Characteristic analysis of scattering field in two-layer media by Green's function

The problem of three-dimensional(3D) acoustic scattering in a complex medium has aroused considerable interest of researchers for many years. An ultrasonic scattered field calculating technique is proposed to study the scattering echo from strongly scattered materials in a two-layer medium in this work. Firstly, with the high frequency stationary phase method,the Green's function of two-layer fluid media is derived. And then based on the idea of integral equation discretization,the Green's function method is extended to two-layer fluid media to derive the scattering field expression of defects in a complex medium. With this method, the scattering field of 3D defect in a two-layer medium is calculated and the characteristics of received echoes are studied. The results show that this method is able to solve the scattering P wave field of 3D defect with arbitrary shape at any scattering intensity in two-layer media. Considering the circumstance of waterimmersion ultrasonic non-destructive test(NDT), the scattering sound field characteristics of different types of defects are analyzed by simulation, which will help to optimize the detection scheme and corresponding imaging method in practice so as to improve the detection quality.

Selective Determination of Nanogram γ-Globulin in Human Blood Serum by Resonance Light Scattering of Functionalized NanoPbS

Functionalized nano-PbS has been prepared and characterized. The functionalized nanoparticles have good dispersibility in water. Reaction of functionalized nanoPbS with gglobulin (gIgG) results an enhanced resonance light scattering (RLS) around 385 nm. However, when the content of HSA is lower than 0.5 mg ml-1 the RLS enhancement is very weak and is nonlinear to concentration of HSA. Based on these results, a new direct quantitative determination method for gglobulin in blood serum samples without separation is established. Under optimal conditions, the enhanced RLS intensity is in proportion to the gIgG concentration in the range 10500 ng/mL. The limit of detection is 2.75 ng/mL. This method is proved to be very sensitive, rapid, simple and selective for detection of gIgG in blood serum.

Stability of the Dividing Distribution Function Method for ParticleSize Distribution Analysis in Small Angle X－Ray Scattering

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.

A whole-space transform formula of cylindrical wave functions for scattering problems

The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion,and the wave function expansion technique has been widely used in many subjects.To supply the essential tools for solving wave scattering problems induced by an eccentric source or multi-sources as well as multi-scatters,a whole-space transform formula of cylindrical wave functions is presented and its applicability to some simple cases is demonstrated in this study.The transforms of wave functions in cylindrical coordinates can be classifi ed into two basic types: interior transform and exterior transform,and the existing Graf’s addition theorem is only suitable for the former.By performing a new replacement between the two coordinates,the exterior transform formula is fi rst deduced.It is then combined with Graf’s addition theorem to establish a whole-space transform formula.By using the whole-space transform formula,the scattering solutions by the sources outside and inside a cylindrical cavity are constructed as examples of its application.The effectiveness and advantages of the whole-space transform formula is illustrated by comparison with the approximate model based on a large cycle method.The whole-space transform formula presented herein can be used to perform the transform between two different cylindrical coordinates in the whole space.In addition,its concept and principle are universal and can be further extended to establish the coordinate transform formula of wave functions in other coordinate systems.

Approximations of the Scattering Phase Functions of Particles

Based on anomalous diffraction theory and the modified Rayleigh-Debye approximation, a physically realistic model in bridging form is described to approximate the scattering phase function of particles. When compared with the exact method, the bridging technique reported here provides a reasonable approximation to the Mie results over a broader range of angles and size parameters, and it demonstrates the advantage of being computationally economic. In addition, the new phase function model can be essentially extended to other shapes and conveniently used in more complicated scattering and emission problems related to the solutions of the radiative transfer equations.

A Study on Ionospheric HF Channel with Bitemporal Response and Scattering Function

At first the bitemporal response method is introduced to solve the scattering function of the ionospeeric channel. We can get the scattering function, as a function, of the group path time delay and Doppler frequency. Thus Doppler effect resulting from the continuous movement of the ionosphere is analyzed to study the characteristics of the various ionospheric irregularities and diturbance. many possible problems and correction are researched lastly.

Finite Volume Time Domain with the Green Function Method for Electromagnetic Scattering in Schwarzschild Spacetime

The finite volume time domain(FVTD) algorithm and Green function algorithm are extended to Schwarzschild spacetime for numerical simulation of electromagnetic scattering. The FVTD method in Schwarzschild spacetime is developed by filling the flat spacetime with an equivalent medium. The Green function in Schwarzschild spacetime is acquired by solving initial value problems. Both the FVTD code and the Green function code are validated by numerical results. Scattering in Schwarzschild spacetime is simulated with these methods.

Scattering of Geometric Algebra Wave Functions and Collapse in Measurements

The research considers wavelike objects that are elements of even subalgebra of geometric algebra in three dimensions. The used formalism particularly eliminates long existing confusion about the reasons behind the appearance of the imaginary unit in quantum mechanics and introduces clear definition of wave functions. When a wave function acts through the Hopf fibration on a localized geometric algebra element, that is executing a measurement, the result can be named as “collapse” of the wave function.

Solving the atmospheric scattering optical transfer function using the multi-coupled single scattering method

The atmospheric scattering optical transfer function （OTF） is solved by applying the multi-coupled single scattering （MCSS） method to the three-dimensional radiative transfer equation （RTE） under the periodic ground condition. This approach is a direct hit to the atmospheric scattering OTF using the same original context of modulation transfer function （MTF） measurement, i.e., images of sinusoidal grating at different spatial frequencies. Both the amplitude and phase shift of the OTF at various zenith and azimuth angles can be obtained at an arbitrary spatial frequency.

Reducing the calculation workload of the Green function for electromagnetic scattering in a Schwarzschild gravitational field

When the finite difference time domain(FDTD) method is used to solve electromagnetic scattering problems in Schwarzschild space-time, the Green functions linking source/observer to every surface element on connection/output boundary must be calculated.When the scatterer is electrically extended, a huge amount of calculation is required due to a large number of surface elements on the connection/output boundary.In this paper, a method for reducing the calculation workload of Green function is proposed.The Taylor approximation is applied for the calculation of Green function.New transport equations are deduced.The numerical results verify the effectiveness of this method.

Research on the acoustic scattering function and coherence properties from rough seafloor based on finite element model

Acoustic scattering from a rough sea bottom is recognized as a main source of reverberation. In this study, scattering properties from a layered bottom were exploited based on the finite element model. The scattering strength and loss from the layered rough seabed were investigated by ensembling the realizations of rough interface. They were found to be dependent on the thickness of sediment, and interference was significant in the case of thin sediment. Through verification of the finite element model, the scattering loss could be evaluated using the Eckart model with a proper sound speed in the thick sediment. The multiple scattering effect on the sound field was also exploited. It revealed that the effect depended strongly on the bottom type.

SCATTERING FUNCTION OF POLYMER BLENDS

For a system of flexible polymer molecules, the concepts of two concentrations, namely the segmental and the molecular concentrations, have been proposed in this paper. The former is equivalent to the volume fraction. The latter can be defined as the number of the gravity centers of macromolecules in a unit volume. The two concentrations should be correlated with each other by the conformational function of the polymer chain and should be discussed in different thermodynamic equations. On the basis of these concepts it has been proved that the Flory-Huggins entropy of mixing should be the result of the mixing 'ideal gases of the gravity centers of macromolecules'. The general correlation between the free energy of mixing and the scattering function (structural factor) of polymer blends has been studied based on the general fluctuation theory. When the Flory-Huggins free energy of mixing is adopted, the de Gennes scattering function of a polymer blend can be derived.

VECTOR WAVE FUNCTION EXPANSION FOR SOLVING ELECTROMAGNETIC SCATTERING BY BURIED OBJECTS

An analysis of solving the electromagnetic scattering by buried objects using vectorwave function expansion is presented.For expanding the boundary conditions both on the planarair-earth interface and on the spherical surface,the conversion relations between the cylindricaland spherical vector wave functions are derived.Hence the vector wave function expansion isconveniently applied to solve this complex boundary-value problem.For the excitation of the in-cident plane wave and the dipole above the earth,the scatterlng patterns of the buried conductingand dielectric spheres are presented and discussed.

Multilevel Characteristic Basis Function Method with ACA for Accelerated Solution of Electrically Large Scattering Problems

The multilevel characteristic basis function method(MLCBFM)with the adaptive cross approximation(ACA)algorithm for accelerated solution of electrically large scattering problems is studied in this paper.In the conventional MLCBFM based on Foldy-Lax multiple scattering equations,the improvement is only made in the generation of characteristic basis functions(CBFs).However,it does not provide a change in impedance matrix filling and reducing matrix calculation procedure,which is time-consuming.In reality,all the impedance and reduced matrix of each level of the MLCBFM have low-rank property and can be calculated efficiently.Therefore,ACA is used for the efficient generation of two-level CBFs and the fast calculation of reduced matrix in this study.Numerical results are given to demonstrate the accuracy and efficiency of the 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.

π~±Elastic Scattering and Excitation Function of Pion SCX Reaction on ^(13)C

The elastic scattering of 162 MeV л± from 13C and the excitation function of 13C（л+,л0）13N are analyzed in the frame of the Glauber theory.The nuclear wave function is assumedto be constructed by a valence nucleon plus a core of 12C which is described by an independent αcluster model.A good agreement between the theory and experiment is obtained.

Scattering of SH waves induced by a symmetrical V-shaped canyon: a unified analytical solution

This paper reports a series solution of wave functions for two-dimensional scattering and diffraction of plane SH waves induced by a symmetrical V-shaped canyon with different shape ratios. A half-space with a symmetrical V-shaped canyon is divided into two sub-regions by using a circular-arc auxiliary boundary. The two sub-regions are represented by global and local cylindrical coordinate systems, respectively. In each coordinate system, the wave field satisfying the Helmholtz equation is represented by the separation of variables method, in terms of the series of both Bessel functions and Hankel functions with unknown complex coefficients. Then, the two wave fields are described in the local coordinate system using the Graf addition theorem. Finally, the unknown coefficients are sought by satisfying the continuity conditions of the auxiliary boundary. To consider the phase characteristics of the wave scattering, a parametric analysis is carried out in the time domain by assuming an incident signal of the Ricker type. Surface and subsurface transient responses demonstrate the characteristics and mechanisms of wave propagating and scattering.

SCATTERING FAR FIELD SOLUTION OF SH-WAVE BY MOVABLE RIGID CYLINDRICAL INTERFACE INCLUSION

The Green's function is used to solve the scattering far fieldsolution of SH-wave by a mov- able rigid cylindrical interfaceinclusion in a linear elastic body. First, a suitable Green'sfunction is devel- oped, which is the fundamental displacementsolution of an elastic half space with a movable rigid half-cylin-drical inclusion impacted by out-of-plane harmonic line source loadedat any point of its horizontal surface.

Scattering of SH waves by a scalene triangular hill

The influence of local landforms on ground motion is an important problem. The antiplane response of a scalene triangular hill to incident SH waves is studied in this paper by using a complex function, moving coordinates and auxiliary functions. First, the model is divided into two domains： a scalene triangular hill with a semi-circular bottom; and a half space with a semi-circular canyon. Wave functions that satisfy the zero-stress condition at the triangular wedges and at the horizontal surface are constructed in both domains. Then, considering the displacement continuity and stress equilibrium, algebraic equations are established. Finally, numerical examples are provided to illustrate the influence of the geometry of the hill and the characteristics of the incident waves on the ground motions.

Dynamic stress concentration and scattering of SH-wave by interface elliptic cylindrical cavity

In this paper,the dynamic stress concentration and scattering of SH-waves by bi-material structures that possess an interface elliptic cavity are investigated.First,by using the complex function method,the Green's function is constructed.This yields the solution of the displacement field for an elastic half space with a semi-elliptic canyon impacted by an anti-plane harmonic line source loading on the horizontal surface.Then,the problem is divided into an upper and lower half space along the horizontal interface,regarded as a harmony model.In order to satisfy the integral continuity condition, the unknown anti-plane forces are applied to the interface.The integral equations with unknown forces can be established through the continuity condition,and after transformation,the algebraic equations are solved numerically.Finally,the distribution of the dynamic stress concentration factor(DSCF)around the elliptic cavity is given and the effect of different parameters on DSCF is discussed.