雪层覆盖地面电磁散射的矩量法

为实现分层介质粗糙面电磁散射的矩量法研究,给出一种分层介质粗糙面电磁积分方程的区域分解方法.将格林定理应用于粗糙面所分的各子空间,结合波动方程和格林函数推导分层粗糙面的电磁积分方程,利用矩量法对其进行离散,数值计算得到雪层覆盖地面散射系数的角分布曲线,其中,粗糙表面由一维带限Weierstrass分形谱和Monte Carlo方法模拟.通过与时域有限差分法数值结果的比对,验证该方法的准确性,并分析散射系数随雪和地面参数、介质参数以及入射波参数的变化,获得了较完整的散射特征.     

A new approach of solving Green’s function for wave propagation in an inhomogeneous absorbing medium

A new approach is developed to solve the Green's function that satisfies the Hehmholtz equation with complex refractive index. Especially, the Green's function for the Helmholtz equation can be expressed in terms of a one-dimensional integral, which can convert a Helmholtz equation into a Schr?dinger equation with complex potential. And the Schr?dinger equation can be solved by Feynman path integral. The result is in excellent agreement with the previous work.     

A Weak Form of the Conjugate Gradient FFT Method for Two-Dimensional Elastodynamics

The problem of two-dimensional scattering of elastic waves by an elastic inclusion can be formulated in terms of a domain integral equation, in which the grad-div operator acts on a vector potential. The vector potential is the spatial convolution of a Green's function with the product of the density and the displacement over the domain of interest. A weak form of the integral equation for the unknown displacement is obtained by testing it with rooftop functions. This method shows excellent numerical performance.     

A method of images for a penetrable acoustic waveguide

In this paper the complex-image approximation to the reflection coefficient for water over a seabed half-space is used to generate an image representation for a bounded acoustic waveguide with an underlying layered seabed. The images are true point sources; they have constant amplitudes which are raypath independent and, in the case of a Pekeris waveguide, frequency-independent. This image representation is ideal for constructing the Green's function kernel of the boundary integral equation method for target scattering in a waveguide. The singular behavior of the Green's function for an infinitesimal source/receiver separation, possibly with the target adjacent to one of the interfaces, is modeled correctly and the image expansion has a simple analytic form which can be analytically differentiated. The method is also accurate for significant source/receiver separations, which means that it can be used in the modeling of scattering from large-sized objects and can also be used as an efficient and accurate short-range propagation model for harmonic and broadband propagation in a penetrable waveguide.     

Scattering of a scalar wave from a two-dimensional randomly rough Neumann surface

We present a reciprocity and unitarity preserving formulation of the scattering of a scalar plane wave from a two-dimensional, randomly rough surface on which the Neumann boundary condition is satisfied. The theory is formulated on the basis of the Rayleigh hypothesis in terms of a single-particle Green's function G(q_‖|k_‖) for the surface electromagnetic waves that exist at the surface due to its roughness, where k_‖ and q_‖ are the projections on the mean scattering plane of the wave vectors of the incident and scattered waves, respectively. The specular scattering is expressed in terms of the average of this Green's function over the ensemble of realizations of the surface profile function (G(q_‖|k_‖)). The Dyson equation satisfied by (G(q_‖|k_‖)) is presented, and the properties of the solution are discussed, with particular attention to the proper self-energy in terms of which the averaged Green's function is expressed. The diffuse scattering is expressed in terms of the ensemble average of a two-particle Green's function, which is the product of two single-particle Green's functions. The Bethe-Salpeter equation satisfied by the averaged two-particle Green's function is presented, and properties of its solution are discussed. In the small roughness limit, and with the irreducible vertex function approximated by the sum of the contribution from the maximally-crossed diagrams, which represent the coherent interference between all time-reversed scattering sequences, the solution of the Bethe-Salpeter equation predicts the presence of enhanced backscattering in the angular dependence of the intensity of the waves scattered diffusely.     

A boundary integral method to compute Green's functions for the radiative transport equation

The Green's function for the time-independent radiative transport equation in the whole space can be computed as an expansion in plane wave solutions. Plane wave solutions are a general class of solutions for the radiative transport equation. Because plane wave solutions are not known analytically in general, we calculate them numerically using the discrete ordinate method. We use the whole space Green's function to derive boundary integral equations. Through the solution of the boundary integral equations, we compute the Green's function for bounded domains. In particular we compute the Green's function for the half space, the slab, and the two-layered half space. The boundary conditions used here are in their most general form. Hence, this theory can be applied to boundaries with any kind of reflection and transmission law.     

微波电热推进器中等离子体的吸收特性

提出了一个谐振腔内微波与等离子体相互作用的简化模型。通过对格林函数并矢的渐进展开,用Fredholm矢量积分方程计算了等离子体散射区的电场分布和等离子体的吸收效率。对非均匀性,等离子体密度等素对吸收效率的影响进行了分析。     

Rough surface Green's function based on the first-order modified perturbation and smoothed diagram methods

This paper presents an analytical theory of rough surface Green's functions based on the extension of the diagram method of Bass, Fuks, and Ito with the smoothing approximation used by Watson and Keller. The method is a modification of the perturbation method and is applicable to rough surfaces with small RMS height. But the range of validity is considerably greater than for the conventional perturbation solutions. We consider one-dimensional rough surfaces with a Dirichlet boundary condition. The coherent Green's function is obtained from the smoothed Dyson's equation using a spatial Fourier transform. The mutual coherence function for the Green's function is obtained by first-order iteration of the smoothing approximation applied to the Bethe-Salpeter equation in terms of a quadruple Fourier transform. These integrals are evaluated by the saddle-point technique. The equivalent bistatic cross section per unit length of the surface is compared with that for the conventional perturbation method and the Watson-Keller result. With respect to the Watson-Keller result, it should be noted that our result is reciprocal, while the Watson-Keller result is non-reciprocal. Included in this paper is a discussion of the specific intensity at a given observation point. The theory developed will be useful for RCS signature related problems and low grazing angle scattering when both the transmitter and the object are close to the surface.     

Electromagnetic volume scattering in the half-space: a moment-method analysis without Sommerfeld integrals or their approximations

Traditionally, in moment-method analyses of electromagnetic scattering, the elements of the impedance matrix are calculated as convolutions of the basis elements with the appropriate dyadic Green's function. However, for scattering in the half-space, the vertical and azimuthal copolar terms of the Green's function require evaluation of Sommerfeld integrals which are computationally burdensome. In this paper, it is shown that, in populating the impedance matrix for the half-space problem, evaluation of Sommerfeld integrals is, in fact, not necessary. For monochromatic excitation, the plane-wave expansion of the scattered field constitutes a Fourier transform, in the horizontal plane, of a vector spectral function. This vector function results from the convolution, in the vertical dimension, of the respective angular spectra of the Green's function and the equivalent current. On application of the moment method, through the Weyl identity, the impedance-matrix elements corresponding to the singular terms of the Green's function are convolutions in the horizontal plane of spherical potentials, and Fourier transforms of scalar spectral functions. These scalar functions are derived from the basis elements and, with a judicious choice of basis, they are well behaved and of compact support, and consequently their Fourier transforms can be computed as FFTs.     

Radiative transfer theory with time delay for the effect of pulse entrapping in a resonant random medium: General transfer equation and point-like scatterer model

Abstract

A pulse propagation of a vector electromagnetic wave field in a discrete random medium under the condition of Mie resonant scattering is considered on the basis of the Bethe–Salpeter equation in the two-frequency domain in the form of an exact kinetic equation which takes into account the energy accumulation inside scatterers. The kinetic equation is simplified using the transverse field and far wave zone approximations which give a new general tensor radiative transfer equation with strong time delay by resonant scattering. This new general radiative transfer equation, being specified in terms of the low-density limit and the resonant point-like scatterer model, takes the form of a new tensor radiative transfer equation with three Lorentzian time-delay kernels by resonant scattering. In contrast to the known phenomenological scalar Sobolev equation with one Lorentzian time-delay kernel, the derived radiative transfer equation does take into account effects of (i) the radiation polarization, (ii) the energy accumulation inside scatterers, (iii) the time delay in three terms, namely in terms with the Rayleigh phase tensor, the extinction coefficient and a coefficient of the energy accumulation inside scatterers, respectively (i.e. not only in a term with the Rayleigh phase tensor). It is worth noting that the derived radiative transfer equation is coordinated with Poynting's theorem for non-stationary radiation, unlike the Sobolev equation. The derived radiative transfer equation is applied to study the Compton–Milne effect of a pulse entrapping by its diffuse reflection from the semi-infinite random medium when the pulse, while propagating in the medium, spends most of its time inside scatterers. This specific albedo problem for the derived radiative transfer equation is resolved in scalar approximation using a version of the time-dependent invariance principle. In fact, the scattering function of the diffusely reflected pulse is expressed in terms of a generalized time-dependent Chandrasekhar H-function which satisfies a governing nonlinear integral equation. Simple analytic asymptotics are obtained for the scattering function of the front and the back parts of the diffusely reflected Dirac delta function incident pulse, depending on time, the angle of reflection, the mean free time, the microscopic time delay and a parameter of the energy accumulation inside scatterers. These asymptotics show quantitatively how the rate of increase of the front part and the rate of decrease of the rear part of the diffusely reflected pulse become slower with transition from the regime of conventional radiative transfer to that of pulse entrapping in the resonant random medium.     

Anisotropic surface relief diffraction gratings under arbitrary plane wave incidence

A modal method is used for the analysis under oblique incidence of a diffraction grating made of anisotropic material. The problem is studied viewing the structure as the cascade of junctions between periodic arrays of anisotropic slab waveguides with the same period and different heights. This diffraction problem is formulated in terms of an integral equation that enforces the continuity of the transverse magnetic field at the junction. The unknown is the transverse electric field at the junction. It is possible to use also another formulation, where the role of the two fields is exchanged. The kernels of these equations are the relevant Green's functions, which are expressed in terms of eigenfunction expansions. The determination of the modes of the various regions composed of arrays of anisotropic dielectric slabs has been carried out by the method of spectral elements, whereby the field components are represented in a polynomial basis and the original differential eigenvalue problem is converted into an algebraic one. The integral equation is solved numerically by the method of moments and each junction is characterized by its generalized scattering matrix (GSM). Finally, the diffraction efficiencies of the grating are obtained by combining the various GSM's.     

An analytic and numerical solution with spectral Green's function method for transport equation in spherical geometry

Since in many cases curvilinear geometry is more appropriate than cartesian geometry for precise modeling of the complex systems for reactor calculation, we have developed the spectral Green's function (SGF) method which is employed to obtain angular and scalar flux distributions in heterogeneous sphere geometry with isotropic scattering. In this study, we showed that the neutron transport problems of homogeneous spheres could be reduced to the solution of plane geometry equation.Finally, some results are discussed and compared with those already obtained by diamond difference scheme to test the accuracy of the results. The agreement is satisfactory. SGF method is very suitable for the numerical solution of the neutron transport equation with isotropic scattering.     

A derivation of the radiation transfer theory for random media

The wave propagation in a medium with randomly varying material parameters is considered. Starting from a quite general form of the Bethe-Salpeter equation for the two-point moment of the field, a spectral balance equation is derived. In a first step, a Wigner transformation is carried out which converts the two-point moment into a function depending on position, time, wave vector and frequency. Then, for wavelengths which are long compared to the correlation length of the medium, this function is split up into a relevant part and a background. Eliminating the background leads to the usual radiation transfer theory and provides us a general and concise expression for the effective scattering in terms of the effective operators involved in the Bethe-Salpeter equation. In the case of weak heterogeneity, the result reduces to those previously obtained.     

Factorization of correlation functions and the replica limit of the Toda lattice equation

Exact microscopic spectral correlation functions are derived by means of the replica limit of the Toda lattice equation. We consider both Hermitian and non-Hermitian theories in the Wigner–Dyson universality class (class A) and in the chiral universality class (class AIII). In the Hermitian case we rederive two-point correlation functions for class A and class AIII as well as several one-point correlation functions in class AIII. In the non-Hermitian case the average spectral density of non-Hermitian complex random matrices in the weak non-Hermiticity limit is obtained directly from the replica limit of the Toda lattice equation. In the case of class A, this result describes the spectral density of a disordered system in a constant imaginary vector potential (the Hatano–Nelson model) which is known from earlier work. New results are obtained for the average spectral density in the weak non-Hermiticity limit of a quenched chiral random matrix model at non-zero chemical potential. These results apply to the ergodic or ϵ domain of the quenched QCD partition function at non-zero chemical potential. Our results have been checked against numerical results obtained from a large ensemble of random matrices. The spectral density obtained is different from the result derived by Akemann for a closely related model, which is given by the leading order asymptotic expansion of our result. In all cases, the replica limit of the Toda lattice equation explains the factorization of spectral one- and two-point functions into a product of a bosonic (non-compact integral) and a fermionic (compact integral) partition function. We conclude that the fermionic partition functions, the bosonic partition functions and the supersymmetric partition function are all part of a single integrable hierarchy. This is the reason that it is possible to obtain the supersymmetric partition function, and its derivatives, from the replica limit of the Toda lattice equation.     

Functional integral approach to the single impurity Anderson model

Recently, a functional integral representation was proposed by Weller [1], in which the fermionic fields strictly satisfy the constraint of no double occupancy at each lattice site. This is achieved by introducing spin dependent Bose fields. The functional integral method is applied to the single impurity Anderson model both in the Kondo and mixed-valence regime. Thef-electron Green's function and susceptibility are calculated using an Ising-like representation for the Bose fields. We discuss the difficulty to extract a spectral function from the knowledge of the imaginary time Green's function. The results are compared with NCA calculations.     

Numerical investigation of the effect of soot aggregation on the radiative properties in the infrared region and radiative heat transfer

The effect of aggregation on soot radiative properties in the infrared region of the spectrum is numerically investigated using Rayleigh-Debye-Gans theory for fractal aggregates (RDG-FA). In order to use the RDG-FA theory for a wide range of aggregate sizes and wavelengths, the predicted phase functions, scattering and absorption coefficients are compared with a more accurate theory, the integral equation formulation for scattering—IEFS. The importance of scattering when compared with absorption is investigated, as well as the effect of aggregation on the phase function shape and on the scattering cross section. It is concluded that in the case of small aggregates formed with small primary particles the scattering coefficient is negligible compared with the absorption coefficient, and scattering and aggregation of primary particles can be ignored. Thus, the Rayleigh approximation can be used leading to isotropic scattering. In the case of large aggregates constituted by large primary particles, aggregation becomes important and the scattering cross section is of the same order of magnitude of the absorption cross section. Moreover, the phase function becomes highly peaked in the forward direction. Therefore, the Rayleigh and the equivalent volume Mie sphere approximations are not valid, and the RDG-FA method emerges as a good compromise between accuracy and simplicity of application. However, radiative transfer calculations between two infinite, parallel, black walls show that scattering may always be neglected in the calculation of total radiative heat source and heat fluxes to the walls. The minor influence of scattering on the accuracy of the predictions is explained by the shift between the spectral region where scattering is important and the region where the spectral radiative heat source is large.     

Adiabatic behavior of sine-Gordon solitons in the presence of perturbations

The behavior of sine-Gordon solitons in the presence of weak perturbations is considered. The procedure is based on the exact inverse scattering solution of the unperturbed sine-Gordon equation. Accounting for perturbations such as those arising from impurities, external forces as well damping and spatially inhomogeneous frequencies the corresponding perturbed operator equation can be solved by the Green's function technique if one expands the Green's operator in terms of a set of biorthogonal eigenfunctions. Ordinary linear differential equations prescribing the time evolution of the scattering data are obtained. Instead of solving the inverse scattering problem completely the adiabatic assumption is then used anticipating the result that solitons maintain their integrity to a high degree. Explicit solutions for the one-soliton dynamics are presented.Work supported by the Deutsche Forschungsgemeinschaft through the Sonderforschungsbereich Nr. 162 Plasmaphysik Bochum/Jülich     

三维漫射光谱法检测猪肉嫩度的初步研究

猪肉是光的强散射物质,嫩度是评价猪肉品质优劣的重要标准之一,提出一种基于三维漫射光谱法的猪肉嫩度检测方式。将猪肉样本更多的散射信息引入光谱分析中。利用实验室搭建的数据采集系统,通过采集距光源入射点不同距离处的样本漫反射光信号构建了64个猪肉样本的三维漫射光谱。经过小波消噪处理后,利用多维偏最小二乘法(NPLS)建立了三维漫射光谱与猪肉嫩度之间的分析模型,模型的校正决定系数R2_Cal是0.883 1,校正标准差RMSEC是3.685 0N,预测决定系数R2_Pred是0.874 7,预测标准差RMSEP是3.9756N。实验结果表明, 与常规的漫反射光谱法相比,三维漫射光谱法所建立的猪肉嫩度NPLS模型具有更高的校正精度和预测稳健性,有望为猪肉嫩度及其他品质的快速检测提供一种新的途径。     

THE PHONON DENSITY OF STATES AND THE NEUTRON SCATTERING FACTOR FOR A DISORDERED POLYMER CHAIN

In this paper we calculated the phonon density of states and the neutron scattering factor in a model of a random polymer chain embedded as a self-avoiding walk on a diamond lattice by using the equation of motion method of Green's function. The Iiadltonian of the mdel includes stretching force, bending force and dihedral force. The result showea that the gap near ω=0 disappeared,which is in good agreement with experiment. It is also found that peaks of the spectrunr at low frequencies are sensitive to the degree of crystallization. This indicates that they are related only to the vibration of the crystalline region.     

On the solution of the kinetic equation for a heat flux between concentric spheres

The problem of calculating a heat flux in a spherical layer is considered. The results are obtained in terms of the Bhatnagar-Gross-Krook model and the Boltzmann collision integral. A general (independent of the form of the kinetic equation and the solution method) expression for the heat flux as a function of the energy accommodation coefficient is derived. The results are compared with the experiment and the analytical results obtained previously.