This work continues the studies on searching for plasma media with the inverse electron energy distribution function(EEDF)and providing recommendations for setting up subsequent experiments.The inverse EEDF is a distr...This work continues the studies on searching for plasma media with the inverse electron energy distribution function(EEDF)and providing recommendations for setting up subsequent experiments.The inverse EEDF is a distribution function that increases with an increase in energy at zero electron energy.The inverse EEDF plays a central role in the problem of negative conductivity.Based on the previously obtained criterion for the formation of an inverse EEDF in a spatially inhomogeneous plasma,a heuristic method is proposed that allows one to avoid resource-intensive calculations for spatially two-dimensional(2D)kinetic modeling on a large array of different glow discharges.It is shown that the conditions for EEDF inversion can be realized in two-chamber discharge structures due to violating the known Boltzmann distribution for electron density.The theoretical conclusions are validated by numerical modeling of lowpressure two-chamber inductively-coupled plasma(ICP)discharges in the COMSOL Multiphysics environment.As a result,areas of conditions with inverse EEDF were found for subsequent detailed kinetic analysis and experimental studies.展开更多
In recent years,many phase space distributions have been proposed,and one of the more independently interesting is the Bai distribution function(BDF).The BDF has been shown to interpolate between the instantaneous aut...In recent years,many phase space distributions have been proposed,and one of the more independently interesting is the Bai distribution function(BDF).The BDF has been shown to interpolate between the instantaneous auto-correlation function and the Wigner distribution function,and be applied in linear frequency modulated signal parameter estimation and optical partial coherence areas.Currently,the BDF is only defined for continuous signals.However,for both simulation and experimental purposes,the signals must be discrete.This necessitates the development of a BDF analysis workflow for discrete signals.In this work,we analyze the sampling requirements imposed by the BDF and demonstrate their correctness by comparing the continuous BDFs of continuous test signals with their numerically approximated counterparts.Our results permit more accurate simulations using BDFs,which will be useful in applying them to problems such as partial coherence.展开更多
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
Permanent plots in the montane tropical rain forests in Xishuangbanna, southwest China, were established, and different empirical models, based on observation data of these plots in 1992, were built to model diameter ...Permanent plots in the montane tropical rain forests in Xishuangbanna, southwest China, were established, and different empirical models, based on observation data of these plots in 1992, were built to model diameter frequency distributions. The focus of this study is on predicting accuracy of stem number in the larger diameter classes, which is much more important than that of the smaller trees, from the view of forest management, and must be adequately considered in the modelling and estimate. There exist 3 traditional ways of modelling the diameter frequency distribution: the negative exponential function model, limiting line function model, and Weibull distribution model. In this study, a new model, named as the logarithmic J-shape function, together with the others, was experimented and was found as a more suitable model for modelling works in the tropical forests.展开更多
The probability distributions of wave characteristics from three groups of sampled ocean data with different significant wave heights have been analyzed using two transformation functions estimated by non-parametric a...The probability distributions of wave characteristics from three groups of sampled ocean data with different significant wave heights have been analyzed using two transformation functions estimated by non-parametric and parametric methods. The marginal wave characteristic distribution and the joint density of wave properties have been calculated using the two transformations, with the results and accuracy of both transformations presented here. The two transformations deviate slightly between each other for the calculation of the crest and trough height marginal wave distributions, as well as the joint densities of wave amplitude with other wave properties. The transformation methods for the calculation of the wave crest and trough height distributions are shown to provide good agreement with real ocean data. Our work will help in the determination of the most appropriate transformation procedure for the prediction of extreme values.展开更多
The atomic pair distribution function（PDF） reveals the interatomic distance in a material directly in real-space. It is a very powerful method to characterize the local structure of materials. With the help of the t...The atomic pair distribution function（PDF） reveals the interatomic distance in a material directly in real-space. It is a very powerful method to characterize the local structure of materials. With the help of the third generation synchrotron facility and spallation neutron source worldwide, the PDF method has developed quickly both experimentally and theoretically in recent years. Recently this method was successfully implemented at the Shanghai Synchrotron Radiation Facility（SSRF）. The data quality is very high and this ensures the applicability of the method to study the subtle structural changes in complex materials. In this article, we introduce in detail this new method and show some experimental data we collected.展开更多
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
Phytoplankton and environment factors were investigated in 2015 and phytoplankton functional groups were used to understand their temporal and spatial distribution and their driving factors in Wanfeng Reservoir. Seven...Phytoplankton and environment factors were investigated in 2015 and phytoplankton functional groups were used to understand their temporal and spatial distribution and their driving factors in Wanfeng Reservoir. Seventeen functional groups(B, D, E, F, G, J, Lo, MP, P, S1, T, W1, W2, X1, X2, Xph, Y) were identified based on 34 species. The dominant groups were: J/B/P/D in dry season, X1/J/Xph/G/T in normal season and J in flood season. Phytoplankton abundance ranged from 5.33×10~4 cells/L to 3.65×10~7 cells/L, with the highest value occurring in flood season and lowest in dry season. The vertical profi le of dominant groups showed little differentiation except for P, which dominated surface layers over 20 m as a result of mixing water masses and higher transparency during dry season. However, the surface waters presented higher values of phytoplankton abundance than other layers, possibly because of greater irradiance. The significant explaining variables and their ability to describe the spatial distribution of the phytoplankton community in RDA diff ered seasonally as follows: dry season, NH4-N, NO_3-N, NO_2-N, TN:TP ratio and transparency(SD); normal season, temperature(WT), water depth, TN, NH4-N and NO_3-N; flood season, WT, water depth, NO_3-N and NO_2-N. Furthermore, nitrogen, water temperature, SD and water depth were significant variables explaining the variance of phytoplankton communities when datasets included all samples. The results indicated that water physical conditions and hydrology were important in phytoplankton community dynamics, and nitrogen was more important than phosphorus in modifying phytoplankton communities. Seasonal differences in the relationship between the environment and phytoplankton community should be considered in water quality management.展开更多
We propose a method that uses linear chirp modulated Gaussian functions as the elementary functions, by adaptively adjusting variances, time frequency centers and sweep rates, to decompose signals. By taking WVD, an ...We propose a method that uses linear chirp modulated Gaussian functions as the elementary functions, by adaptively adjusting variances, time frequency centers and sweep rates, to decompose signals. By taking WVD, an improved adaptive time frequency distribution is developed, which is non negative, free of cross term interference, and of better time frequency resolution. The paper presents an effective numerical algorithm to estimate the optimal parameters of the basis. Simulations indicate that the proposed approach is effective in analyzing signal's time frequency behavior.展开更多
This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew(PFGS)plates.The effective material properties of...This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew(PFGS)plates.The effective material properties of the PFGS plates are obtained from the modified power-law equations in which gradation varies through the thickness of the PFGS plate.A nonlinear finite element(FE)formulation for the overall PFGS plate is derived by adopting first-order shear deformation theory(FSDT)in conjunction with von Karman’s nonlinear strain displacement relations.The governing equations of the PFGS plate are derived using the principle of virtual work.The direct iterative method and Newmark’s integration technique are espoused to solve nonlinear mathematical relations.The influences of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the PFGS plate for different skew angles are studied in various parameters.The effects of volume fraction grading index and skew angle on the plate’s nonlinear dynamic responses for various porosity distributions are illustrated in detail.展开更多
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
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
Battery materials are of vital importance in powering a elean and sustainable society.Improving their performance relies on a clear and fundamental understanding of their properties,in particular,structural properties...Battery materials are of vital importance in powering a elean and sustainable society.Improving their performance relies on a clear and fundamental understanding of their properties,in particular,structural properties.Pair distribution function(PDF) analysis,which takes into account both Bragg scattering and diffuse scattering,can probe structures of both crystalline and amorphous phases in battery materials.This review first introduces the principle of PDF,followed by its application in battery materials.It shows that PDF is an effective tool in studying a series of key scientific topics in battery materials.They range from local ordering,nano-phase quantification,anion redox reaction,to lithium storage mechanism,and so on.展开更多
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
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
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
The structure transitions in cluster-cluster aggregation (CCA) and diffusion-limited aggregation (DLA) under external electric fields have been investigated by computer simulations. With the increase of external elect...The structure transitions in cluster-cluster aggregation (CCA) and diffusion-limited aggregation (DLA) under external electric fields have been investigated by computer simulations. With the increase of external electric field, there exists a structure transition from disorder to order, i. e., the aggregates change from fractals of diffusion-limited CCA and DLA to the electrorheological chains parallel to electric field. Pair distribution shows, the system changes from local order to long-range order gradually with the external field rising.展开更多
Traditional methods for early warning of dam displacements usually assume that residual displacements follow a normal distribution.This assumption deviates from the reality,thereby affecting the reliability of early w...Traditional methods for early warning of dam displacements usually assume that residual displacements follow a normal distribution.This assumption deviates from the reality,thereby affecting the reliability of early warning results and leading to misjudgments of dam displacement behavior.To solve this problem,this study proposed an early warning method using a non-normal distribution function.A new early warning index was developed using cumulative distribution function(CDF)values.The method of kernel density estimation was used to calculate the CDF values of residual displacements at a single point.The copula function was used to compute the CDF values of residual displacements at multiple points.Numerical results showed that,with residual displacements in a non-normal distribution,the early warning method proposed in this study accurately reflected the dam displacement behavior and effectively reduced the frequency of false alarms.This method is expected to aid in the safe operation of dams.展开更多
The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, <img src="Edit_699140d3-f569-463e-b835-7ccdab822717.png" width="290" height="22" ...The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, <img src="Edit_699140d3-f569-463e-b835-7ccdab822717.png" width="290" height="22" alt="" /><img src="Edit_bdd10470-9b63-4b2d-9cec-636969547ca5.png" width="90" height="22" alt="" /><span style="white-space:normal;">and <img src="Edit_e9cd6876-e2b8-45cf-ba17-391f054679b4.png" width="90" height="21" alt="" /></span>where <span style="white-space:nowrap;"><em>α</em>,<span style="white-space:nowrap;"><em>η</em></span><em></em></span> and <span style="white-space:nowrap;"><em>β</em></span> are real or complex constants are evaluated in terms of the confluent hypergeometric function <sub>1</sub><em>F</em><sub>1</sub> and the hypergeometric function <sub>1</sub><em>F</em><sub>2</sub>. The hyperbolic and Euler identities are used to derive some identities involving exponential, hyperbolic, trigonometric functions and the hypergeometric functions <sub style="white-space:normal;">1</sub><em style="white-space:normal;">F</em><sub style="white-space:normal;">1</sub> and <sub style="white-space:normal;">1</sub><em style="white-space:normal;">F</em><sub style="white-space:normal;">2</sub>. Having evaluated, these non-elementary integrals, some new probability measures generalizing the gamma-type and Gaussian distributions are also obtained. The obtained generalized probability distributions may, for example, allow to perform better statistical tests than those already known (e.g. chi-square (<span style="white-space:nowrap;"><em>x</em><sup>2</sup></span>) statistical tests and other statistical tests constructed based on the central limit theorem (CLT)), while avoiding the use of computational approximations (or methods) which are in general expensive and associated with numerical errors.展开更多
By using the technique of integration within an ordered product （IWOP） of operator we derive Wigner function of density operator for negative binomial distribution of radiation field in the mixed state case, then we...By using the technique of integration within an ordered product （IWOP） of operator we derive Wigner function of density operator for negative binomial distribution of radiation field in the mixed state case, then we derive the Wigner function of squeezed number state, which yields negative binomial distribution by virtue of the entangled state representation and the entangled Wigner operator.展开更多
基金supported by the National Key R&D Program of China(No.2022YFE0204100)National Natural Science Foundation of China(Nos.12205067 and 12375199)the Fundamental Research Funds for the Central University(No.HIT.D?J.2023178)。
文摘This work continues the studies on searching for plasma media with the inverse electron energy distribution function(EEDF)and providing recommendations for setting up subsequent experiments.The inverse EEDF is a distribution function that increases with an increase in energy at zero electron energy.The inverse EEDF plays a central role in the problem of negative conductivity.Based on the previously obtained criterion for the formation of an inverse EEDF in a spatially inhomogeneous plasma,a heuristic method is proposed that allows one to avoid resource-intensive calculations for spatially two-dimensional(2D)kinetic modeling on a large array of different glow discharges.It is shown that the conditions for EEDF inversion can be realized in two-chamber discharge structures due to violating the known Boltzmann distribution for electron density.The theoretical conclusions are validated by numerical modeling of lowpressure two-chamber inductively-coupled plasma(ICP)discharges in the COMSOL Multiphysics environment.As a result,areas of conditions with inverse EEDF were found for subsequent detailed kinetic analysis and experimental studies.
基金the support of the University College Dublin through a John Sheridan Scholarship.Min Wan thanks 4TU.RECENTRE program(Award No.OA102070)the National Growth Fund programme PhotonDelta in The Netherlands.
文摘In recent years,many phase space distributions have been proposed,and one of the more independently interesting is the Bai distribution function(BDF).The BDF has been shown to interpolate between the instantaneous auto-correlation function and the Wigner distribution function,and be applied in linear frequency modulated signal parameter estimation and optical partial coherence areas.Currently,the BDF is only defined for continuous signals.However,for both simulation and experimental purposes,the signals must be discrete.This necessitates the development of a BDF analysis workflow for discrete signals.In this work,we analyze the sampling requirements imposed by the BDF and demonstrate their correctness by comparing the continuous BDFs of continuous test signals with their numerically approximated counterparts.Our results permit more accurate simulations using BDFs,which will be useful in applying them to problems such as partial coherence.
文摘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
文摘Permanent plots in the montane tropical rain forests in Xishuangbanna, southwest China, were established, and different empirical models, based on observation data of these plots in 1992, were built to model diameter frequency distributions. The focus of this study is on predicting accuracy of stem number in the larger diameter classes, which is much more important than that of the smaller trees, from the view of forest management, and must be adequately considered in the modelling and estimate. There exist 3 traditional ways of modelling the diameter frequency distribution: the negative exponential function model, limiting line function model, and Weibull distribution model. In this study, a new model, named as the logarithmic J-shape function, together with the others, was experimented and was found as a more suitable model for modelling works in the tropical forests.
基金Supported by the Marine Engineering Equipment Scientific Research Project of Ministry of Industry and Information Technology of PRCthe National Science and Technology Major Project of China(Grant No.2016ZX05057020)National Natural Science Foundation of China(Grant No.51809067)
文摘The probability distributions of wave characteristics from three groups of sampled ocean data with different significant wave heights have been analyzed using two transformation functions estimated by non-parametric and parametric methods. The marginal wave characteristic distribution and the joint density of wave properties have been calculated using the two transformations, with the results and accuracy of both transformations presented here. The two transformations deviate slightly between each other for the calculation of the crest and trough height marginal wave distributions, as well as the joint densities of wave amplitude with other wave properties. The transformation methods for the calculation of the wave crest and trough height distributions are shown to provide good agreement with real ocean data. Our work will help in the determination of the most appropriate transformation procedure for the prediction of extreme values.
基金Project supported by the National Natural Science Foundation of China(Grant No.U1232112)the National Key Basic Research Program of China(Grant No.2012CB825700)
文摘The atomic pair distribution function（PDF） reveals the interatomic distance in a material directly in real-space. It is a very powerful method to characterize the local structure of materials. With the help of the third generation synchrotron facility and spallation neutron source worldwide, the PDF method has developed quickly both experimentally and theoretically in recent years. Recently this method was successfully implemented at the Shanghai Synchrotron Radiation Facility（SSRF）. The data quality is very high and this ensures the applicability of the method to study the subtle structural changes in complex materials. In this article, we introduce in detail this new method and show some experimental data we collected.
文摘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.
基金Supported by the Department of Science and Technology of Guizhou Province(Nos.[2014]7001,[2015]2001,[2015]10)the Water Resources Department of Guizhou Province(No.KT201401)
文摘Phytoplankton and environment factors were investigated in 2015 and phytoplankton functional groups were used to understand their temporal and spatial distribution and their driving factors in Wanfeng Reservoir. Seventeen functional groups(B, D, E, F, G, J, Lo, MP, P, S1, T, W1, W2, X1, X2, Xph, Y) were identified based on 34 species. The dominant groups were: J/B/P/D in dry season, X1/J/Xph/G/T in normal season and J in flood season. Phytoplankton abundance ranged from 5.33×10~4 cells/L to 3.65×10~7 cells/L, with the highest value occurring in flood season and lowest in dry season. The vertical profi le of dominant groups showed little differentiation except for P, which dominated surface layers over 20 m as a result of mixing water masses and higher transparency during dry season. However, the surface waters presented higher values of phytoplankton abundance than other layers, possibly because of greater irradiance. The significant explaining variables and their ability to describe the spatial distribution of the phytoplankton community in RDA diff ered seasonally as follows: dry season, NH4-N, NO_3-N, NO_2-N, TN:TP ratio and transparency(SD); normal season, temperature(WT), water depth, TN, NH4-N and NO_3-N; flood season, WT, water depth, NO_3-N and NO_2-N. Furthermore, nitrogen, water temperature, SD and water depth were significant variables explaining the variance of phytoplankton communities when datasets included all samples. The results indicated that water physical conditions and hydrology were important in phytoplankton community dynamics, and nitrogen was more important than phosphorus in modifying phytoplankton communities. Seasonal differences in the relationship between the environment and phytoplankton community should be considered in water quality management.
文摘We propose a method that uses linear chirp modulated Gaussian functions as the elementary functions, by adaptively adjusting variances, time frequency centers and sweep rates, to decompose signals. By taking WVD, an improved adaptive time frequency distribution is developed, which is non negative, free of cross term interference, and of better time frequency resolution. The paper presents an effective numerical algorithm to estimate the optimal parameters of the basis. Simulations indicate that the proposed approach is effective in analyzing signal's time frequency behavior.
文摘This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew(PFGS)plates.The effective material properties of the PFGS plates are obtained from the modified power-law equations in which gradation varies through the thickness of the PFGS plate.A nonlinear finite element(FE)formulation for the overall PFGS plate is derived by adopting first-order shear deformation theory(FSDT)in conjunction with von Karman’s nonlinear strain displacement relations.The governing equations of the PFGS plate are derived using the principle of virtual work.The direct iterative method and Newmark’s integration technique are espoused to solve nonlinear mathematical relations.The influences of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the PFGS plate for different skew angles are studied in various parameters.The effects of volume fraction grading index and skew angle on the plate’s nonlinear dynamic responses for various porosity distributions are illustrated in detail.
文摘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.
基金The project supported by National Natural Science Foundation of China under Grant No. 40390150 and the International Collaboration Research Team Program of the Chinese Academy of Sciences
文摘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.
文摘Battery materials are of vital importance in powering a elean and sustainable society.Improving their performance relies on a clear and fundamental understanding of their properties,in particular,structural properties.Pair distribution function(PDF) analysis,which takes into account both Bragg scattering and diffuse scattering,can probe structures of both crystalline and amorphous phases in battery materials.This review first introduces the principle of PDF,followed by its application in battery materials.It shows that PDF is an effective tool in studying a series of key scientific topics in battery materials.They range from local ordering,nano-phase quantification,anion redox reaction,to lithium storage mechanism,and so on.
基金Project (No. 10372090) supported by the National Natural Science Foundation of China
文摘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.
基金supported by the National Natural Science Foundation of China(Grants 11472313,11232015,and 11572355)the Guangdong Province Research Fund for Applied Research
文摘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.
文摘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.
文摘The structure transitions in cluster-cluster aggregation (CCA) and diffusion-limited aggregation (DLA) under external electric fields have been investigated by computer simulations. With the increase of external electric field, there exists a structure transition from disorder to order, i. e., the aggregates change from fractals of diffusion-limited CCA and DLA to the electrorheological chains parallel to electric field. Pair distribution shows, the system changes from local order to long-range order gradually with the external field rising.
基金supported by the National Natural Science Foundation of China(Grant No.52109156)the Science and Technology Project of the Jiangxi Provincial Education Department(Grant No.GJJ190970).
文摘Traditional methods for early warning of dam displacements usually assume that residual displacements follow a normal distribution.This assumption deviates from the reality,thereby affecting the reliability of early warning results and leading to misjudgments of dam displacement behavior.To solve this problem,this study proposed an early warning method using a non-normal distribution function.A new early warning index was developed using cumulative distribution function(CDF)values.The method of kernel density estimation was used to calculate the CDF values of residual displacements at a single point.The copula function was used to compute the CDF values of residual displacements at multiple points.Numerical results showed that,with residual displacements in a non-normal distribution,the early warning method proposed in this study accurately reflected the dam displacement behavior and effectively reduced the frequency of false alarms.This method is expected to aid in the safe operation of dams.
文摘The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, <img src="Edit_699140d3-f569-463e-b835-7ccdab822717.png" width="290" height="22" alt="" /><img src="Edit_bdd10470-9b63-4b2d-9cec-636969547ca5.png" width="90" height="22" alt="" /><span style="white-space:normal;">and <img src="Edit_e9cd6876-e2b8-45cf-ba17-391f054679b4.png" width="90" height="21" alt="" /></span>where <span style="white-space:nowrap;"><em>α</em>,<span style="white-space:nowrap;"><em>η</em></span><em></em></span> and <span style="white-space:nowrap;"><em>β</em></span> are real or complex constants are evaluated in terms of the confluent hypergeometric function <sub>1</sub><em>F</em><sub>1</sub> and the hypergeometric function <sub>1</sub><em>F</em><sub>2</sub>. The hyperbolic and Euler identities are used to derive some identities involving exponential, hyperbolic, trigonometric functions and the hypergeometric functions <sub style="white-space:normal;">1</sub><em style="white-space:normal;">F</em><sub style="white-space:normal;">1</sub> and <sub style="white-space:normal;">1</sub><em style="white-space:normal;">F</em><sub style="white-space:normal;">2</sub>. Having evaluated, these non-elementary integrals, some new probability measures generalizing the gamma-type and Gaussian distributions are also obtained. The obtained generalized probability distributions may, for example, allow to perform better statistical tests than those already known (e.g. chi-square (<span style="white-space:nowrap;"><em>x</em><sup>2</sup></span>) statistical tests and other statistical tests constructed based on the central limit theorem (CLT)), while avoiding the use of computational approximations (or methods) which are in general expensive and associated with numerical errors.
基金the Natural Science Foundation of Heze University of Shandong Province of China under Grant Nos.XY07WL01 and XY05WL01the University Experimental Technology Foundation of Shandong Province of China under Grant No.S04W138
文摘By using the technique of integration within an ordered product （IWOP） of operator we derive Wigner function of density operator for negative binomial distribution of radiation field in the mixed state case, then we derive the Wigner function of squeezed number state, which yields negative binomial distribution by virtue of the entangled state representation and the entangled Wigner operator.
