Effect of multiple coulomb scattering on the beam tests of silicon pixel detectors

In the research and development of new silicon pixel detectors,a collimated monoenergetic charged-particle test beam equipped with a high-resolution pixel-beam telescope is crucial for prototype verification and performance evaluation.When the beam energy is low,the effect of multiple Coulomb scattering on the measured resolution of the Device Under Test(DUT)must be considered to accurately evaluate the performance of the pixel chips and detectors.This study aimed to investigate the effect of multiple Coulomb scattering on the measured resolution,particularly at low beam energies.Simulations were conducted using Allpix^(2) to study the effects of multiple Coulomb scattering under different beam energies,material budgets,and telescope layouts.The simulations also provided the minimum energy at which the effect of multiple Coulomb scattering could be ignored.Compared with the results of a five-layer detector system tested with an electron beam at DESY,the simulation results were consistent with the beam test results,confirming the reliability of the simulations.

A simulation method on target strength and circular SAS imaging of Xrudder UUV including multiple acoustic scattering

Target strength(TS)and circular synthetic aperture sonar(CSAS)images provide essential information for active acoustic detection and recognition of non-cooperative unmanned undersea vehicles(UUVs),which pose a significant threat to underwater preset facilities.To access them,we propose an iterative physical acoustics(IPA)-based method to simulate the multiple acoustic scattered fields on rigid surfaces in high-frequency cases.It uses the Helmholtz integral equation with an appropriate Green's function in terms of the Neumann series,and then incorporates the ideas of triangulation and iteration into a numerical implementation.Then two approximate analytic formulae with precise physical meanings are derived to predict the TS and CSAS images of concave targets,respectively.There are no restrictions on the surface's curvature and the order of multiple scattering.The method is validated against the finite element method(FEM)for acoustic scattering from a sphere segment and against an experiment involving an X-rudder UUV's stern.On this basis,we simulate and analyze the TS and CSAS images of an X-rudder UUV.In addition,the influence of the angle of adjacent rudders on the multiple scattering characteristics is discussed.Results show that this method can potentially predict accurate UUV features,especially the multiple scattered features.

Scattering of SH-wave by multiple circular cavities in half space

In this paper,an analytic method is developed to address steady SH-wave scattering and perform dynamic analysis of multiple circular cavities in half space.The scattered wave function used for scattering of SH-waves by multiple circular cavities,which automatically satisfies the stress-free condition at the horizontal surface,is constructed by applying the symmetry of the SH-wave scattering and the method of multi-polar coordinates system.Applying this scattered wave function and method of moving coordinates,the original problem can be transformed to the problem of SH-wave scattering by multiple circular cavities in the full space.Finally,the solution of the problem can be reduced to a series of algebraic equations and solved numerically by truncating the infinite algebraic equations to the finite ones.Numerical examples are provided for case with two cavities to show the effect of wave number,and the distances between the centers of the cavities and from the centers to the ground surface on the dynamic stress concentration around the cavity impacted by incident steady SH-wave.

Three-dimensional positions of scattering centers reconstruction from multiple SAR images based on radargrammetry

A method and procedure is presented to reconstruct three-dimensional(3D) positions of scattering centers from multiple synthetic aperture radar(SAR) images. Firstly, two-dimensional(2D) attribute scattering centers of targets are extracted from 2D SAR images. Secondly, similarity measure is developed based on 2D attributed scatter centers' location, type, and radargrammetry principle between multiple SAR images. By this similarity, we can associate 2D scatter centers and then obtain candidate 3D scattering centers. Thirdly, these candidate scattering centers are clustered in 3D space to reconstruct final 3D positions. Compared with presented methods, the proposed method has a capability of describing distributed scattering center, reduces false and missing 3D scattering centers, and has fewer restrictionson modeling data. Finally, results of experiments have demonstrated the effectiveness of the proposed method.

Scattering of plane P waves by canyons containing multiple circular-arc-shaped layers

By expressing the wave functions in the form of Fourier-Bessel series, the analytical solution for the two-dimension scattering problem of plane P waves by the cylindrical canyon topography that contains arbitrary number of circular-arc-shaped layers is presented firstly. And then, the convergence of the proposed series solution with the truncation number of terms is discussed, which demonstrates that the analytical solution can converge even for very high frequencies of the incident P wave. Finally, using this solution, the influences that are imposed on the stationary ground motion by the number and the sequence of alluvial layers, as well as the stiffness of soft interlayer contained in the canyon, are studied,

Multiple scattering of light by water cloud droplets with external and internal mixing of black carbon aerosols

The mixture of water cloud droplets with black carbon impurities is modeled by external and internal mixing models.The internal mixing model is modeled with a two-layered sphere（water cloud droplets containing black carbon（BC） inclusions）,and the single scattering and absorption characteristics are calculated at the visible wavelength of 0.55 μm by using the Lorenz-Mie theory.The external mixing model is developed assuming that the same amount of BC particles are mixed with the water droplets externally.The multiple scattering characteristics are computed by using the Monte Carlo method.The results show that when the size of the BC aerosol is small,the reflection intensity of the internal mixing model is bigger than that of the external mixing model.However,if the size of the BC aerosol is big,the absorption of the internal mixing model will be larger than that of the external mixing model.

Analysis of multiple scattering from two-dimensional dielectric sea surface with iterative Kirchhoff approximation

An iterative method in the Kirchhoff approximation is proposed for high frequency multiple electromagnetic scattering from two-dimensional dielectric sea surface. The multiple interaction of the scattering field is characterized with the corrected electromagnetic currents of the wind-driven sea surface. The actual surface currents are approximated with the iterative solution of the corrected currents. A newly developed sea spectrum, Elfouhaily spectrum, is utilized to build the sea surface model. The shadowing correction is improved by the Dept-Buffer algorithm. The validity of the iterative Kirchhoff approximation is verified by the agreement of backscattering coefficients with the measured data.

ON DECOMPOSITION METHOD FOR ACOUSTIC WAVE SCATTERING BY MULTIPLE OBSTACLES

Consider acoustic wave scattering by multiple obstacles with different sound properties on the boundary, which can be modeled by a mixed boundary value problem for the Helmholtz equation in frequency domain. Compared with the standard scattering problem for one obstacle, the difficulty of such a new problem is the interaction of scattered wave by different obstacles. A decomposition method for solving this multiple scattering problem is developed. Using the boundary integral equation method, we decompose the total scattered field into a sum of contributions by separated obstacles. Each contribution corresponds to scattering problem of single obstacle. However, all the single scattering problems are coupled via the boundary conditions, representing the physical interaction of scattered wave by different obstacles. We prove the feasibility of such a decomposition. To compute these contributions efficiently, an iteration algorithm of Jacobi type is proposed, decoupling the interaction of scattered wave from the numerical points of view. Under the well-separation assumptions on multiple obstacles, we prove the convergence of iteration sequence generated by the Jacobi algorithm, and give the error estimate between exact scattered wave and the iteration solution in terms of the obstacle size and the minimal distance of multiple obstacles. Such a quantitative description reveals the essences of wave scattering by multiple obstacles. Numerical examples showing the accuracy and convergence of our method are presented.

Improve the Prediction Accuracy of Apple Tree Canopy Nitrogen Content through Multiple Scattering Correction Using Spectroscopy

Method: Use Multiple Scattering Correction to eliminate the interference of scattering on spectrum in the process of field measurement so as to improve the accuracy of prediction model of tree canopy nitrogen content. Apple trees in Qixia of Yantai City were taken as the test material. The spectral reflectivity of apple tree canopy went through the First Derivative (FD) and Multiple Scattering Correction (MSC) plus first derivative, respectively. The correlation coefficients were calculated between spectral reflectivity and nitrogen content. The Support Vector Machine (SVM) method was used to establish the prediction model. The result indicates that the MSC pre-processing can improve the correlation between spectral reflectivity and nitrogen content. The SVM model with MSC + FD pre-processing was a good way to predict the nitrogen content. The calibration R2 of the model was 0.746;the validation R2 was 0.720;and its RMSE was 0.452 g·kgˉ1. MSC can commendably eliminate scattering error to improve the prediction accuracy of prediction model.

Accuracy of radar-based precipitation measurement: An analysis of the influence of multiple scattering and non-spherical particle shape

Two assumptions are typically made when radar echo signals from precipitation are analyzed to determine the micro-physical parameters of raindrops:(1) the raindrops are assumed to be spherical;(2) multiple scattering effects are ignored. Radar cross sections(RCS) are usually calculated using Rayleigh's scattering equation with the simple addition method in the radar meteorological equation.We investigate the extent to which consideration of the effects of multiple scattering and of the non-spherical shapes within actual raindrop swarms would result in RCS values significantly different from those obtained by conventional analytical methods. First, we establish spherical and non-spherical raindrop models, with Gamma, JD, JT, and MP size distributions, respectively. We then use XFDTD software to calculate the radar cross sections of the above raindrop models at the S, C, X and Ku radar bands. Our XFDTD results are then compared to RCS values calculated by the Rayleigh approximation with simple addition methods. We find that:(1) RCS values calculated using multiple scattering XFDTD software differ significantly from those calculated by the simple addition method at the same band for the same model. In particular, for the spherical raindrop models, the relative differences in RCS values between the methods range from a maximum of 89.649% to a minimum of 43.701%; for the non-spherical raindrop models, the relative differences range from a maximum of 85.868% to a minimum of 11.875%.(2) Our multiple scattering XFDTD results, compared to those obtained from the Rayleigh formula,again differ at all four size distributions, by relative errors of 169.522%, 37.176%, 216.455%, and 63.428%, respectively. When nonspherical effects are considered, differences in RCS values between our XFDTD calculations and Rayleigh calculations are smaller; at the above four size distributions the relative errors are 0.213%, 0.171%, 7.683%, and 44.514%, respectively. RCS values computed by considering multiple scattering and non-spherical particle shapes are larger than Rayleigh RCS results, at all of the above four size distributions; the relative errors between the two methods are 220.673%, 129.320%, 387.240%, and 186.613%, respectively. After changing the arrangement of particles at four size distributions in the case of multiple scattering effect and non-spherical effect, the RCS values of Arrangement 2 are smaller than those of Arrangement 1; the relative errors for Arrangement 2, compared to Rayleigh, are 60.558%, 76.263%, 85.941%,64.852%, respectively. We have demonstrated that multiple scattering, non-spherical particle shapes, and the arrangement within particle swarms all affect the calculation of RCS values. The largest influence appears to be that of the multiple scattering effect.Consideration of particle shapes appears to have the least influence on computed RCS values. We conclude that multiple scattering effects must be considered in practical meteorological detection.

Multiple scattering and modeling of laser in fog

When a laser is transmitted in fog, and the water droplets will scatter and absorb the laser, which affects the intensity of the laser transmission and the accuracy of radar detection. Therefore, it is of great significance to study the laser transmission in the fog. At present, the main method of calculating the scattering and attenuation characteristics of fog is based on the radiation transmission theory, which is realized by a large number of numerical calculations or physical simulation methods, which takes time and cannot meet the requirements for obtaining the fast and accurate results. Therefore, in this paper established are a new laser forward attenuation model and backward attenuation model in low visibility fog. It is found that in low visibility environments, the results calculated by the Monte Carlo method are more accurate than those from most of the existing forward attenuation models. For the cases of 0.86-μm, 1.06-μm, 1.315-μm, 10.6-μm typical lasers incident on different fogs with different visibilities, a backscatter model is established, the error between the fitting result and the calculation result is analyzed, the backward attenuation fitting parameters of the new model are tested, and a more accurate fitting result is obtained.

Classification of Multiple Scattering Sequences in the Glauber Amplitude for Nucleus-Nucleus Scattering

A procedure is proposed to classify multiple scattering sequences in nucleus-nucleus scattering,with α-12C taken as an example.

INELASTIC MULTIPLE SCATTERING BY ACTIVE RANDOMLY DISTRIBUTED SPHERICAL SCATTERERS

According to the model of equivalent dipoles for active molecules, the analysisof inelastic EM scattering by active molecules embedded in a sphere is given by the method ofdyadic Green’s functions at the first, and then based on the theory of elastic multiple scattering byrandomly distributed spherical scatterers, a new theory for analysis of inelastic multiple scatteringby active molecules embedded in randomly distributed spherical scatterers also is developed. Thistheory gives the expansions of the multiple scattering fields in all space region in terms of vectorspherical wave functions in which the expansion coefficients can be solved from a set of coupledlinear equations.

Elastic Multiple Scattering By Randomly Distributed Spherical Scatterers

Starting from the basic integral equation for multiple scattered fields,a set of coupledlinear equations for the expansion coefficients of elastic multiple scattered fields by randomlydistributed spherical scatterers has been derived by using the expansions of the fields and thetranslational addition theorems of vector spherical wave functions.Thus,a new theory for thiskind of problems is developed.Different from the others,this theory gives the multiple elasticallyscattered fields in all space regions.

A NEW APPROXIMATE SOLUTION TO THE MULTIPLE SCATTERING THEORY FOR THE ELASTIC PROPERTIES OF HETEROGENEOUS MATERIALS

The multiple scattering theory has been a powerful tool in determining the effective properties of heterogeneous materials. In this paper , a simple relationship between the scattering theory and the micromechanics theory based on the Eshelby principle has been suggested. According to the relationship, a new and simple approximate solution to the exact multiple scattering theory has been given in terms of Eshelby' s S-tensor. The solution easily shows those known results for isotropic composites with spherical inclusions and for tracnsversely isotropic composites, and first gives non-setf-consistent (average t-matrix) and symmetric self-consistent (effective medium or coherent potential) approximate results for isotropic composites with spheroidal inclusions.

Multiple scattering approach to X-ray absorption spectroscopy

In this paper we present the state of the art of the theoretical background needed for analyzing X-ray absorption spectra in the whole energy range. The multiple-scattering (MS) theory is presented in detail with some applications on real systems. We also describe recent progress in performing geometrical fitting of the XANES (X-ray absorption near-edge structure) energy region and beyond using a full multiple-scattering approach.

Inverse scattering method and soliton solution family for the Einstein-Maxwell theory with multiple Abelian gauge fields

A Hauser-Ernst-type extended hyperbolic complex linear system given in our previous paper [Gao Y J 2004 Chin. Phys. 13 602] is slightly modified and used to develop a new inverse scattering method for the stationary axisymmetric Einstein-Maxwell theory with multiple Abelian gauge fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the inverse scattering method be fine and effective in practical application. As an example, a concrete family of soliton solutions for the considered theory is obtained.

MULTIPLE-SCATTERING STUDIES OF ADSORPTION STRUCTURE OF C_2D_2/Si(111)7×7

The multiple scattering cluster (MSC) method has been employed to perform a theoretical analysis on carbon is near edge X-ray absorption fine structure of the deuteron acetylene (C2 D2) adsorbed on Si(111)7× 7 at room temperature. From the MSC study. it is confirmed that the (22D2 molecule is bonded to a pair of adjacent Si adatom and Si restatom with C-Si bond length about 0.18nm. The carbon-deuteron bond is bent away front the surface and the CCD bond angle is about 120°. The molecule plane tilt slightly away from the surface normal. Compared with C2D2 in gas phase, the C-C bond and C-D bond are elongated by about 0.03nm and 0.02nm respectively when acetylene was adsorbed on the subtrate. Keyowrds: adsorption of deuteron acetylene on Si(111)7×7. near edge X- ray absorption fine structure. multiple scattering cluster method

Multiple Scattering Between Adjacent Sound Sources in Head-Related Transfer Function Measurement System

To accelerate head-related transfer functions(HRTFs)measurement,two or more independent sound sources are usually employed in the measurement system.However,the multiple scattering between adjacent sound sources may influence the accuracy of measurement.On the other hand,the directivity of sound source could induce measurement error.Therefore,a model consisting of two spherical sound sources with approximate omni-directivity and a rigid-spherical head is proposed to evaluate the errors in HRTF measurement caused by multiple scattering between sources.An example of analysis using multipole re-expansion indicates that the error of ipsilateral HRTFs are within the bound of±1.0 dB below a frequency of 20 kHz,provided that the sound source radius does not exceed 0.025 m,the source distance relative to head center is not less than 0.5 m,and the angular interval between two adjacent sources is not less than 20 degrees.Similar conclusions under different conditions can also be analyzed and discussed by using this calculation method.Furthermore,the results are verified by measurements of HRTFs for a rigid sphere and a KEMAR artificial head.

MULTIPLE SCATTERING THEORY OF EFFECTIVE MECHANICAL PROPERTIES OF INHOMOGENEOUS MEDIA

The rate of hydrothermal reaction of SiO_2 and/or A1_2O_3 in the system of CaO-Al_2O_3-SiO_2-H_2O at 200℃ and the factors which influence the reactions are investigated by determining the reaction ratio.The rate of reactions depends on the reactive activities of raw materials, initial composition of mixture and relative activity of SiO_2 and A12O3. The hydrothermal reaction can be accelerated by sodium hydroxide,in the case of silica,which has low activity, this is quite obvious.