We present the Empirical Formula (EF) to calculate the phantom scatter factor, S<sub>p</sub>, of small radiation fields under charge particle dis-equilibrium conditions. The Empirical Formula (EF) was veri...We present the Empirical Formula (EF) to calculate the phantom scatter factor, S<sub>p</sub>, of small radiation fields under charge particle dis-equilibrium conditions. The Empirical Formula (EF) was verified by examining the calculated data with experimentally measured data utilizing the anthropomorphic phantom in twelve different combinations of beam entry and point location, where the value for S<sub>p</sub> per tissue composition was within 3% in 8/12 cases, 5% in 1/12 cases, and 10% in 3/12 cases. Our results showed a good agreement with experimental data to less than 1% when the ion chamber was surrounded by the homogeneous tissue, whether lung, soft tissue, or bone. Indicating that the prediction of the equation is valid, and it can be reliably used for phantom scatter factor calculation for different homogeneous media under charge particle dis- equilibrium conditions.展开更多
Classic maximum entropy quantile function method(CMEQFM) based on the probability weighted moments(PWMs) can accurately estimate the quantile function of random variable on small samples, but inaccurately on the very ...Classic maximum entropy quantile function method(CMEQFM) based on the probability weighted moments(PWMs) can accurately estimate the quantile function of random variable on small samples, but inaccurately on the very small samples. To overcome this weakness, least square maximum entropy quantile function method(LSMEQFM) and that with constraint condition(LSMEQFMCC) are proposed. To improve the confidence level of quantile function estimation,scatter factor method is combined with maximum entropy method to estimate the confidence interval of quantile function. From the comparisons of these methods about two common probability distributions and one engineering application, it is showed that CMEQFM can estimate the quantile function accurately on the small samples but inaccurately on the very small samples(10 samples); LSMEQFM and LSMEQFMCC can be successfully applied to the very small samples;with consideration of the constraint condition on quantile function, LSMEQFMCC is more stable and computationally accurate than LSMEQFM; scatter factor confidence interval estimation method based on LSMEQFM or LSMEQFMCC has good estimation accuracy on the confidence interval of quantile function, and that based on LSMEQFMCC is the most stable and accurate method on the very small samples(10 samples).展开更多
Assessment of the radiative forcing of aerosols in models still lacks sufficient input data for aerosol hygroscopicity. The light scattering enhancement factor [ f(RH, λ)] is a crucial parameter for describing aeroso...Assessment of the radiative forcing of aerosols in models still lacks sufficient input data for aerosol hygroscopicity. The light scattering enhancement factor [ f(RH, λ)] is a crucial parameter for describing aerosol hygroscopic growth properties.In this paper, we provide a survey of f(RH, λ) studies in China for the past seven years, including instrument developments of humidified nephelometers, ambient f(RH, λ) measurements in China, f(RH, λ) parameterization schemes, and f(RH, λ)applications in aerosol measurements. Comparisons of different f(RH, λ) parameterizations are carried out to check their performance in China using field measurement datasets. We also summary the parameterization schemes for predicting f(RH, λ)with aerosol chemical compositions. The recently developed methods to observe other aerosol properties using f(RH, λ)measurements, such as calculating the aerosol hygroscopicity parameter, cloud condensation nuclei number concentration,aerosol liquid water content, and aerosol asymmetry factor, are introduced. Suggestions for further research on f(RH, λ) in China are given.展开更多
This paper is concerned with the inverse scattering problems for Schrdinger equations with compactly supported potentials.For purpose of reconstructing the support of the potential,we derive a factorization of the s...This paper is concerned with the inverse scattering problems for Schrdinger equations with compactly supported potentials.For purpose of reconstructing the support of the potential,we derive a factorization of the scattering amplitude operator A and prove that the ranges of (A A) 1/4 and G which maps more general incident fields than plane waves into the scattering amplitude coincide.As an application we characterize the support of the potential using only the spectral data of the operator A.展开更多
The scattering factor of C60 molecule have been calculated according toX-ray diffraction theory. By comparing it with the atomic scattering factor of carbon,it is found that the scattering factor of C60 molecule is a ...The scattering factor of C60 molecule have been calculated according toX-ray diffraction theory. By comparing it with the atomic scattering factor of carbon,it is found that the scattering factor of C60 molecule is a sine-oscillating attenuate finction of sinθ/λ depending on the direction of the incident beam, which is attenuatedmore quickly than that of single carbon atom. However, there is nO evident differencefor the different directions when 0.00≤sinθ/λ≤0.15.展开更多
Total atomic scattering factors for the 1s^23s^2S states for the lithium isoelectronic sequence from Z=3～10 are calculated by using the full core plus correlation wave function.The influence of electron correlation o...Total atomic scattering factors for the 1s^23s^2S states for the lithium isoelectronic sequence from Z=3～10 are calculated by using the full core plus correlation wave function.The influence of electron correlation on total atomic scattering factors is considered sufficiently in our calculation.For the 1s^23s^2S states of the lithium isoelectronic sequence, the general functional behaviour of total atomic scattering factors is analyzed together for each state of the isoelectronic sequence.展开更多
In this paper, we consider the inverse scattering problem of reconstructing a bounded obstacle in a three-dimensional planar waveguide from the scattered near-field data measured on a finite cylindrical surface contai...In this paper, we consider the inverse scattering problem of reconstructing a bounded obstacle in a three-dimensional planar waveguide from the scattered near-field data measured on a finite cylindrical surface containing the obstacle and corresponding to infinitely many incident point sources also placed on the measurement surface. The obstacle is allowed to be an impenetrable scatterer or a penetrable scatterer. We establish the validity of the factorization method with the nearfield data to characterize the obstacle in the planar waveguide by constructing an outgoing-to-incoming operator which is an integral operator defined on the measurement surface with the kernel given in terms of an infinite series.展开更多
The method of complex function and the method of (Green’s) function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an ...The method of complex function and the method of (Green’s) function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an elliptical hole, and the solution of dynamic stress intensity factor at the crack tip was given. A (Green’s) function was constructed for the problem, which is a basic solution of displacement field for an elastic half space containing a half elliptical gap impacted by anti-plane harmonic linear source force at any point of its horizontal boundary. With division of a crack technique, a series of integral equations can be established on the conditions of continuity and the solution of dynamic stress intensity factor can be obtained. The influence of an elliptical hole on the dynamic stress intensity factor at the crack tip was discussed.展开更多
Particle shape contributes to understanding the physical and chemical processes of the atmosphere and better ascertaining the origins and chemical compositions of the particles. The particle shape can be classified by...Particle shape contributes to understanding the physical and chemical processes of the atmosphere and better ascertaining the origins and chemical compositions of the particles. The particle shape can be classified by the aspect ratio,which can be estimated through the asymmetry factor measured with angularly resolved light scattering. An experimental method of obtaining the asymmetry factor based on simultaneous small forward angle light scattering and aerodynamic size measurements is described briefly. The near forward scattering intensity signals of three detectors in the azimuthal angles at 120?offset are calculated using the methods of T-matrix and discrete dipole approximation. Prolate spheroid particles with different aspect ratios are used as the shape models with the assumption that the symmetry axis is parallel to the flow axis and perpendicular to the incident light. The relations between the asymmetry factor and the optical size and aerodynamic size at various equivalent sizes, refractive indices, and mass densities are discussed in this paper. The numerically calculated results indicate that an elongated particle may be classified at diameter larger than 1.0 μm, and may not be distinguished from a sphere at diameter less than 0.5 μm. It is estimated that the lowest detected aspect ratio is around 1.5:1 in consideration of the experimental errors.展开更多
Based on the statistical characteristics of remote sensing data, the spatial geometric structure characteristics of spectral data and distribution of background, interference and alteration information in characterist...Based on the statistical characteristics of remote sensing data, the spatial geometric structure characteristics of spectral data and distribution of background, interference and alteration information in characteristic space were researched through the analysis of two-dimensional and three-dimensional scatter diagrams. The results indicate that the hyper-space of remote sensing multi-data aggregation belongs to low-dimensional geometric structure, i.e. hyperplane form, and anomalous point groups including alteration information usually dissociate out of hyperplane. Scatter diagrams of remote sensing data band are mainly presented as two distribution forms of single-ellipse and dual-ellipse. Clarifying the relations of three objects of background, disturbance and alteration information in remote sensing images provides an important technical thought and guidance for accurately detecting and extracting remote sensing alteration information.展开更多
The scattering of SH wave by a cylindrical piezoelectric inclusion partially debonded from its surrounding piezoelectric material is investigated using the wave function expansion method and singular integral equation...The scattering of SH wave by a cylindrical piezoelectric inclusion partially debonded from its surrounding piezoelectric material is investigated using the wave function expansion method and singular integral equation technique. The debonding regions are modeled as mul- tiple arc-shaped interface cracks with non-contacting faces. By expressing the scattered ?elds as wave function expansions with unknown coe?cients, the mixed boundary value problem is ?rstly reduced to a set of simultaneous dual series equations. Then dislocation density functions are introduced as unknowns to transform these dual series equations into Cauchy singular integral equations of the ?rst type, which can be numerically solved easily. The solution is valid for arbi- trary number and size of the debonds. Finally, numerical results of the dynamic stress intensity factors are presented for the cases of one debond and two debonds. The e?ects of incidence direc- tion, crack con?guration and various material parameters on the dynamic stress intensity factors are respectively discussed. The solution of this problem is expected to ?nd applications in the investigation of dynamic fracture properties of piezoelectric materials with cracks.展开更多
Base on the principle of absolute quantification of size exclusion chromatography(SEC),a light scattering(LS) detector coupled with a concentration detector(refractive index detector) is utilized to determine the comp...Base on the principle of absolute quantification of size exclusion chromatography(SEC),a light scattering(LS) detector coupled with a concentration detector(refractive index detector) is utilized to determine the compositions of complicated binary mixtures.A theoretical analysis predicts that the response factors for both LS and RI detectors are linear functions with the composition of any specified polymer mixtures in the binary polymer mixtures.Two pairs of complicated binary mixtures were used to test the theory mentioned in the present paper,and the experimental results show an excellent accordance with the theory.展开更多
In this paper, we consider the numerical treatment of an inverse acoustic scattering problem that involves an impenetrable obstacle embedded in a layered medium. We begin by employing a modified version of the well kn...In this paper, we consider the numerical treatment of an inverse acoustic scattering problem that involves an impenetrable obstacle embedded in a layered medium. We begin by employing a modified version of the well known <em>factorization method</em>, in which a computationally effective numerical scheme for the reconstruction of the shape of the scatterer is presented. This is possible, due to a <em>mixed reciprocity principle</em>, which renders the computation of the Green function at the background medium unnecessary. Moreover, to further refine our inversion algorithm, an efficient Tikhonov parameter choice technique, called <em>Improved Maximum Product Criterion</em> (IMPC) is exploited. Our regularization parameter is computed via a fast iterative algorithm which requires no <em>a priori</em> knowledge of the noise level in the far-field data. Finally, the effectiveness of IMPC is illustrated with various numerical examples.展开更多
The compression of soil grain and pore fluid as well as viscid coupling of pore fluid and soil skeleton is considered, the scattering problem of incident plane P1 wave (fast compressional wave) by an infinite cylindri...The compression of soil grain and pore fluid as well as viscid coupling of pore fluid and soil skeleton is considered, the scattering problem of incident plane P1 wave (fast compressional wave) by an infinite cylindrical shell deeply embedded in isotropic saturated soils is studied by adopting the amended Biot model, amplitude equations about potential functions of scattering and refracting fields are obtained, and the effect of dimensionless frequencies and shell thickness on the back-scattering spectra and dynamic stress concentration factors of two types of cylindrical shells with high and low rigidity are numerically computed and analyzed.展开更多
Simulation of stress intensity factor as function of rolling contact fatigue cracks of railway tracks and the vehicle load is made with the help of COMSOL Multiphysics software. It is found that the critical stress in...Simulation of stress intensity factor as function of rolling contact fatigue cracks of railway tracks and the vehicle load is made with the help of COMSOL Multiphysics software. It is found that the critical stress intensity factor i.e. 41.6 MPa. m1/2 is reached at a stress level of 32 MPa and at the crack size 11.5 × 10-2 m.Noting the power law variation of acoustic emission count with increase in crack size (analogous to Paris Law), the simulation was further carried out to model the dependence of measured AE count with the stress intensity factor ahead of a growing RCF crack tip. It is demonstrated that AE measurement can be effective to trigger a control loop for avoidance of fatigue failure of railway track. In view of potential difference in the intensity of back scattered light from surface irregularities, a model is developed to find out the threshold intensity of scattered light that insures safety in the railway system against fatigue failure.展开更多
文摘We present the Empirical Formula (EF) to calculate the phantom scatter factor, S<sub>p</sub>, of small radiation fields under charge particle dis-equilibrium conditions. The Empirical Formula (EF) was verified by examining the calculated data with experimentally measured data utilizing the anthropomorphic phantom in twelve different combinations of beam entry and point location, where the value for S<sub>p</sub> per tissue composition was within 3% in 8/12 cases, 5% in 1/12 cases, and 10% in 3/12 cases. Our results showed a good agreement with experimental data to less than 1% when the ion chamber was surrounded by the homogeneous tissue, whether lung, soft tissue, or bone. Indicating that the prediction of the equation is valid, and it can be reliably used for phantom scatter factor calculation for different homogeneous media under charge particle dis- equilibrium conditions.
文摘Classic maximum entropy quantile function method(CMEQFM) based on the probability weighted moments(PWMs) can accurately estimate the quantile function of random variable on small samples, but inaccurately on the very small samples. To overcome this weakness, least square maximum entropy quantile function method(LSMEQFM) and that with constraint condition(LSMEQFMCC) are proposed. To improve the confidence level of quantile function estimation,scatter factor method is combined with maximum entropy method to estimate the confidence interval of quantile function. From the comparisons of these methods about two common probability distributions and one engineering application, it is showed that CMEQFM can estimate the quantile function accurately on the small samples but inaccurately on the very small samples(10 samples); LSMEQFM and LSMEQFMCC can be successfully applied to the very small samples;with consideration of the constraint condition on quantile function, LSMEQFMCC is more stable and computationally accurate than LSMEQFM; scatter factor confidence interval estimation method based on LSMEQFM or LSMEQFMCC has good estimation accuracy on the confidence interval of quantile function, and that based on LSMEQFMCC is the most stable and accurate method on the very small samples(10 samples).
基金supported by the National Natural Science Foundation of China(Grant No.41590872)
文摘Assessment of the radiative forcing of aerosols in models still lacks sufficient input data for aerosol hygroscopicity. The light scattering enhancement factor [ f(RH, λ)] is a crucial parameter for describing aerosol hygroscopic growth properties.In this paper, we provide a survey of f(RH, λ) studies in China for the past seven years, including instrument developments of humidified nephelometers, ambient f(RH, λ) measurements in China, f(RH, λ) parameterization schemes, and f(RH, λ)applications in aerosol measurements. Comparisons of different f(RH, λ) parameterizations are carried out to check their performance in China using field measurement datasets. We also summary the parameterization schemes for predicting f(RH, λ)with aerosol chemical compositions. The recently developed methods to observe other aerosol properties using f(RH, λ)measurements, such as calculating the aerosol hygroscopicity parameter, cloud condensation nuclei number concentration,aerosol liquid water content, and aerosol asymmetry factor, are introduced. Suggestions for further research on f(RH, λ) in China are given.
基金The Major State Basic Research Development Program Grant (2005CB321701)the Heilongjiang Education Committee Grant (11551364) of China
文摘This paper is concerned with the inverse scattering problems for Schrdinger equations with compactly supported potentials.For purpose of reconstructing the support of the potential,we derive a factorization of the scattering amplitude operator A and prove that the ranges of (A A) 1/4 and G which maps more general incident fields than plane waves into the scattering amplitude coincide.As an application we characterize the support of the potential using only the spectral data of the operator A.
文摘The scattering factor of C60 molecule have been calculated according toX-ray diffraction theory. By comparing it with the atomic scattering factor of carbon,it is found that the scattering factor of C60 molecule is a sine-oscillating attenuate finction of sinθ/λ depending on the direction of the incident beam, which is attenuatedmore quickly than that of single carbon atom. However, there is nO evident differencefor the different directions when 0.00≤sinθ/λ≤0.15.
基金supported by National Natural Science Foundation of China under Grant No.10774063Basic Research Foundation of Beijing Institute of Technology under Grant No.20070742006
文摘Total atomic scattering factors for the 1s^23s^2S states for the lithium isoelectronic sequence from Z=3～10 are calculated by using the full core plus correlation wave function.The influence of electron correlation on total atomic scattering factors is considered sufficiently in our calculation.For the 1s^23s^2S states of the lithium isoelectronic sequence, the general functional behaviour of total atomic scattering factors is analyzed together for each state of the isoelectronic sequence.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61421062 and 61520106004)the Microsoft Research Fund of Asia
文摘In this paper, we consider the inverse scattering problem of reconstructing a bounded obstacle in a three-dimensional planar waveguide from the scattered near-field data measured on a finite cylindrical surface containing the obstacle and corresponding to infinitely many incident point sources also placed on the measurement surface. The obstacle is allowed to be an impenetrable scatterer or a penetrable scatterer. We establish the validity of the factorization method with the nearfield data to characterize the obstacle in the planar waveguide by constructing an outgoing-to-incoming operator which is an integral operator defined on the measurement surface with the kernel given in terms of an infinite series.
文摘The method of complex function and the method of (Green’s) function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an elliptical hole, and the solution of dynamic stress intensity factor at the crack tip was given. A (Green’s) function was constructed for the problem, which is a basic solution of displacement field for an elastic half space containing a half elliptical gap impacted by anti-plane harmonic linear source force at any point of its horizontal boundary. With division of a crack technique, a series of integral equations can be established on the conditions of continuity and the solution of dynamic stress intensity factor can be obtained. The influence of an elliptical hole on the dynamic stress intensity factor at the crack tip was discussed.
基金Project supported by the National Natural Science Foundation of China(Grant No.41275132)
文摘Particle shape contributes to understanding the physical and chemical processes of the atmosphere and better ascertaining the origins and chemical compositions of the particles. The particle shape can be classified by the aspect ratio,which can be estimated through the asymmetry factor measured with angularly resolved light scattering. An experimental method of obtaining the asymmetry factor based on simultaneous small forward angle light scattering and aerodynamic size measurements is described briefly. The near forward scattering intensity signals of three detectors in the azimuthal angles at 120?offset are calculated using the methods of T-matrix and discrete dipole approximation. Prolate spheroid particles with different aspect ratios are used as the shape models with the assumption that the symmetry axis is parallel to the flow axis and perpendicular to the incident light. The relations between the asymmetry factor and the optical size and aerodynamic size at various equivalent sizes, refractive indices, and mass densities are discussed in this paper. The numerically calculated results indicate that an elongated particle may be classified at diameter larger than 1.0 μm, and may not be distinguished from a sphere at diameter less than 0.5 μm. It is estimated that the lowest detected aspect ratio is around 1.5:1 in consideration of the experimental errors.
基金Project supported by the National Natural Science Foundation of China （Grant No 10375064）, and the National High Technology Inertial Confinement Fusion.
基金Project(2006BAB01A06) supported by the National Science and Technology Pillar Program Project during the 11th Five-Year Plan PeriodProject(1212010761503) supported by Land and Resources Investigation Project
文摘Based on the statistical characteristics of remote sensing data, the spatial geometric structure characteristics of spectral data and distribution of background, interference and alteration information in characteristic space were researched through the analysis of two-dimensional and three-dimensional scatter diagrams. The results indicate that the hyper-space of remote sensing multi-data aggregation belongs to low-dimensional geometric structure, i.e. hyperplane form, and anomalous point groups including alteration information usually dissociate out of hyperplane. Scatter diagrams of remote sensing data band are mainly presented as two distribution forms of single-ellipse and dual-ellipse. Clarifying the relations of three objects of background, disturbance and alteration information in remote sensing images provides an important technical thought and guidance for accurately detecting and extracting remote sensing alteration information.
基金Project supported by the Research Fund for Doctors of Hebei Province China (No. B2001213).
文摘The scattering of SH wave by a cylindrical piezoelectric inclusion partially debonded from its surrounding piezoelectric material is investigated using the wave function expansion method and singular integral equation technique. The debonding regions are modeled as mul- tiple arc-shaped interface cracks with non-contacting faces. By expressing the scattered ?elds as wave function expansions with unknown coe?cients, the mixed boundary value problem is ?rstly reduced to a set of simultaneous dual series equations. Then dislocation density functions are introduced as unknowns to transform these dual series equations into Cauchy singular integral equations of the ?rst type, which can be numerically solved easily. The solution is valid for arbi- trary number and size of the debonds. Finally, numerical results of the dynamic stress intensity factors are presented for the cases of one debond and two debonds. The e?ects of incidence direc- tion, crack con?guration and various material parameters on the dynamic stress intensity factors are respectively discussed. The solution of this problem is expected to ?nd applications in the investigation of dynamic fracture properties of piezoelectric materials with cracks.
基金supported by the National Natural Science Foundation of China(No.50633030)
文摘Base on the principle of absolute quantification of size exclusion chromatography(SEC),a light scattering(LS) detector coupled with a concentration detector(refractive index detector) is utilized to determine the compositions of complicated binary mixtures.A theoretical analysis predicts that the response factors for both LS and RI detectors are linear functions with the composition of any specified polymer mixtures in the binary polymer mixtures.Two pairs of complicated binary mixtures were used to test the theory mentioned in the present paper,and the experimental results show an excellent accordance with the theory.
文摘In this paper, we consider the numerical treatment of an inverse acoustic scattering problem that involves an impenetrable obstacle embedded in a layered medium. We begin by employing a modified version of the well known <em>factorization method</em>, in which a computationally effective numerical scheme for the reconstruction of the shape of the scatterer is presented. This is possible, due to a <em>mixed reciprocity principle</em>, which renders the computation of the Green function at the background medium unnecessary. Moreover, to further refine our inversion algorithm, an efficient Tikhonov parameter choice technique, called <em>Improved Maximum Product Criterion</em> (IMPC) is exploited. Our regularization parameter is computed via a fast iterative algorithm which requires no <em>a priori</em> knowledge of the noise level in the far-field data. Finally, the effectiveness of IMPC is illustrated with various numerical examples.
文摘The compression of soil grain and pore fluid as well as viscid coupling of pore fluid and soil skeleton is considered, the scattering problem of incident plane P1 wave (fast compressional wave) by an infinite cylindrical shell deeply embedded in isotropic saturated soils is studied by adopting the amended Biot model, amplitude equations about potential functions of scattering and refracting fields are obtained, and the effect of dimensionless frequencies and shell thickness on the back-scattering spectra and dynamic stress concentration factors of two types of cylindrical shells with high and low rigidity are numerically computed and analyzed.
文摘Simulation of stress intensity factor as function of rolling contact fatigue cracks of railway tracks and the vehicle load is made with the help of COMSOL Multiphysics software. It is found that the critical stress intensity factor i.e. 41.6 MPa. m1/2 is reached at a stress level of 32 MPa and at the crack size 11.5 × 10-2 m.Noting the power law variation of acoustic emission count with increase in crack size (analogous to Paris Law), the simulation was further carried out to model the dependence of measured AE count with the stress intensity factor ahead of a growing RCF crack tip. It is demonstrated that AE measurement can be effective to trigger a control loop for avoidance of fatigue failure of railway track. In view of potential difference in the intensity of back scattered light from surface irregularities, a model is developed to find out the threshold intensity of scattered light that insures safety in the railway system against fatigue failure.
