Hard X-ray polarization measured with a Compton polarimeter at synchrotron radiation facility

A hard X-ray polarimeter with CdTe detectors has been developed for measurement of the degree of X-ray polarization at synchrotron radiation facilities. It utilizes 90° Compton scattering from the low Z targets. Measurements were performed at both facilities of the beamline BL38B1 in SPring-8 and the beamline BL14A in KEK-PF. The degrees of X-ray polarization for 20 keV X-rays are 99% and 82% at the BL38B1 in SPring-8 and BL14A in KEK-PF, respectively. The polarization degrees in the energy range of 15 and 40 keV correspond to 99.6±0.2% and 96.1±0.2% at the beamline BL38B1 in SPring-8. The analyzing power of the polarimeter was estimated by the Monte Carlo simulation with EGS4. The synchrotron radiation facilities provide highly polarized X-ray beams at energies above 15 keV.     

Gamma-gamma density and lithology tools simulation based on GEANT4 advanced low energy Compton scattering (GALECS) package

Geophysical bore-hole data represent the physical properties of rocks, such as density and formation lithology, as a function of depth in a well. Properties of rocks are obtained from gamma ray transport logs. Transport of gamma rays, from a ¹³⁷Cs point gamma source situated in a bore-hole tool, through rock media to detectors, has been simulated using a GEANT4 radiation transport code. The advanced Compton scattering concepts were used to gain better analyses about well formation. The simulation and understanding of advanced Compton scattering highly depends on how accurately the effects of Doppler broadening and Rayleigh scattering are taken into account. A Monte Carlo package that simulates the gamma-gamma well logging tools based on GEANT4 advanced low energy Compton scattering (GALECS).     

三维介质体的时域散射分析

用时间递推（marching—on in-time，MOT）方法求解了电磁场时域耦合积分方程，计算了均匀介质体的表面等效电流和表面等效磁流，得到时域散射远场并给出了详细推导过程。举例比较了将时域散射用Fourier变化后在频域的RCS和频域直接求得的RCS，以说明该算法的正确性。     

Water-wave scattering by two submerged plane vertical barriers—Abel integral-equation approach

The classical problem of surface water-wave scattering by two identical thin vertical barriers submerged in deep water and extending infinitely downwards from the same depth below the mean free surface, is reinvestigated here by an approach leading to the problem of solving a system of Abel integral equations. The reflection and transmission coefficients are obtained in terms of computable integrals. Known results for a single barrier are recovered as a limiting case as the separation distance between the two barriers tends to zero. The coefficients are depicted graphically in a number of figures which are identical with the corresponding figures given by Jarvis (J Inst Math Appl 7:207–215, 1971) who employed a completely different approach involving a Schwarz–Christoffel transformation of complex-variable theory to solve the problem.     

Numerical resolution of the boundary integral equations for elastic scattering by a plane crack

The problem of wave scattering by a plane crack is solved, either in the case of acoustic waves or in the case of elastic waves incidence using the boundary integral equation method. A collocation method is often used to solve that equation, but here we will use a variational method, first writing the problem of Fourier variables, and then writing the associated integrals in the sesquilinear form with weak singularity kernels. This representation is used in the numerical approach, made with a finite element method in the surface of the crack. Numerical tests were made with circular and elliptical cracks, but this method can be extended to other shapes, with the same convergence profiles. Extensive results are given concerning the crack opening displacement, the scattering cross-section, the back-scattered amplitude and far-field patterns.     

Extending integral equation time domain acoustic scattering analysis to larger problems

A method is presented to accelerate the execution of integral equation time domain analyses of exterior acoustic scattering problems. Conventionally, these have costs which scale with the fifth power of the frequency of the excitation, and practical limits to such computations are reached when bodies approach perhaps ∼5–10 wavelengths long. The fast approach presented is based on exploiting the pulsed nature of the illumination to omit much nugatory calculation. There is an associated slight accuracy loss; this is investigated. The method has costs which can scale with frequency to the power as low as ∼3, such that, for example, costs on a 18·5 wavelength body are reduced by a factor of about 28, with this factor itself increasing with roughly the square of the body size. Associated with the reduction in operations is a reduction in the scaling of storage required, from the third to the second power of frequency. Examples of analysis of large scatterers are presented, extending to a ∼22000 node ‘almond’. Copyright © 1999 John Wiley & Sons, Ltd.     

A Galerkin BEM for transient acoustic scattering by an absorbing obstacle

This paper deals with the numerical resolution of the so‐called time‐domain boundary integral equations. The scattering problem by an absorbing obstacle serves as the model for this discussion. A new system of retarded potential boundary integral equations (RPBIE) is set up to solve the problem. Using an energy identity, we are able to prove the unconditional stability for standard conforming Galerkin approximation of the RPBIE. The actual space–time boundary elements are described in some detail, and their implementation has confirmed that stability in a wide range of situations and for large run times never reached before. Copyright © 2003 John Wiley & Sons, Ltd.     

Regularized integral equations and fast high‐order solvers for sound‐hard acoustic scattering problems

This text introduces the following: (1) new regularized combined field integral equations (CFIE‐R) for frequency‐domain sound‐hard scattering problems; and (2) fast, high‐order algorithms for the numerical solution of the CFIE‐R and related integral equations. Similar to the classical combined field integral equation (CFIE), the CFIE‐R are uniquely‐solvable integral equations based on the use of single and double layer potentials. Unlike the CFIE, however, the CFIE‐R utilize a composition of the double‐layer potential with a regularizing operator that gives rise to highly favorable spectral properties—thus making it possible to produce accurate solutions by means of iterative solvers in small numbers of iterations. The CFIE‐R‐based fast high‐order integral algorithms introduced in this text enable highly accurate solution of challenging sound‐hard scattering problems, including hundred‐wavelength cases, in single‐processor runs on present‐day desktop computers. A variety of numerical results demonstrate the qualities of the numerical solvers as well as the advantages that arise from the new integral equation formulation. Copyright © 2012 John Wiley & Sons, Ltd.     

Partial-differential-equation-constrained amplitude-based shape detection in inverse acoustic scattering

In this article we discuss a formal framework for casting the inverse problem of detecting the location and shape of an insonified scatterer embedded within a two-dimensional homogeneous acoustic host, in terms of a partial-differential-equation-constrained optimization approach. We seek to satisfy the ensuing Karush–Kuhn–Tucker first-order optimality conditions using boundary integral equations. The treatment of evolving boundary shapes, which arise naturally during the search for the true shape, resides on the use of total derivatives, borrowing from recent work by Bonnet and Guzina [1–4] in elastodynamics. We consider incomplete information collected at stations sparsely spaced at the assumed obstacle’s backscattered region. To improve on the ability of the optimizer to arrive at the global optimum we: (a) favor an amplitude-based misfit functional; and (b) iterate over both the frequency- and wave-direction spaces through a sequence of problems. We report numerical results for sound-hard objects with shapes ranging from circles, to penny- and kite-shaped, including obstacles with arbitrarily shaped non-convex boundaries. Partial support for this work was provided by the US National Science Foundation under grant award CMS-0348484.     

Investigation of the scattering of harmonic elastic waves by two collinear symmetric cracks using non-local theory

In this paper, the scattering of harmonic waves by two collinear symmetric cracks is studied by use of non-local theory. To overcome the mathematical difficulties, a one-dimensional non-local kernel is used instead of a two-dimensional one for the dynamic problem to obtain the stress occurring at the crack tips. The Fourier transform is applied and a mixed boundary-value problem is formulated. The solutions are obtained by means of the Schmidt method. This method is more exact and more appropriate than Eringen's for solving this kind of problem. Contrary to the classical elasticity solution, it is found that no stress singularity is present at the crack tip. The non-local dynamic elastic solutions yield a finite hoop stress near the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the lattice parameter and the circular frequency of the incident wave.     

Real time X-ray scattering study of the formation of ZnS nanoparticles using synchrotron radiation

We investigate the growth of ZnS nanoparticles by a real-time simultaneous small and wide angle X-ray scattering (SAXS, WAXS) study using synchrotron radiation. Zinc chloride and elemental sulfur were dissolved in oleylamine. The formation of nanoparticles was induced by heating to 170 °C and 215 °C. The influence of temperature, reaction time, and sulfur concentration was investigated. After a short phase of rapid growth, saturation in size and a slower growth is observed depending on the temperature. The final size of the nanoparticles ranges between 2 and 6 nm for the investigated growth conditions and increases with the reaction temperature and sulfur concentration. SAXS analysis allows for determination of the size of the nanoparticles and proves also the existence of an organized layer of oleylamine molecules covering the nanoparticles' surfaces, which, however, appears only for diameters of the nanoparticles larger than approximately 2.8 nm. The investigation of the measured structure factor of the nanoparticle assemblies showed that the distance of an attractive interaction is 2.5 nm, which was interpreted as a consequence of the ordered oleylamine surface layer.     

A mixed hexahedral finite element to model the scattering of a deformed microstrip antenna

Microstrip antennas have a major interest in aeronautical applications due to their low profile. This paper deals with the impact of mechanical strain on the scattering properties of these antennas. Considering a weak coupling between electromagnetism and mechanical behavior, the same 3D hexahedral finite element discretization is used to solve both problems. A node-based approximation is used for mechanical displacement, while for the determination of the electromagnetic fields, a vector finite approximation is implemented to ensure a better consideration of electromagnetic boundary conditions. The weak electromagnetic formulation inducing integrals on open infinite domains, a Boundary Integral Method is used.     

快速预估水下圆形角反射体散射声场的修正声束弹跳方法

针对水下圆形角反射体散射声场计算速度问题,在声束弹跳法基础上,提出了一种快速预估散射声场的修正声束弹跳法。对组成圆形三面角反射体的弧形边缘进行离散化,相邻离散点与角反射体顶点构成板块元,并与声源点构成入射声束,利用几何声学计算每条声束在角反射体反射面上的反射,同时得到反射面上每条声束"照射"后再次构成的板块元,用物理声学方法计算所有板块元的散射声场,叠加求和得到整个角反射的散射声场。通过与原始的声束弹跳法计算结果的对比,两者计算结果一致,修正声束弹跳法降低了计算量。     

Numerical expansion-iterative method for analysis of integral equation models arising in one- and two-dimensional electromagnetic scattering

Most integral equations of the first kind are ill-posed, and obtaining their numerical solution needs often to solve a linear system of algebraic equations of large condition number. So, solving this system may be difficult or impossible. Since many problems in one- and two-dimensional scattering from perfectly conducting bodies can be modeled by Fredholm integral equations of the first kind, this paper presents an effective numerical expansion-iterative method for solving them. This method is based on vector forms of block-pulse functions. By using this approach, solving the first kind integral equation reduces to solve a recurrence relation. The approximate solution is most easily produced iteratively via the recurrence relation. Therefore, computing the numerical solution does not need to directly solve any linear system of algebraic equations and to use any matrix inversion. Also, the method practically transforms solving of the first kind Fredholm integral equation which is inherently ill-posed into solving second kind Fredholm integral equation. Another advantage is low cost of setting up the equations without applying any projection method such as collocation, Galerkin, etc. To show convergence and stability of the method, some computable error bounds are obtained. Test problems are provided to illustrate its accuracy and computational efficiency, and some practical one- and two-dimensional scatterers are analyzed by it.