The complex equivalent source method for sound propagation over an impedance plane

The sound field caused by a monopole source above an impedance plane can be calculated by using a superposition of equivalent point sources located along a line in the mirror space below the plane. Originally, such an approach for representing the half-space Green's function was described by Sommerfeld at the beginning of the last century, in order to treat half-space problems of heat conduction. However, the representation converges only for masslike impedances and cannot be used for the more important case of reflecting planes with springlike surface impedances. The singular part of the line integral can be transformed into a Hankel function, which shows that surface waves are contained in the whole solution. Unfortunately, this representation suffers from the lack of validity at certain receiver points and from restrictions on wave number and impedance range to ensure the necessary convergence. The main idea of the present method is to use also a superposition of equivalent point sources, but to allow that these sources can be located at complex source points. The corresponding form of the half-space Green's function is suitable for both masslike and springlike surface impedances, and can be used as a cornerstone for a boundary element method.     

Efficient calculation of two-dimensional periodic and waveguide acoustic Green's functions

New representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane, and for the Green's function for sound propagation in the canyon formed by two infinitely high, parallel rigid or sound soft walls and an impedance ground surface. The infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a Laplace-type integral. A pole subtraction technique is used to remove poles in the integrand which lie near the path of integration, obtaining a smooth integrand, more suitable for numerical integration, and a specific numerical integration method is proposed. Numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types. It is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts, and for problems of scattering by periodic surfaces.     

A TIGHT-BINDING CALCULATION OF LAYERED ULTRTHIN COHERENT STRUCTURES(LUCS)

The present article describes the calculation of the sub-band structure and atomic plane projected model of newly reported artificial materials,Layered Ultrathin Coherent Strucures (LUCS),by means of the Green's function method in the tight-binding approximation while only taking into account the nearest neighbor matrix elements.A formulation of a more accurate method for he same purpose,in terms of linear combinations of muffin-tin orbitals and interface plane wave orbitals is given in the appendix.     

Sound propagation around rigid barriers laterally confined by tall buildings

This paper focuses on the propagation of sound waves in the presence of acoustic barriers placed close to very tall buildings. The boundary element method (BEM) is used to model the acoustic barrier, while the presence of the tall buildings is taken into account by using the image source method. Different geometries are analyzed, representing the cases of a single building, two buildings forming a corner and three buildings defining a laterally confined space. The acoustic barrier is assumed to be non-absorbing, and all the buildings and the ground are modeled as infinite rigid plane surfaces. Calculations are performed in the frequency domain and time signals are then obtained by means of Inverse Fourier Transforms. The sound pressure loss provided by the acoustic barrier is computed, illustrating the importance of the lateral confinements.     

层状超薄共格结构(LUCS)电子态的紧束缚计算

本文就一种简单的模型,在紧束缚近似下,只计及最近邻之间的矩阵元,用格林函数方法计算了新近出现的人工材料——层状超薄共格结构——电子能带的亚结构,和投影于各层原子平面的电子局域态密度,在附录中,我们表述了用丸盒轨道(MTO)和界面平面波轨道(IPWO)的线性组合,更精密地计算电子结构的方法。 关键词：     

A conjugated infinite element method for half-space acoustic problems

Many acoustic problems (especially in environmental acoustics) involve half-space domains bounded by a plane subjected to normal admittance boundary conditions. In the "low" frequency domain, the numerical treatment of such problems usually relies on boundary element methods based on a particular Green's function suited for the half-(admittance) plane. In the present paper, an alternative hybrid finite/infinite element scheme is proposed. The method relies on a direct treatment of nonhomogeneous boundary conditions along infinite element edges (or faces). The procedure is validated through comparisons with an available reference solution.     

Momentum Space Quantum Monte Carlo on Twisted Bilayer Graphene

We report an implementation of the momentum space quantum Monte Carlo(QMC) method on the interaction model for the twisted bilayer graphene(TBG). The long-range Coulomb repulsion is treated exactly with the flat bands, spin and valley degrees of freedom of electrons taking into account. We prove the absence of the minus sign problem for QMC simulation when either the two valleys or the two spin degrees of freedom are considered.By taking the realistic parameters of the twist angle and interlayer tunnelings into the simulation, we benchmark the QMC data with the exact band gap obtained at the chiral limit, to reveal the insulating ground states at the charge neutrality point(CNP). Then, with the exact Green's functions from QMC, we perform stochastic analytic continuation to obtain the first set of single-particle spectral function for the TBG model at CNP. Our momentum space QMC scheme therefore offers the controlled computation pathway for systematic investigation of the electronic states in realistic TBG model at various electron fillings.     

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.     

A Modified Helmholtz Equation with Impedance Boundary Conditions

Here considered is the problem of transient electromagnetic scattering from overfilled cavities embedded in an impedance ground plane. An artificial boundary condition is introduced on a semicircle enclosing the cavity that couples the fields from the infinite exterior domain to those fields inside. A Green's function solution is obtained for the exterior domain, while the interior problem is solved using finite element method. Well-posedness of the associated variational formulation is achieved and convergence and stability of the numerical scheme are confirmed. Numerical experiments show the accuracy and robustness of the method.     

铁磁金属的表面阻抗与自旋波共振

本文计算了铁磁金属在平行磁场中的表面阻抗。计算中考虑了交换作用所引起的磁化率空间色散及趋肤效应的反常性。分别讨论了磁矩的两种边界条件m=0和(?m)/(?n)=0。同时研究了导电电子在表面散射性质的影响。利用Азбель-Канер在迴旋共振理论中的方法,计算了考虑电导率旋磁性条件下的表面阻抗。     

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.     

Spectral domain analysis of coupled microstrip lines on magnetized ferrite substrates

Dispersion characteristics of coupled microstrip lines on ferrimagnetic substrates are presented and their features discussed. The Hertz vector potentials in the spectral domain method are used to calculate the dyadic Green's functions in an impedance matrix form. The behavior of the propagation constants is obtained by using the spectral Galerkin's technique. Numerical results are found as a function of various geometrical parameters and of the externally applied static magnetic field. Nonreciprocal behavior is mainly observed when the static magnetic field is applied in the transverse direction, parallel to the ground plane.     

半空间电大涂敷目标散射的高频分析方法

研究了半空间内(海面,地面)电大尺寸涂敷目标散射的高频求解方法.将半空间并矢格林函数引入物理光学方法中,对半空间复杂环境影响进行考虑,并利用阻抗边界条件考虑涂敷目标表面的复杂电磁散射,推导出半空间物理光学分析方法,同时结合图形电磁学,对半空间电大涂敷目标进行消隐判断,提取像素面元法矢量和深度缓存等有效信息,快速有效地计算了半空间电大涂敷目标的雷达散射截面.数值结果证明了方法的有效性和准确性. 关键词： 半空间物理光学方法 半空间并矢格林函数 图形电磁学 雷达散射截面     

Vector Green's function algorithm for radiative transfer in plane-parallel atmosphere

Green's function is a widely used approach for boundary value problems. In problems related to radiative transfer, Green's function has been found to be useful in land, ocean and atmosphere remote sensing. It is also a key element in higher order perturbation theory. This paper presents an explicit expression of the Green's function, in terms of the source and radiation field variables, for a plane-parallel atmosphere with either vacuum boundaries or a reflecting (BRDF) surface. Full polarization state is considered but the algorithm has been developed in such way that it can be easily reduced to solve scalar radiative transfer problems, which makes it possible to implement a single set of code for computing both the scalar and the vector Green's function.     

Accounting for convective effects in zero-Mach-number thermoacoustic models

This paper presents a methodology to account for some mean-flow effects on thermoacoustic instabilities when using the zero-Mach-number assumption. It is shown that when a computational domain is represented under the M=0 assumption, a nonzero-Mach-number element can simply be taken into account by imposing a proper acoustic impedance at the boundaries so as to mimic the mean flow effects in the outer, not computed flow domain. A model that accounts for the coupling between acoustic and entropy waves is presented. It relies on a “delayed entropy coupled boundary condition” (DECBC) for the Helmholtz equation satisfied by the acoustic pressure. The model proves able to capture low-frequency entropic modes even without mean-flow terms in the fluctuating-pressure equation.     

声学超表面抑制Mack第2模态机理与优化设计

从理论上推导了声学超表面对平面声波的作用模型,该理论模型计及声波高阶衍射模态,从而能够计及超表面微结构之间的声学干扰.通过与数值结果对比,该模型预测的反射频率精度得到了一定程度的提高,并能够分辨出相邻孔声场之间的耦合模态.讨论了声学超表面吸声特性与阻抗特性对高超声速边界层内Mack第2模态的抑制机理,研究发现通过设计超表面阻抗特性,使得入射声波与反射声波在壁面处相位相反,同样可以抑制Mack第2模态.基于理论模型,分别优化设计得到最优的微结构几何尺寸,并通过对Mach 6平板边界层流动进行稳定性分析,验证了超表面不同声学特性的抑制效果.      

Influence of scattering, atmospheric refraction, and ground effect on sound propagation through a pine forest

Sound propagation through a forest is affected by the microclimate in the canopy, scattering by trunks and stems, and ground reflection. Each of these effects is such a strong contributor to the attenuation of sound that mutual interactions between the phenomena could become important. A sound propagation model for use in a forest has been developed that incorporates scattering from trunks and branches and atmospheric refraction by modifying the effective wave number in the Green's function parabolic equation model. The ground effect for a hard-backed pine straw layer is approximated as a local reaction impedance condition. Comparisons to experimental data are made for frequencies up to 4,200 Hz. Cumulative influences of the separate phenomena are examined. The method developed in this paper is compared to previously published methods. The overall comparison with spectral transmission data is good, suggesting that the model captures the necessary details.     

Damping of the magnetoplasmon propagating along a rough dielectric-semiconductor interface

The damping of a surface magnetoplasmon propagating along a rough dielectric-semiconductor interface is considered. The interaction between charge carriers in the semiconductor and the boundary has been taken into account both in the “specularity parameter” and a microscopic model of the boundary. The effective surface relaxation frequency has been analyzed as a function of the boundary parameters and the magnetic field.     

General problems of fast-electron transfer

A computation method is given in this article for the transfer of fast electrons in a plate of matter with nonuniform electric field. The kinetic equation with boundary conditions taken into account is transformed into a system of recurrence relations for the angular moments of the harmonic coefficients for the distribution function; this enables one to construct a simple computation algorithm. The Green's function is obtained for segments of a particle trajectory. Special features of calculations are given as well as results.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol, 10, pp. 32–38, October, 1973.The authors would like to express their thanks to A. A. Vorob'ev and B. A. Kononov for the interest they have shown in this work.