应用压缩传感求解宽角度电磁散射问题

基于矩量法中阻抗矩阵与电磁波入射方向的无关性,引入压缩传感技术,构建一种全新的含有丰富角度信息的入射源.在该入射源照射下利用矩量法获得感应电流的测度,在数次测度之后,通过快速正交匹配追踪算法可恢复各个角度入射下的激励电流.与传统的矩量法相比,计算结果保持很高的精度,且计算时间减少为原来的三分之一,从而降低了宽角度电磁响应分析的计算复杂度.     

Green's function for arbitrarily shaped dielectric bodies of revolution

In this paper, a solution is developed to calculate the electric field at one point in space due to an electric dipole exciting an arbitrarily shaped dielectric body of revolution (BOR). Specifically, the electric field is determined from the solution of coupled surface integral equations (SIE) for the induced surface electric and magnetic currents on the dielectric body excited by an elementary electric current dipole source. Both the interior and exterior fields to the dielectric BOR may be accurately evaluated via this approach. For a highly lossy dielectric body, the numerical Green's function is also obtainable from an approximate integral equation (AIE) based on a surface boundary condition. If this equation is solved by the method of moments, significant numerical efficiency over SIE is realized. Numerical results obtained by both SIE and AIE approaches agree with the exact solution for the special case of a dielectric sphere. With this numerical Green's function, the complicated radiation and scattering problems in the presence of an arbitrarily shaped dielectric BOR are readily solvable by the method of moments.     

A new single surface integral equation for light scattering by circular dielectric cylinders

A new single surface integral equation is derived for light scattering by circular dielectric cylinders. Without adopting the concept of equivalent electric or magnetic surface currents, our formulation is directly derived from coupled-surface integral equations by the property of commutative matrices of Green functions. Further development by such matrix equations leads to only one unknown function for circular dielectric-coated cylinders. In addition, numerical simulations show that even applied to elliptic scatters our equation still gives reasonably good approximate solutions in the sub-wavelength limit.     

基于渐进添边的准循环压缩感知时延估计算法

针对时延估计问题中压缩感知类算法现有测量矩阵需要大量数据存储量的问题,提出了一种基于渐进添边的准循环压缩感知时延估计算法,实现了稀疏测量矩阵条件下接收信号时延的准确估计.该算法首先建立压缩感知与最大似然译码之间的理论桥梁,然后推导基于低密度奇偶校验码的测量矩阵的设计准则,引入渐进添边的思想构造具有准循环结构的稀疏测量矩阵,最后利用正交匹配追踪算法正确估计出时延.对本文算法的计算复杂度与测量矩阵的数据存储量进行理论分析.仿真结果表明,所提算法在测量矩阵维数相同的条件下正确重构概率高于高斯随机矩阵和随机奇偶校验测量矩阵,相比于随机奇偶校验矩阵,在数据存储量相等的条件下,以较少的计算复杂度代价得到了重构概率的较大提高.     

基于压缩感知的一维海面与二维舰船复合后向电磁散射快速算法研究

矩量法作为数值方法中积分方程方法的代表, 具有计算精度高、所用格林函数自动满足辐射条件、无须额外设置边界条件等优点. 但是在舰船目标与海面复合后向电磁散射仿真中, 传统矩量法需针对每个入射角反复求解矩阵方程组, 导致其在处理后向散射问题时计算量大, 耗时长, 仿真效率低下. 为解决上述问题, 本文提出了一种基于压缩感知技术的矩量法的改进算法. 该算法在求解复合后向散射问题时, 首先利用观测矩阵与传统矩量法中的电压矩阵相乘, 得到一组新的低维度的电压矩阵; 其次通过求解新电压矩阵下的矩阵方程组, 获得电流矩阵的观测值; 最后利用恢复算法(本文采用正交匹配追踪算法)重构出所需的原始入射源照射下的电流系数. 通过与传统矩量法的计算结果对比, 表明本文所提算法能够在保证计算精度的前提下, 明显减少计算时间, 提高计算效率.     

旋转体时域有限差分法的另一推导方法和单向波方程吸收边界条件

提出了旋转体时域有限差分法的另一推导方法.基于这一方法,推导了旋转体电磁波的波动方程,进一步得出了旋转体时域有限差分法的单向波方程吸收边界条件.数值实验证实了该吸收边界条件的正确性.     

一种基于压缩感知的三维导体目标电磁散射问题的快速求解方法

提出了一种将压缩感知和特征基函数结合的方法来计算三维导体目标的雷达散射截面.利用压缩感知理论,将随机选择的矩量法阻抗矩阵作为测量矩阵,将激励电压视为测量值,然后再用恢复算法可实现二维或二维半目标感应电流的求解.对于三维导体目标,使用Rao-Wilton-Glisson基函数表示的感应电流在常用的离散余弦变换基、小波基等稀疏基上不稀疏.为此,本文将计算出的目标特征基函数作为稀疏基,用广义正交匹配追踪算法作为恢复算法来加速恢复过程,并应用到三维导体目标的雷达散射截面计算中.数值结果证明了本文方法的准确性与高效性.     

Acoustic analysis of a rectangular cavity with general impedance boundary conditions

A Fourier series method is proposed for the acoustic analysis of a rectangular cavity with impedance boundary conditions arbitrarily specified on any of the walls. The sound pressure is expressed as the combination of a three-dimensional Fourier cosine series and six supplementary two-dimensional expansions introduced to ensure (accelerate) the uniform and absolute convergence (rate) of the series representation in the cavity including the boundary surfaces. The expansion coefficients are determined using the Rayleigh-Ritz method. Since the pressure field is constructed adequately smooth throughout the entire solution domain, the Rayleigh-Ritz solution is mathematically equivalent to what is obtained from a strong formulation based on directly solving the governing equations and the boundary conditions. To unify the treatments of arbitrary nonuniform impedance boundary conditions, the impedance distribution function on each specified surface is invariantly expressed as a double Fourier series expansion so that all the relevant integrals can be calculated analytically. The modal parameters for the acoustic cavity can be simultaneously obtained from solving a standard matrix eigenvalue problem instead of iteratively solving a nonlinear transcendental equation as in the existing methods. Several numerical examples are presented to demonstrate the effectiveness and reliability of the current method for various impedance boundary conditions, including nonuniform impedance distributions.     

Excitation of a waveguide transformer

Integral immitance equations for steady-state excitation of a shielded waveguide transformer with any number of arbitrarily arranged adjoint semi-infinite waveguides are derived in the general formulation. Excitation can be carried by arbitrary inner sources (extraneous electric and magnetic currents), as well as by normal modes incident from infinity. The results are extended to the case of nonideal walls for magnetodielectric and metallic inclusions. The results give a generalization of the familiar integral impedance and admittance equations for inhomogeneous waveguides.     

Dispersion properties of helical waves in radially inhomogeneous elastic media

In this paper, a method describing dispersion curve calculation for waves propagating in radially layered, inhomogeneous isotropic elastic waveguides is developed. Particular emphasis is placed on the helical waves with noninteger azimuthal wavenumbers, which can be potentially applied in such fields as nondestructive evaluation, acoustic tomography, etc., stipulating their practical importance. To solve the problem under consideration, the matrix Riccati equation is formulated for an impedance matrix. The use of the latter yields a simple form of the dispersion equation. Numerical computation of dispersion curves can encounter difficulties, which are due to potential singularities of the impedance matrix and the necessity to separate roots of the dispersion equation. These difficulties are overcome by employing the Cayley transform and invoking the parametric continuation method. The method developed by the authors is demonstrated by calculating dispersion diagrams in support of helical waves for several models of practical interest. Such computations for an inhomogeneous layer and its approximation by a set of homogeneous layers using a transfer matrix and Riccati equation methods revealed higher computational accuracy of the latter. Dispersion curves calculated for layers with different types of inhomogeneity demonstrated significant discrepancies at low frequencies.     

Surface impedance design with ground corrugation for mitigation of large-calibre gun blast noise

The surface impedance design approach is proposed for mitigating large-calibre gun blast noise. Surrounding the blast noise, we employ a group of concentric trenches with critical depths to dampen the propagation of the acoustic wave. These trenches behave like quarter-wavelength resonators and produce acoustic soft surfaces at their openings. The sound pressure is then mitigated over these soft surfaces by destructive interference and the wave attenuates rapidly along the ground surface. To evaluate the overall acoustic performance of such a design, we develop an efficient numerical solver by treating the geometry as a body of revolution (BOR). The symmetry of the structure in the revolution direction allows the 3D boundary integral equation (BIE) for acoustic wave scattering to be reduced to a 2D integral equation by the use of Fourier series expansions. Numerical experiments show that this model can effectively suppress the acoustic wave propagation horizontally and the reduction can reach about 15 dB for large-calibre gun noise with very low-frequency components.     

基于多模光纤散斑的压缩感知在光学图像加密中的应用

为了安全高效地对图像信息进行传输,提出了一种新颖的基于多模光纤散斑的压缩感知结合双随机相位编码的光学图像加密方法.多模光纤产生的光斑作为压缩感知的测量矩阵,完成对图像的第一次压缩和加密,并且充当第一级密钥;再利用双随机相位编码技术进行第二次加密,实现对图像的完整加密过程,随机相位掩模板充当第二级密钥,解密过程与此相反.通过将光斑测量矩阵与用于压缩感知的常用随机测量矩阵进行对比研究后发现,使用光斑测量矩阵解密后的图像质量更好,而且相比于其他随机测量矩阵在硬件实现上的复杂性与高成本,光斑矩阵可以很容易地通过简单的光学器件来获得,且可以利用工作波长的改变来进行变换,也即第一级密钥非常容易变换.同时经研究表明,本文方法可以有效抵抗统计分析、噪声干扰和剪切等攻击,且对密钥敏感性高,具有良好的鲁棒性和安全性.因此,本文提出的这种基于光斑矩阵的压缩感知与双随机相位编码结合起来的加密方法,可以获得良好的加密效果与极大的密钥空间,并且易于在光学领域整合.     

Studies on Fast Algorithm for the Scattering of a Large Array of Waveguide-Fed Wide-Slot Antennas in Millimeter Wave Region

We present an effective numerical technique to characterize the scattering of wide-slot antennas fed by waveguides with arbitrary terminations in terms of the method of moment (MoM) and the mixed potential integral equation (MPIE). In particular, the precorrected-fast Fourier transform (P-FFT) eliminates the need to generate and store the usual square impedance matrix andthus leads to speed up the matrix-vector multiplication in the resultant system. This property makes the Rao-Wilton-Glisson (RWG) functions to be useful in simulating electrically large-scale problems. In addition, the scattering from the finite ground surfaces is accounted for in the total scattered field by using the method of equivalent edge currents. The numerical results are presented and compared with both the traditional method of moment results obtained using the entire-domain basis functions and the experimental results, to demonstrate the proposed method to be a good candidate for study on the scattering of arbitrary wide-slot large array.     

Giant magnetoimpedance in composite wires with insulator layer between non-magnetic core and soft magnetic shell

A method for calculation of the magnetoimpedance in composite wires having an insulator layer between non-magnetic core and soft magnetic shell is described. It is assumed that the magnetic shell has a helical anisotropy and the driving current flows through the core only. The distribution of eddy currents and expressions for the impedance are found by means of a solution of Maxwell equations taking into account the magnetization dynamics within the shell governed by the Landau–Lifshitz equation. The effect of the insulator layer on the magnetoimpedance is analyzed.     

On the initial-boundary value problems for soliton equations

We present a novel approach to solving initial-boundary value problems on the segment and the half line for soliton equations. Our method is illustrated by solving a prototypal and widely applied dispersive soliton equation—the celebrated nonlinear Schroedinger equation. It is well known that the basic difficulty associated with boundaries is that some coefficients of the evolution equation of the (x) scattering matrix S(k, t) depend on unknown boundary data. In this paper, we overcome this difficulty by expressing the unknown boundary data in terms of elements of the scattering matrix itself to obtain a nonlinear integrodifferential evolution equation for S(k, t). We also sketch an alternative approach in the semiline case on the basis of a nonlinear equation for S(k, t), which does not contain unknown boundary data; in this way, the “linearizable” boundary value problems correspond to the cases in which S(k, t) can be found by solving a linear Riemann-Hilbert problem.     

Numerical simulation of Gaussian beam scattering by complex particles of arbitrary shape and structure

An efficient numerical method based on the surface integral equations is introduced to simulate the scattering of Gaussian beam by complex particles that consist of an arbitrarily shaped host particle and multiple internal inclusions of arbitrary shape. In particular, the incident focused Gaussian beam is described by the Davis fifth-order approximate expressions in combination with rotation defined by Euler angles. The established surface integral equations are discretized with the method of moments, where the unknown equivalent electric and magnetic currents induced on the surfaces of the host particle and the internal inclusions are expanded using the Rao–Wilton–Glisson (RWG) basis functions. The resultant matrix equations are solved by using the parallel conjugate gradient method. The proposed numerical method is validated and its capability illustrated in several characteristic examples.     

Solitary wave solutions for a generalized Hirota–Satsuma coupled KdV equation by homotopy perturbation method

In this Letter, He's homotopy perturbation method (HPM), which does not need small parameter in the equation is implemented for solving the nonlinear Hirota–Satsuma coupled KdV partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of Adomian's decomposition method has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering.     

合肥光源镀膜陶瓷真空室纵向阻抗计算

 在估计合肥光源新注入系统中回形镀膜陶瓷真空室的耦合阻抗时，对于规则轴对称边界，可以采用场匹配技术求解柱坐标系中Maxwell方程得到耦合阻抗解析表达式。对于非规则形状，解析求解困难，须根据同轴线方法测量纵向阻抗基本原理，数值计算镀膜陶瓷真空室耦合阻抗。计算结果表明，陶瓷真空室内表面镀金属膜可以大大降低束流耦合阻抗，但镀膜陶瓷真空室仍是合肥光源储存环的主要阻抗来源之一。     

托卡马克理想磁流体不稳定性的统一描述 (I)

在与平衡磁面相联系的坐标系下，用剪切阿尔芬波近似给出了统一描述托卡马克等离子体理想磁流体线性运动的本征模方程。利用此方程，可以进一步给出大尺度扰动（扭曲模、低模数气球模、阿尔芬模）和小尺度扰动（高模数气球模、Mercier模）的本征模方程。本文详细讨论了小尺度扰动的本征模方程。     

On the possibility of an analytic solution of the three-body problem

Three-body Faddeev equations in the Noyes-Fiedeldey form are rewritten as a matrix analog of a one-dimensional nonrelativistic Schrödinger equation. Unlike the method of K-harmonics, where a similar equation was obtained by expansion of a three-body Schrödinger equation wavefunction into the orthogonal set of functions of two variables (K-harmonics), the use of the Noyes-Fiedeldey form of Faddeev equations allows us to limit ourselves to the expansion in functions of one variable only. The solutions of the above mentioned matrix equation are obtained. These solutions converge uniformly within every interval of continuity of the matrix, which corresponds to the potential of that equation. Their asymptotic behavior for large interparticle distances is discussed. The solutions for the harmonic oscillator, inverse-square, and Coulomb-Kepler potentials are found. It is shown that energy levels in the last case may be calculated from a simple formula which is very similar to the corresponding formula for the two-body Coulomb-Kepler problem. This formula can be easily generalized to the case of n particles interacting with inverse distance potentials.