第二类静电边值问题中对称性格林函数的一种制作方法

着重研究了Ｎｅｕｍａｎｎ静电边值问题中对称性格林函数的制作，并以同心球壳之间空间格林函数的制作为例加以说明，同时给出了Ｄｉｒｉｃｈｌｅｔ静电边值问题的相应结果。     

Quantum thermal transport in nanostructures

In this colloquia review we discuss methods for thermal transport calculations for nanojunctions connected to two semi-infinite leads served as heat-baths. Our emphases are on fundamental quantum theory and atomistic models. We begin with an introduction of the Landauer formula for ballistic thermal transport and give its derivation from scattering wave point of view. Several methods (scattering boundary condition, mode-matching, Piccard and Caroli formulas) of calculating the phonon transmission coefficients are given. The nonequilibrium Green's function (NEGF) method is reviewed and the Caroli formula is derived. We also give iterative methods and an algorithm based on a generalized eigenvalue problem for the calculation of surface Green's functions, which are starting point for an NEGF calculation. A systematic exposition for the NEGF method is presented, starting from the fundamental definitions of the Green's functions, and ending with equations of motion for the contour ordered Green's functions and Feynman diagrammatic expansion. In the later part, we discuss the treatments of nonlinear effects in heat conduction, including a phenomenological expression for the transmission, NEGF for phonon-phonon interactions, molecular dynamics (generalized Langevin) with quantum heat-baths, and electron-phonon interactions. Some new results are also shown. We briefly review the experimental status of the thermal transport measurements in nanostructures.     

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.     

Exact wave field simulation for finite-volume scattering problems

An exact boundary condition is presented for scattering problems involving spatially limited perturbations of arbitrary magnitude to a background model in generally inhomogeneous acoustic media. The boundary condition decouples the wave propagation on a perturbed domain while maintaining all interactions with the background model, thus eliminating the need to regenerate the wave field response on the full model. The method, which is explicit, relies on a Kirchhoff-type integral extrapolation to update the boundary condition at every time step of the simulation. The Green's functions required for extrapolation through the background model are computed efficiently using wave field interferometry.     

电磁学中的格林函数

文章回顾了电磁学中的格林函数理论与格林函数方法。首先,引入标量波动方程对应的格林函数,并与信号系统中的冲击响应函数作类比。其次,引入矢量波动方程对应的并矢格林函数,包括均匀和非均匀介质中的格林函数,并探讨其与电磁理论中的互易定理、等效原理之间的联系。最后,介绍了考虑介质的运动效应和电磁场的量子效应下的格林函数理论。此外,文章也探讨了电磁格林函数在无线通信、电磁兼容等工程领域的应用。     

Method of green's functions in the theory of quantum kinetic equations. II

The kinetic and antikinetic equations are obtained for the single-particle Wigner function in the context of the method of Green's time-temperature functions for an inhomogeneous system of weakly interacting particles situated in a time-dependent electric field. The kinetic equation is derived here from the equation of motion for Green's function, satisfying the causality condition.     

Fast convergent dyadic Green's function in a rectangular waveguide

Alternative formulas for the dyadic Green's function in a rectangular waveguide are presented. These new functions are deduced by modifying part of Rahmat-Samii's derivation procedures by employing the Poisson summation technique. The Green's function obtained owns fast convergence property and is proved to be more suitable for numerical applications.     

半无限-和无限平方晶格的格林函数的关系及其应用

利用半无限平方晶格的晶格格林函数的积分表达式(见:物理学报,44(1995),987)以及由此导出的它与无限平方晶格的晶格格林函数之间的内在关系式,计算了半无限平方晶格的局部态密度和表面具有单点对角杂质时定域态的存在条件.     

The Green's matrix and the boundary integral equations for analysis of time-harmonic dynamics of elastic helical springs

Helical springs serve as vibration isolators in virtually any suspension system. Various exact and approximate methods may be employed to determine the eigenfrequencies of vibrations of these structural elements and their dynamic transfer functions. The method of boundary integral equations is a meaningful alternative to obtain exact solutions of problems of the time-harmonic dynamics of elastic springs in the framework of Bernoulli-Euler beam theory. In this paper, the derivations of the Green's matrix, of the Somigliana's identities, and of the boundary integral equations are presented. The vibrational power transmission in an infinitely long spring is analyzed by means of the Green's matrix. The eigenfrequencies and the dynamic transfer functions are found by solving the boundary integral equations. In the course of analysis, the essential features and advantages of the method of boundary integral equations are highlighted. The reported analytical results may be used to study the time-harmonic motion in any wave guide governed by a system of linear differential equations in a single spatial coordinate along its axis.     

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.     

2D Green's functions for semi-infinite transversely isotropic electro-magneto-thermo-elastic composite

Green's functions play an important role in the analyses of electro-magneto-thermo-elastic composite. However, most works available on this topic are in case of identical temperature. Based on the compact 2D general solution of transversely isotropic electro-magneto-thermo-elastic composite, which is expressed in harmonic functions, and employing the trial-and-error method, the 2D Green's function for a steady point heat source in a semi-infinite electro-magneto-thermo-elastic plane is presented by five newly induced harmonic functions. Numerical results are given graphically by contours.     

Nonequilibrium real time Green's functions and the condition of weakening of initial correlation

A new method is given to calculate real-time Green's functions in nonequilibrium from the hierarchy of equations of motion in connection with the boundary condition of weakening of initial correlations. The way of deriving a generalized quantum Boltzmann equation is shown.     

On the sound field of a shallow spherical shell in an infinite baffle

A method is presented for calculating the far field sound radiation from a shallow spherical shell in an acoustic medium. The shell has a concentrated ring mass boundary condition at its perimeter representing a loudspeaker voice coil and is excited by a concentrated ring force exerted by the end of the voice coil. A Green's function is developed for a shallow spherical shell, which is based upon Reissner's solution to the shell wave equation [Q. Appl. Math. 13, 279-290 (1955)]. The shell is then coupled to the surrounding acoustic medium using an eigenfunction expansion, with unknown coefficients, for its deflection. The resulting surface pressure distribution is solved using the King integral together with the free space Green's function in cylindrical coordinates. In order to eliminate the need for numerical integration, the radiation (coupling) integrals are solved analytically to yield fast converging expansions. Hence, a set of simultaneous equations is obtained which is solved for the coefficients of the eigenfunction expansion. These coefficients are finally used in formulas for the far field sound radiation.     

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.     

Lattice Green's Function for Infinite Square Lattice in the Second Nearest-Neighbour Interaction Approximation

In dealing with the square lattice model,we replace the traditionally needed Born-Von Karmann periodic boundary condition with additional Hamiltonian terms to make up a ring lattice.In doing so,the lattice Green's function of an infinite square lattice in the second nearest-neighbour interaction approximation can be derived by means of the matrix Green's function method.It is shown that the density of states may change when the second nearest-neighbour interaction is turned on.     

A modified Green's function determination of the conduction and insulator limit conductivities of the one-dimensional, half-filled band, Hubbard model

A modified Green's function determination of the conduction and insulator limit conductivities of the one-dimensional, half-filled band, Hubbard model is presented in a simplified version to avoid the difficulties which are encountered in some instances in utilizing commutator Green's functions in first order response determinations to external perturbations.     

压电晶体表面激发的二维声表面波Green函数

最近,我们研究了在压电晶体半空间表面激发的二维广义Green函数。在本文将仔细讨论广义Green函数的表面波部分。用稳相法给出声表面波远场渐近解。但是由于这样的渐近解在接近慢度曲线的拐点处失效,我们发展了用变型Airy函数表示的普适渐近解,从而解决了在拐点附近的解的衔接问题。
对于Y切LINbO₃,进行了声表面波Green函数分量和功率流密度的数值计算,结果表明在Y切LiNbO₃的Z方向上出现聚焦现象.     

电磁场标量格林函数在奇异点邻域内的普适特性

讨论电磁理论中标量格林函数在源点附近的等值线或等值面分布情况。包括各种有界及无界空间两维及三维格林函数。分析表明,无论边界形状如何,在奇异点附近的邻域内,两维格林函数的等值线趋于圆,三维格林函数的等值面趋于球面。有边界约束的格林函数无论形式上如何复杂,都与相应的自由空间格林函数一样,具有普适性。这为积分方程的正则化分析带来很大方便。     

有耗半空间上方导体目标电磁散射的多层快速多极子算法

提出基于高阶拟合的多层快速多极子算法,用于分析有耗半空间上方导体目标的电磁散射.采用高阶拟合方法将远区相互作用单元的半空间空域格林函数用级数表示,对高阶拟合项作加法定理展开,进而应用多层快速多极子算法.该方法具有分组小,内存需求低,易于实现的优点.用数值算例验证其正确性与有效性.     

Retrieval of Green's function and generalized optical theorem for the scattering of complete dyadic fields

Green's function retrieval has been widely used in different research fields due to the fact that the Green's function can be extracted by cross-correlating the records at two receivers. In this paper, the retrieval of the dyadic Green's function is studied by investigating the representation theorem. The generalized optical theorem for the dyadic fields is derived based on the elastic dynamic interferometric equation. By addressing the cross-correlation recorded at two receivers, the important role of the generalized optical theorem and energy equipartition in retrieving the exact Green's function is shown. The presented derivation also shows the Newton-Marchenko equation holdsif the condition of equipartition is not satisfied.