Calculation of electromechanical coupling coefficient of Lamb waves in multilayered plates

Two methods have been always used to calculate the electromechanical coupling coefficient of a Lamb wave in a multilayered plate: one is an approximate method using the acoustic velocity difference under different electric boundary conditions and the other is the Green's function method. The Green's function method is more accurate but more complicated, because an 8N-order matrix is used for calculating the electromechanical coupling coefficient of the Lamb wave in an N-layered plate, which induces great computation loads and some calculation deviations. In this paper, a transfer matrix method is used for calculating the electromechanical coupling coefficient of Lamb waves in a multilayered plate, in which only an 8-order matrix is needed regardless of the number of layers of the plate. The results show that the transfer matrix method can obtain the same accuracy as those by the Green's function method, but the computation load and deviation are greatly decreased by avoiding the use of a high order matrix used in the Green's function method.     

Extracting the Green's function from measurements of the energy flux

Existing methods for Green's function extraction give the Green's function from the correlation of field fluctuations recorded at those points. In this work it is shown that the Green's function for acoustic waves can be retrieved from measurements of the integrated energy flux through a closed surface taken from three experiments where two time-harmonic sources first operate separately, and then simultaneously. This makes it possible to infer the Green's function in acoustics from measurements of the energy flux through an arbitrary closed surface surrounding both sources. The theory is also applicable to quantum mechanics where the Green's function can be retrieved from measurement of the flux of scattered particles through a closed surface.     

A representation for Green's function retrieval by multidimensional deconvolution

Green's function retrieval by crosscorrelation may suffer from irregularities in the source distribution, asymmetric illumination, intrinsic losses, etc. Multidimensional deconvolution (MDD) may overcome these limitations. A unified representation for Green's function retrieval by MDD is proposed. From this representation, it follows that the traditional crosscorrelation method gives a Green's function of which the source is smeared in space and time. This smearing is quantified by a space-time point-spread function (PSF), which can be retrieved from measurements at an array of receivers. MDD removes this PSF and thus deblurs and deghosts the source of the Green's function obtained by correlation.     

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.     

夸克-反夸克束缚态的B-S相互作用核的封闭表示式(英文)

根据从 QCD生成泛函所建立的夸克和反夸克的传播子、四点格林函数及其它类型的格林函数所满足的运动方程 ,推导出了夸克 -反夸克束缚态的 Bethe- Salpeter方程中相互作用核的明显且封闭的表示式 ,给出了这个表示式的未重整化和重整化了的形式 .这个表示式不仅易于进行微扰计算 ,而且适于进行非微扰的计算 ,特别是它提供了求解夸克禁闭问题一个恰当的理论出发点.The interaction kernel in the Bethe-Salpeter equation for quark-antiquark bound states is derived from the Bethe-Salpeter equations satisfied by the quark-antiquark four-point Green s function. The latter equations are established based on the equations of motion obeyed by the quark and antiquark propagators, the four-point Green s function and some other kinds of Green s functions which follow directly from the QCD generating function. The Bethe-Salpeter kernel derived is an exact...     

Efficient Evaluation of the Green's Function for an Array of Magnetic-Current Sheets Periodically Located on the Surface of a Metal Cylinder

We propose an effective method for calculating the Green's function of an array of identical magnetic-current sheets periodically located on the surface of a circular metal cylinder. The idea of our approach consists in that we explicitly isolate the field singularity at the source by improving the convergence in the Green's function representation. As a result, the residual part of the Green's function can efficiently be calculated numerically. We present numerical results showing the behavior of the Green's function. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 4, pp. 331–339, April 2005     

Wave propagation in a transient plasma-development of a Green'sfunction

The effect of a transient plasma on a source wave, when the rise time of the electron density profile is comparable to the source wave period, is considered. The problem is not amenable to a sudden-switching approximation or an adiabatic approximation. It is investigated by developing a causal Green's function for temporally unlike media. A perturbation series based on the Green's function gives the solution to the desired accuracy. As compared to the numerical methods that give the total fields, this method has the intrinsic advantage of processing the forward propagating and backward propagating waves explicitly. The validity of the method is illustrated by comparing the perturbation solution to the exact solution of a linear profile. The scattering coefficients for a “hump profile,” which has no obvious exact solution, are obtained to illustrate the general applicability of the new approach     

The asymptotic behaviour of the exact and approximative ν = 1/2 Chern-Simons Green's functions

We consider the asymptotic behaviour of the Chern-Simons Green's function of the ν = 1/ system for an infinite area in position-time representation. We calculate explicitly the asymptotic form of the Green's function of the interaction free Chern-Simons system for small times. The calculated Green's function vanishes exponentially with the logarithm of the area. Furthermore, we discuss the form of the divergence for all τ and also for the Coulomb interacting Chern-Simons system. We compare the asymptotics of the exact Chern-Simons Green's function with the asymptotics of the Green's function in the Hartree-Fock as well as the random-phase approximation (RPA). The asymptotics of the Hartree-Fock Green's function correspondence well with the exact Green's function. In the case of the RPA Green's function we do not get the correct asymptotics. At last, we calculate the self consistent Hartree-Fock Green's function. Received 5 July 2001 and Received in final form 30 November 2001     

Scalar Green's functions in an Euclidean space with a conical-type line singularity

In an Euclidean space with a conical-type line singularity, we determine the Green's function for a charged massive scalar field interacting with a magnetic flux running through the line singularity. We give an integral expression of the Green's function and a local form in the neighbourhood of the point source, where it is the sum of the usual Green's function in Euclidean space and a regular term. As an application, we derive the vacuum energy-momentum tensor in the massless case for an arbitrary magnetic flux.Supported by a grant from CNPq (Brazilian government agency FA)     

The mobility edge problem: Continuous symmetry and a conjecture

An apparently overlooked symmetry of the disordered electron problem is derived. It yields the well-known Ward-identity connecting the one- and two-particle Green's function. This symmetry and the apparent shortrange behaviour of the averaged one-particle Green's function are used to conjecture that the critical behaviour near the mobility edge coincides with that of interacting matrices which have two different eigenvalues of multiplicity zero (due to replicas). As a consequence the exponents of the d.c. conductivity is expected to approach 1 for real matrices and 1/2 for complex matrices as the dimensionality of the system approaches two from above. In two dimensions no metallic conductivity is expected.     

Construction of the Green's function for the pseudoharmonical oscillator

In the present paper we have constructed the Green's function for the pseudoharmonical potential, which is considered as an intermediate potential between the harmonic and anharmonic potentials. We have used a hybrid method, by combining the Laplace transformation method and the Green's function technique. The Green's function is used for obtaining the density matrix for a quantum-statistical system, in coordinate representation. Even if this is not a new result, the method can be applied to a class of exactly solvable potentials.     

Krylov-space approach to the equilibrium and nonequilibrium single-particle Green's function

The zero-temperature single-particle Green's function of correlated fermion models with moderately large Hilbert-space dimensions can be calculated by means of Krylov-space techniques. The conventional Lanczos approach consists of finding the ground state in a first step, followed by an approximation for the resolvent of the Hamiltonian in a second step. We analyze the character of this approximation and discuss a numerically exact variant of the Lanczos method which is formulated in the time domain. This method is extended to obtain the nonequilibrium single-particle Green's function defined on the Keldysh-Matsubara contour in the complex time plane which describes the system's nonperturbative response to a sudden parameter switch in the Hamiltonian. The proposed method will be important as an exact-diagonalization solver in the context of self-consistent or variational cluster-embedding schemes. For the recently developed nonequilibrium cluster-perturbation theory, we discuss its efficient implementation and demonstrate the feasibility of the Krylov-based solver. The dissipation of a strong local magnetic excitation into a non-interacting bath is considered as an example for applications.     

Double-time Green's functions for crystals with defects

A general method for the calculation of the double-time Green's function of displacements for a crystal with arbitrary symmetry and arbitrary point defect is given in a harmonic approximation. Green's function is derived in two forms. In the first form Green's function of the ideal crystal is modified by the defect, in the second form Green's function of the defect molecule is modified by the ideal part of the crystal.     

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。     

Localized partial traps in diffusion processes and random walks

Reaction-diffusion equations, in which the reaction is described by a sink term consisting of a sum of delta functions, are studied. It is shown that the Laplace transform of the reactive Green's function can be analytically expressed in terms of the Green's function for diffusion in the absence of reaction. Moreover, a simple relation between the Green's functions satisfying the radiation boundary condition and the reflecting boundary condition is obtained. Several applications are presented and the formalism is used to establish the relationship between the time-dependent geminate recombination yield and the bimolecular reaction rate for diffusion-influenced reactions. Finally, an analogous development for lattice random walks is presented.     

Green's functions for a volume source in an elastic half-space

Green's functions are derived for elastic waves generated by a volume source in a homogeneous isotropic half-space. The context is sources at shallow burial depths, for which surface (Rayleigh) and bulk waves, both longitudinal and transverse, can be generated with comparable magnitudes. Two approaches are followed. First, the Green's function is expanded with respect to eigenmodes that correspond to Rayleigh waves. While bulk waves are thus ignored, this approximation is valid on the surface far from the source, where the Rayleigh wave modes dominate. The second approach employs an angular spectrum that accounts for the bulk waves and yields a solution that may be separated into two terms. One is associated with bulk waves, the other with Rayleigh waves. The latter is proved to be identical to the Green's function obtained following the first approach. The Green's function obtained via angular spectrum decomposition is analyzed numerically in the time domain for different burial depths and distances to the receiver, and for parameters relevant to seismo-acoustic detection of land mines and other buried objects.     

Dyadic Green‘s function for an unbounded gyroelectric chiral medium in cylindrical coordinates

The dyadic Green‘s function for an unbounded gyroelectric chiral medium is formulated in the Fourier domain in cylindrical coordinates.After a triple Fourier integral of the dyadic Green‘s function has been obtained,the integral is reduced by performing the integration over the transverse Fourier variable.     

各向异性立方晶体的弹性格林函数及其应用

本文计算了各向异性立方晶体的弹性格林函数的级数展开式,给出了直到二级近似的展开式的系数。将所得结果应用于弹性偶极子模型,给出了对称中心所产生的位移场及两对称中心间的弹性相互作用的表示式。应用于Cu,K等强各向异性立方晶体,虽然级数的收敛较慢,但所得关于对称中心的位移场,及二对称中心间的互作用能的数值结果,竟与基于点阵的不连续性作出的点阵静力学计算所得的结果基本一致。从而表明,本文给出的直到二级近似的弹性格林函数的解析表示提供了一个可以普遍应用的简便的方法。它可以较准确地描述立方晶体的某些力学行为。 关键词：     

Ocean acoustic interferometry

Ocean acoustic interferometry refers to an approach whereby signals recorded from a line of sources are used to infer the Green's function between two receivers. An approximation of the time domain Green's function is obtained by summing, over all source positions (stacking), the cross-correlations between the receivers. Within this paper a stationary phase argument is used to describe the relationship between the stacked cross-correlations from a line of vertical sources, located in the same vertical plane as two receivers, and the Green's function between the receivers. Theory and simulations demonstrate the approach and are in agreement with those of a modal based approach presented by others. Results indicate that the stacked cross-correlations can be directly related to the shaded Green's function, so long as the modal continuum of any sediment layers is negligible.     

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.