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Representation of three-dimensional mass distribution of the Earth's interior by biorthogonal series and its use for studying internal structure of the planet
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作者 Mykhailo Fys Mariana Yurkiv +1 位作者 Andrii Brydun Andrii Sohor 《Geodesy and Geodynamics》 EI CSCD 2024年第3期264-275,共12页
This paper utilizes the mathematical concept of approximation within an ellipsoid from a single viewpoint to present the spatial mass distribution function of the Earth's interior and its internal potential.The pr... This paper utilizes the mathematical concept of approximation within an ellipsoid from a single viewpoint to present the spatial mass distribution function of the Earth's interior and its internal potential.The primary focus lies in constructing the volume distribution of masses in the planet's interior, with the expansion coefficients being linear combinations of the Stokes constants. Several possible approaches are suggested for determining accurately these coefficients employing three-dimensional(biorthogonal)polynomials. By expressing the mass distribution function of the Earth's interior and its internal potential as a series, an algorithm is introduced for the calculation of gravitational energy. It allows us to estimate fluctuations in gravitational energy. The implementation of this algorithm offers the means of establishing the extent to which the Earth deviates from a state of hydrostatic equilibrium as a celestial body.Due to the aforementioned method, calculations have been conducted to validate its effectiveness and reliability. This example is given as an illustration of a given method for studying the internal structure of planets. 展开更多
关键词 Mass distribution function Potential Stokes constants Biorthogonal polynomials
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Approximating the Radial Distribution Function of the Electron in a Hydrogen Atom by a Normal Distribution Suggests That Magnetic Confinement Fusion Would Be Less Energy Efficient than Inertial Confinement Fusion
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作者 Motohisa Osaka 《Applied Mathematics》 2024年第9期585-593,共9页
Since the position of the electron in a hydrogen atom cannot be determined, the region in which it resides is said to be determined stochastically and forms an electron cloud. The probability density function of the s... Since the position of the electron in a hydrogen atom cannot be determined, the region in which it resides is said to be determined stochastically and forms an electron cloud. The probability density function of the single electron in 1s orbit is expressed as φ2, a function of distance from the nucleus. However, the probability of existence of the electron is expressed as a radial distribution function at an arbitrary distance from the nucleus, so it is estimated as the probability of the entire spherical shape of that radius. In this study, it has been found that the electron existence probability approximates the radial distribution function by assuming that the probability of existence of the electron being in the vicinity of the nucleus follows a normal distribution for arbitrary x-, y-, and z-axis directions. This implies that the probability of existence of the electron, which has been known only from the distance information, would follow a normal distribution independently in the three directions. When the electrons’ motion is extremely restricted in a certain direction by the magnetic field of both tokamak and helical fusion reactors, the probability of existence of the electron increases with proximity to the nucleus, and as a result, it is less likely to be liberated from the nucleus. Therefore, more and more energy is required to free the nucleus from the electron in order to generate plasma. 展开更多
关键词 Electron Cloud Radial distribution Function Nuclear Fusion TOKAMAK Laser
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Simulation of Haloxylon Ammodendron Stand Basic Diameter Structure Based on Fuzzy Distribution Function
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作者 Shaohua Wang Chuanqiang Liu Ting Yang 《Agricultural Sciences》 2024年第1期132-145,共14页
Based on the investigation data of 12 Haloxylon ammodendron plots in the south edge of Gurbantunggut Desert, Fuzzy distribution was introduced into the study of Haloxylon ammodendron base diameter structure fitting ac... Based on the investigation data of 12 Haloxylon ammodendron plots in the south edge of Gurbantunggut Desert, Fuzzy distribution was introduced into the study of Haloxylon ammodendron base diameter structure fitting according to the consistency between the characteristics of Fuzzy distribution function and the distribution series of cumulative percentage of stand base diameter, and the fitting precision and effect of Fuzzy distribution function were discussed. The root mean square error RMSE and determination coefficient R<sup>2</sup> values showed that Fuzzy-Γ<sub>1</sub>, Fuzzy-Γ<sub>2</sub>, Fuzzy-Γ<sub>3</sub>, Fuzzy-Γ<sub>4</sub> had good fitting performance, among which Fuzzy-Γ<sub>1</sub> had relatively high fitting precision, and its parameters were closely related to stand age and density, Fuzzy-Γ<sub>2</sub> distribution function was the second, and Fuzzy-Γ<sub>4</sub> distribution function had the worst fitting effect. By introducing a parameter c from the similarity of four distribution function formulas, a generalized Fuzzy distribution function Fuzzy-Γ<sub>5</sub> is obtained. This function shows the highest fitting accuracy. Most of the values of parameter c are near 1 or 2, which shows that the diameter distribution is mainly approximate to Fuzzy-Γ<sub>1</sub> and Fuzzy-Γ<sub>2</sub>. 展开更多
关键词 Fuzzy distribution Function Haloxylon Ammodendron Base Diameter distribution Stand Factor
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A Novel Statistical Delay Model Based on the Birnbaum-Saunders Distribution for RLC Interconnects in 90nm Technologies
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作者 周磊 孙玲玲 蒋立飞 《Journal of Semiconductors》 EI CAS CSCD 北大核心 2008年第7期1313-1317,共5页
For performance optimization such as placement,interconnect synthesis,and routing, an efficient and accurate interconnect delay metric is critical,even in design tools development like design for yield (DFY) and des... For performance optimization such as placement,interconnect synthesis,and routing, an efficient and accurate interconnect delay metric is critical,even in design tools development like design for yield (DFY) and design for manufacture (DFM). In the nanometer regime, the recently proposed delay models for RLC interconnects based on statistical probability density function (PDF)interpretation such as PRIMO,H-gamma,WED and RLD bridge the gap between accuracy and efficiency. However, these models always require table look-up when operating. In this paper, a novel delay model based on the Birnbaum-Saunders distribution (BSD) is presented. BSD can accomplish interconnect delay estimation fast and accurately without table look-up operations. Furthermore, it only needs the first two moments to match. Experimental results in 90nm technology show that BSD is robust, easy to implement,efficient,and accurate. 展开更多
关键词 delay model INTERCONNECT MOMENT probability distribution function
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Molecular simulation study of the microstructures and properties of pyridinium ionic liquid[HPy][BF_(4)]mixed with acetonitrile
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作者 XU Jian-Qiang MA Zhao-Peng +2 位作者 CHENG Si LIU Zhi-Cong ZHU Guang-Lai 《原子与分子物理学报》 CAS 北大核心 2025年第4期27-32,共6页
The microstructures and thermodynamic properties of mixed systems comprising pyridinium ionic liquid[HPy][BF_(4)]and acetonitrile at different mole fractions were studied using molecular dynamics simulation in this wo... The microstructures and thermodynamic properties of mixed systems comprising pyridinium ionic liquid[HPy][BF_(4)]and acetonitrile at different mole fractions were studied using molecular dynamics simulation in this work.The following properties were determined:density,self-diffusion coefficient,excess molar volume,and radial distribution function.The results show that with an increase in the mole fraction of[HPy][BF_(4)],the self-diffusion coefficient decreases.Additionally,the excess molar volume initially decreases,reaches a minimum,and then increases.The rules of radial distribution functions(RDFs)of characteristic atoms are different.With increasing the mole fraction of[HPy][BF_(4)],the first peak of the RDFs of HA1-F decreases,while that of CT6-CT6 rises at first and then decreases.This indicates that the solvent molecules affect the polar and non-polar regions of[HPy][BF_(4)]differently. 展开更多
关键词 Pyridinium ionic liquids Thermodynamic properties Molecular dynamics simulation Radial distribution functions
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Some Notes of Property of Distribution Function of Many Variables
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作者 孔繁超 张曙光 《Chinese Quarterly Journal of Mathematics》 CSCD 1992年第1期60-64,共5页
In this paper we discuss a step further some convergence and continuity problems of distribution function on R^i. We give the following results: (1)distribution function F(x_1,…,x_k) on R^k is continuous if and only ... In this paper we discuss a step further some convergence and continuity problems of distribution function on R^i. We give the following results: (1)distribution function F(x_1,…,x_k) on R^k is continuous if and only if all marginal distribution functions of F is continuous on R^1. (2)If limF_n(x_1,……,x_k)=F(x_1,…,x_k) and limF_n(x_1—0,…,x_k—0)=F(x_1—0,…,x_k—0) at all non-continuity points of F, then 展开更多
关键词 probability space distribution function
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Joint probability distribution of winds and waves from wave simulation of 20 years (1989-2008) in Bohai Bay 被引量:10
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作者 Xiao-chen YANG Qing-he ZHANG 《Water Science and Engineering》 EI CAS CSCD 2013年第3期296-307,共12页
The joint probability distribution of wind speed and significant wave height in the Bohai Bay was investigated by comparing the Gurnbel logistic model, the Gumbel-Hougaard (GH) copula function, and the Clayton copul... The joint probability distribution of wind speed and significant wave height in the Bohai Bay was investigated by comparing the Gurnbel logistic model, the Gumbel-Hougaard (GH) copula function, and the Clayton copula function. Twenty years of wind data from 1989 to 2008 were collected from the European Centre for Medium-Range Weather Forecasts (ECMWF) database and the blended wind data of the Quick Scatterometer (QSCAT) satellite data set and re-analysis data from the United States National Centers for Environmental Prediction (NCEP). Several typhoons were taken into account and merged with the background wind fields from the ECMWF or QSCAT/NCEP database. The 20-year data of significant wave height were calculated with the unstructured-grid version of the third-generation wind wave model Simulating WAves Nearshore (SWAN) under extreme wind process conditions. The Gumbel distribution was used for univariate and marginal distributions. The distribution parameters were estimated with the method of L-moments. Based on the marginal distributions, the joint probability distributions, the associated return periods, and the conditional probability distributions were obtained. The GH copula function was found to be optimal according to the ordinary least squares (OLS) test. The results show that wind waves are the prevailing type of wave in the Bohai Bay. 展开更多
关键词 wind speed wave simulation joint probability distribution copula function conditional probability distribution
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Estimation of Hourly and Daily Global Solar Radiation at Clear Days Using an Approach Based on Modified Version of Gaussian Distribution 被引量:4
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作者 S.M EI shazly 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 1996年第3期349-358,共10页
The performance of two models,Jam and Baig,based on the modified version of Gaussian distribution function in estimating the daily total of global solar radiation and its distribution through the hours of the day from... The performance of two models,Jam and Baig,based on the modified version of Gaussian distribution function in estimating the daily total of global solar radiation and its distribution through the hours of the day from sunrise to sunset al any clear day is evaluated with our own measured data in the period from June 1992 to May 1993 in Qena Egypt The results show a high relative deviation of calculated values from measured ones,especially for Jain model,in the most hours of the day,except for those near to local noon.This misfit behavior is quite obvious in the early morning and late afternoon A new approach has been proposed in this paper to estimate the daily and hourly global solar radiation This model performs with very high accuracy on the recorded data in our region.The validity of this approach was verified with new measurements in some clear days in June and August 1994.The resultant very low relative deviation of the calculated values of global solar radiation from the measured ones confirms the high performance of the approach proposed in this work 展开更多
关键词 Glohal solar radiation . Measurements Models Gaussian distribution function Statistical treatment
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Developing Weibull-based diameter distributions for the major coniferous species in Heilongjiang Province,China 被引量:3
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作者 Qila Sa Xingji Jin +1 位作者 Timo Pukkala Fengri Li 《Journal of Forestry Research》 SCIE CAS CSCD 2023年第6期1803-1815,共13页
Diameter distribution models play an important role in forest inventories,growth prediction,and management.The Weibull probability density function is widely used in forestry.Although a number of methods have been pro... Diameter distribution models play an important role in forest inventories,growth prediction,and management.The Weibull probability density function is widely used in forestry.Although a number of methods have been proposed to predict or recover the Weibull distribution,their applicability and predictive performance for the major tree species of China remain to be determined.Trees in sample plots of three even-aged coniferous species(Larix olgensis,Pinus sylvestris and Pinus koraiensis)were measured both in un-thinned and thinned stands to develop parameter prediction models for the Weibull probability density function.Ordinary least squares(OLS)and maximum likelihood regression(MLER),as well as cumulative distribution function regression(CDFR)were used,and their performance compared.The results show that MLER and CDFR were better than OLS in predicting diameter distributions of tree plantations.CDFR produced the best results in terms of fitting statistics.Based on the error statistics calculated for different age groups,CDFR was considered the most suitable method for developing prediction models for Weibull parameters in coniferous plantations. 展开更多
关键词 Parameter prediction Maximum likelihood regression Cumulative distribution function regression
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Three-Component Model for Bidirectional Reflection Distribution Function of Thermal Coating Surfaces 被引量:2
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作者 刘宏 朱京平 +2 位作者 王凯 王秀红 徐蓉 《Chinese Physics Letters》 SCIE CAS CSCD 2016年第6期33-36,共4页
We present a bidirectional reflection distribution function (BRDF) model for thermal coating surfaces based on a three-component reflection assumption, in which the specular reflection is given according to the micr... We present a bidirectional reflection distribution function (BRDF) model for thermal coating surfaces based on a three-component reflection assumption, in which the specular reflection is given according to the microfacet theory and Snell's law, the multiple reflection is considered Nth cosine distributed, and the volume scattering is uniformly distributed in reflection angles according to the experimental results. This model describes the reflection characteristics of thermal coating surfaces more completely and reasonably. Simulation and measurement results of two thermal coating samples SR107 and S781 are given to validate that this three-component model significantly improves the modeling accuracy for thermal coating surfaces compared with the existing BRDF models. 展开更多
关键词 for in BRDF Three-Component Model for Bidirectional Reflection distribution Function of Thermal Coating Surfaces of
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Influence of Generalized (r, q) Distribution Function on Electrostatic Waves 被引量:2
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作者 M.N.S. Qureshi SHI Jian-Kui MA Shi-Zhuang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第3期550-554,共5页
Non-Maxwellian particle distribution functions possessing high energy tail and shoulder in the profile of distribution function considerably change the damping characteristics of the waves. In the present paper Landau... Non-Maxwellian particle distribution functions possessing high energy tail and shoulder in the profile of distribution function considerably change the damping characteristics of the waves. In the present paper Landau damping of electron plasma (Langmuir) waves and ion-acoustic waves in a hot, isotropic, unmagnetized plasma is studied with the generalized (r, q) distribution function. The results show that for the Langmuir oscillations Landau damping becomes severe as the spectral index r or q reduces. However, for the ion-acoustic waves Landau damping is more sensitive to the ion temperature than the spectral indices. 展开更多
关键词 generalized (r q) distribution function electrostatic waves DAMPING
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Research on the behavior of fiber orientation probability distribution function in the planar flows 被引量:2
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作者 周锟 林建忠 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2005年第4期257-264,共8页
The equation of two-dimensional fiber direction vector was solved theoretically to give the fiber orientation distri- bution in simple shear flow, flow with two direction shears, extensional flow and arbitrary planar ... The equation of two-dimensional fiber direction vector was solved theoretically to give the fiber orientation distri- bution in simple shear flow, flow with two direction shears, extensional flow and arbitrary planar incompressible flow. The Fok- ker-Planck equation was solved numerically to validify the theoretical solutions. The stable orientation and orientation period of fiber were obtained. The results showed that the fiber orientation distribution is dependent on the relative not absolute magnitude of the matrix rate-of-strain of flow. The effect of fiber aspect ratio on the orientation distribution of fiber is insignificant in most conditions except the simple shear case. It was proved that the results for a planar flow could be generalized to the case of 3-D fiber direction vector. 展开更多
关键词 Fiber suspension flow Orientation distribution Probability distribution function
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Stability of the Dividing Distribution Function Method for ParticleSize Distribution Analysis in Small Angle X-Ray Scattering 被引量:2
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作者 Zhang Jinyuan Liu Chunlan Chen Yan 《Journal of Iron and Steel Research International》 SCIE EI CAS CSCD 1996年第1期51-52,63+54-55,共5页
The Dividing Distribution Function (DDF) method is one of the methods by which the particle size distribution of ultrafine powder can be evaluated from its small angle X-ray scattering data. In this paper, the stabili... The Dividing Distribution Function (DDF) method is one of the methods by which the particle size distribution of ultrafine powder can be evaluated from its small angle X-ray scattering data. In this paper, the stability of the solution obtained from DDF method has been investigated through optimizing the coefficient matrix, introducing a damping factor and a least square treatment. All calculations were accomplished with a microcomputer. It was shown that the average deviations of the size distribution obtained are not larger than the assigned random errors to the scattering intensities as long as the corresponding requirements are satisfied. 展开更多
关键词 ultrafine powder particle size distribution small angle X-ray scattering dividing distribution function method
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A statistical distribution of quad-pol X-band sea clutter time series acquired at a grazing angle 被引量:2
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作者 WANG Yunhua LI Qun ZHANG Yanmin 《Acta Oceanologica Sinica》 SCIE CAS CSCD 2018年第3期94-102,共9页
Although the complex Wishart distribution has been widely used to analyze the statistic properties of quad-pol SAR spatial data, the applicability of this complex distribution to the time series of sea clutter is rare... Although the complex Wishart distribution has been widely used to analyze the statistic properties of quad-pol SAR spatial data, the applicability of this complex distribution to the time series of sea clutter is rarely discussed.The measured data of the quad-pol X-band marine radar demonstrate that the time series of the sea echoes are also satisfied the circular Gaussian distributions if the low intensity signals, which are mainly dominated by a radar noise, in the shadow regions of the large-scale waves are removed. On the basis of this fact, the probability density functions(PDFs) of the intensity as well as the phase, the real and the imaginary parts of the sea echoes obtained by the marine radar have been derived, and the theoretical models are all expressed in closed forms. In order to validate the theoretical results, the PDFs are compared with the experimental data collected by the Mc Master IPIX radar. And the comparisons show that the PDF models are in good agreement with the experimental data. 展开更多
关键词 sea clutter quad-pol coherent X-band radar statistical distribution function
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Extreme value distributions of mixing two sequences with different MDA's 被引量:2
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作者 蒋岳祥 《Journal of Zhejiang University Science》 CSCD 2004年第5期509-517,共9页
Suppose {Xi, i≥1} and {Yi, i≥1} are two independent sequences with distribution functions FX(x) and FY(x), respectively. Zi is the combination of Xi and Yi with a probability pn for each i with 1≤i≤n. The extreme ... Suppose {Xi, i≥1} and {Yi, i≥1} are two independent sequences with distribution functions FX(x) and FY(x), respectively. Zi is the combination of Xi and Yi with a probability pn for each i with 1≤i≤n. The extreme value distribution ,n GZ(x) of this particular triangular array of the i.i.d. random variables Z1, , Z2, ,…, Zn n n ,nis discussed. We found a new form of the extreme value distribution ΛA(ρx)Λ(x)(0<ρ <1), which is not max-stable. It occurs if FX(x) and FY(x) belong to the same MDA(Λ). GZ(x) does not exist as mixture forms of the different types of extreme value distributions. 展开更多
关键词 Extreme value distribution Maximum domain of attraction(MDA) Mixed distribution functions
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A prediction model for the effective thermal conductivity of nanofluids considering agglomeration and the radial distribution function of nanoparticles 被引量:1
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作者 Z.M.Zheng B.Wang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2018年第3期507-514,共8页
Conventional heat transfer fluids usually have low thermal conductivity, limiting their efficiency in many applications. Many experiments have shown that adding nanosize solid particles to conventional fluids can grea... Conventional heat transfer fluids usually have low thermal conductivity, limiting their efficiency in many applications. Many experiments have shown that adding nanosize solid particles to conventional fluids can greatly enhance their thermal conductivity. To explain this anomalous phenomenon, many theoretical investigations have been conducted in recent years. Some of this research has indicated that the particle agglomeration effect that commonly occurs in nanofluids should play an important role in such enhancement of the thermal conductivity, while some have shown that the enhancement of the effective thermal conductivity might be accounted for by the structure of nanofluids, which can be described using the radial distribution function of particles. However, theoretical predictions from these studies are not in very good agreement with experimental results. This paper proposes a prediction model for the effective thermal conductivity of nanofluids, considering both the agglomeration effect and the radial distribution function of nanoparticles. The resulting theoretical predictions for several sets of nanofluids are highly consistent with experimental data. 展开更多
关键词 NANOFLUID Thermal conductivity MODELING AGGLOMERATION Radial distribution function
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Theoretical Approach to Concentration Distribution and Adhesion Efficiency of Fine Particles Around a Rising Bubble in Slurry Systems 被引量:1
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作者 蔡旺锋 许春建 周明 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2002年第5期550-557,共8页
Quantitative prediction of distribution function and adhesionefficiency of particles around a rising bubble in slurry systems ispresented in this work. By solving the convection-diffusion equation(Fokker-Planck equati... Quantitative prediction of distribution function and adhesionefficiency of particles around a rising bubble in slurry systems ispresented in this work. By solving the convection-diffusion equation(Fokker-Planck equation), the influence of Brownian diffusivity offine particles on concentration distribution and adhesion efficiencyis demonstrated with the hydrodynamic force and van der Waalsattractive potential between particles and bubble considered. It isfound that two kinds of mechanism dominate the adhesion process ofparticles on bubble according to different Peclet number or size ofparticles and bubble, as well as other properties of the slurrysystems. In addition, the viscosity ratio of bubble to the suspendingfluid was found to have obvious influence on particle adhesion. 展开更多
关键词 adhesion efficiency Brownian diffusivity distribution function Fokker-Planck equation
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PROBABILITY DISTRIBUTION FUNCTION OF NEAR-WALL TURBULENT VELOCITY FLUCTUATIONS 被引量:1
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作者 周济福 张强 李家春 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第10期1245-1254,共10页
By large eddy simulation (LES), turbulent databases of channel flows at different Reynolds numbers were established. Then, the probability distribution functions of the streamwise and wall-normal velocity fluctuatio... By large eddy simulation (LES), turbulent databases of channel flows at different Reynolds numbers were established. Then, the probability distribution functions of the streamwise and wall-normal velocity fluctuations were obtained and compared with the corresponding normal distributions. By hypothesis test, the deviation from the normal distribution was analyzed quantitatively. The skewness and flatness factors were also calculated. And the variations of these two factors in the viscous sublayer, buffer layer and log-law layer were discussed. Still illustrated were the relations between the probability distribution functions and the burst events-sweep of high-speed fluids and ejection of low-speed fluidsIin the viscous sub-layer, buffer layer and loglaw layer. Finally the variations of the probability distribution functions with Reynolds number were examined. 展开更多
关键词 near-wall turbulence large eddy simulation velocity fluctuation probability distribution function SKEWNESS FLATNESS
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QCD Predictions for Spin Dependence of Parton Distributions 被引量:1
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作者 S.AtashbarTehrani AliN.Khorramian A.Mirjalili 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第6期1087-1098,共12页
We introduce the polarized valon distributions to describe the spin dependence of parton distributions.The polarized valon distributions in the proton and polarized parton distributions inside the valon can help to ob... We introduce the polarized valon distributions to describe the spin dependence of parton distributions.The polarized valon distributions in the proton and polarized parton distributions inside the valon can help to obtain polarized parton distribution in a proton. In order to be able to obtain the spin contribution of sea quarks, we need to improve the valon model We employ the Bernstein polynomial averages to obtain the unknown parameters which exist in our calculations. Our results for the polarized proton structure function, xg1p, are in good agreement with the experimental data for some values of Q2. 展开更多
关键词 valon model parton distribution function moment of structure function bernstein polynomial spin contribution
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A New Research about Pion Parton Distribution Function 被引量:1
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作者 楼立洋 阮建红 《Chinese Physics Letters》 SCIE CAS CSCD 2015年第5期31-34,共4页
A new fit of the pion parton distribution functions is provided. Only valence quark distributions are used at a low evolution scale and are evolved with the modified Dokshitzer- Gribov-Lipatov-Altarelli-Parisi equatio... A new fit of the pion parton distribution functions is provided. Only valence quark distributions are used at a low evolution scale and are evolved with the modified Dokshitzer- Gribov-Lipatov-Altarelli-Parisi equation which is briefly introduced in this work, and the sea quark and gluon distributions are only generated by the quantum chromodynamics processes. We find that the patton distributions can explain the pion-nucleon experiments data well, and it can also be compared with the data from the leading neutron data of experiments at HERA. The momentum distributions among the partons are discussed and our results are consistent with some models. 展开更多
关键词 QCD A New Research about Pion Parton distribution Function GRS AQM
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