAL OF GEOMETRY AND PHYSICS 1995年第2期17卷 185-189页

作者： YAMADA, M MIYATA, M KAWAGUCHI, T UNIV TSUKUBA DEPT ELECTR & INFORMAT SCITSUKUBAIBARAKI 305JAPAN SAITAMA COLL INST INFORMAT SCIKAZO 347JAPAN

Extended parameter spaces were introduced by Kawaguchi et al. (1992) to define the geometrical distance between two probability distributions having different function forms. A statistical interpretation of the extended parameter spaces was introduced. In this paper, the property of the scalar curvature of extended parameter spaces is given.

关键词： probability density functions PARAMETER SPACE CURVATURE

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probability density functions of Channel Estimation for MLSE in Optical Communications

Probability Density Functions of Channel Estimation for MLSE...

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Asia Communications and Photonics Conference and Exhibition (ACP)

作者： Lu, Li Lei, Jianming Ju, Peijian Lei, Yu Peng, Zhan Zou, Xuecheng Huazhong Univ Sci & Technol Dept Elect Sci & Technol Wuhan 430074 Peoples R China Air Force Radar Acad Wuhan 430019 Peoples R China

ISBN: (纸本)9780819489616

In this paper, we propose an effective possibility density functions method of channel estimation with Viterbi algorithm based on transitions. We also investigate the performance of the electronic dispersion compensation schemes via this new channel estimation method. The schemes Simulation results show that it exhibits the similar performance with the sophisticated MLSE scheme.

关键词： probability density functions Viterbi MLSE Channel Estimation Optical Communications

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