Excitation of an elastic half-space by a buried line source of conical waves

A formal solution is obtained to the problem of a buried line source of conical waves propagating at a constant phase velocity c in an isotropic elastic half space. By applying the boundary conditions at the free surface, it is determined that the reflected field, in addition to the incident field, requires addition of a scalar potential and two components of the vector potential. The latter is in contrast to the case of cylindrical waves where only one component of the vector potential is needed. The formal solution for the conical wave source goes over to that for the two dimensional cylindrical wave case in the limit of infinite phase velocity c.     

Radiation transfer for a homogeneous half-space with an internal source

The emergent flux for radiation transfer in a homogeneous half-space with internal source solved in terms of the diffuse reflection problem. An efficient method of analysis which utilizes trial functions based on Cases eigenvalues is developed for solving the problem. Numerical results are given and compared with the previous results.     

Green's functions in an exterior gauge field

We consider the problem of evaluating the fermion Green's functions in an exterior Abelian-like gauge field. It is shown that in the field considered, the fermion Green's functions are expressed in terms of spinor particle Green's functions in some exterior electromagnetic field. The Green's functions are found in a combination of a constant homogeneous field and a plane wave field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 67–70, September, 1987.In conclusion the authors wish to express thanks to V. G. Bagrov and D. M. Gitman for helpful discussions of the problems touched upon in the article.     

Green's functions in an external electromagnetic field

The possibility is discussed of using eigenfunctions to find different propagators in quantum electrodynamics (QED) with an external electromagnetic field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 59–64, May, 1989.The authors are grateful to B. L. Voronov and I. V. Tyutin for useful discussion of the questions examined here.     

Energy distribution between seismic waves of different types produced in an elastic half-space by a source with an arbitrary radiation pattern

The energy distribution between different types of seismic waves produced by a source of longitudinal and transverse waves with an arbitrary radiation pattern in an elastic half-space is considered. With an appropriate choice of the angular distribution functions, this source can model an earthquake source. A direct theoretical comparison of the energy distributions of seismic waves generated by an underground explosion and an earthquake is carried out. Analytical relationships that describe the dependence of the energy distribution between different types of waves on the parameters of the medium and the source are derived.     

Analytical modeling of squeeze film damping for rectangular elastic plates using Green's functions

An analytical method for the solution of squeeze film damping based on Green's function to the nonlinear Reynolds equation considering an elastic plate is presented. This allows calculating the stiffness and damping forces rapidly for various boundary conditions. The elastic plate velocity is applied to the nonlinear Reynolds equation as a forcing term. The nonlinear Reynolds equation is divided into multiple linear nonhomogeneous Helmholtz equations, which then can be solvable using the presented approach. Approximate mode shapes of a rectangular elastic plate are used, enabling the calculation of the damping ratio and frequency shift for the linear case, as well as the complex resistant pressure, for both linear and nonlinear cases.     

The radiation power of elastic waves excited in a solid half-space by a subsurface time-harmonic source

The method of Fourier transforms is used to solve the problem of excitation of longitudinal, transverse, and Rayleigh surface waves by a time-harmonic point source placed in a homogeneous isotropic, perfectly elastic half-space and acting along the normal surface. Expressions for the time-average radiation powers of the aforementioned waves are obtained by the method of radiation reaction without using any approximations. The distribution of radiation power over different types of waves depending on their velocities and the source’s depth is investigated in detail.     

Commutator Green's functions for a spin Hamiltonian

All the commutator Green's functions are calculated for the Heisenberg spin Hamiltonian in the Hartree-Fock approximation. It is shown further that the Tyablikov transverse commutator Green's function corresponds to the Hartree—Fock approximation only for the longitudinal part of the Heisenberg spin Hamiltonian, and to obtain the longitudinal part of the commutator Green's function to the same accuracy as the Tyablikov transverse commutator Green's function it is necessary to go over to the Hartree—Fock approximation only with respect to the transverse part of the Heisenberg spin Hamiltonian.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 62–65, December, 1980.     

Axioms for Euclidean Green's functions

We establish necessary and sufficient conditions for Euclidean Green's functions to define a unique Wightman field theory.Supported by the National Science Foundation under grant GP 31239X.Supported in part by the Air Force Office of Scientific Research, contract AF 44620-70-C-0030.     

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。     

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)     

Forced torsional vibrations of a cylindrical rod connected to an elastic half-space

An analysis is presented of the forced torsional vibrations of a cylindrical rod connected to an elastic half-space under the condition that the circumferential displacement at the free end of the rod, where the disturbing moment is applied, varies proportionally with the distance from the rod axis. Both the Pochhammer-Chree and elementary theory are utilized. The response curve of the rotational amplitude at the free end of the rod, obtained from the Pochhammer-Chree theory, and that obtained from the elementary theory almost coincide with each other except in the case where the rod and the half-space are of the same material. The amplitude attenuation is largest when the rod and the half-space are of the same material. The maximum values of half-space displacement distribution at the interface lie within the rod edge.     

半空间球面波函数叠加法重构声源直接辐射声场

提出了基于半空间球面波函数叠加的声场重构方法,以重构含有限声阻抗边界半空间中声源直接辐射的声场。在半空间中多极子声源声压场的解析解的基础上,构造出以边界声阻抗为参量的半空间球面波函数的正交基;通过求逆获得半空间总声压解的基函数系数,同时也获得声源直接辐射声场即自由空间中的基函数系数,进而重构出声源直接辐射的声场。在边界声阻抗已知和边界声阻抗未知两种条件下,对该方法进行了仿真验证和参数分析,并在全消声室内进行了实验验证。结果表明,所提方法能重构出半空间中典型声源即球形声源和平面声源的直接辐射声场;该方法在边界声阻抗已知时的重构精度与稳定性高于在边界声阻抗未知时的情形。     

Green's functions and Brewster condition for a halfspace bounded by an anisotropic impedance plane

Dyadic Green's functions are obtained for a halfspace bounded by an anisotropic impedance plane. Using the Fresnel reflection coefficients, these functions are derived in planewave spectral forms. The Brewster condition is also obtained.     

On strike-slip Somigliana dislocations in a layered elastic half-space

Summary We consider a vertical strike-slip fault which is embedded in an elastic layer overlying an elastic half-space. The layer and the half-space have different rigidities. In such a model, dislocations on the fault are usually taken to occur with uniform slip, due to the difficulty of solving analytically the general problem of variable-slip (Somigliana) dislocations in this case. We adopt the Somigliana dislocation representing a crack in a homogeneous half-space and examine under which conditions this can be considered a good approximation to a crack in the layered medium. Better approximations can be obtained by super-positions of Chebyshev polynomials of the first kind and odd degree.

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Riassunto Si considera una faglia verticale a scorrimento orizzontale, situata in uno strato elastico sovrastante un semispazio elastico di rigidità diversa Nell'àmbito di questo modello, sono state di solito considerate dislocazioni con scorrimento uniforme su tutta la faglia, a causa della difficoltà di risolvere analiticamente il problema della dislocazione a scorrimento variabile (dislocazione di Somigliana). Nel presente lavoro si adotta la dislocazione di Somigliana che rappresenta una frattura in un semispazioomogeneo e si studiano le condizioni in cui questa può essere considerata una buona approssimazione alla soluzione nel mezzo stratificato. Approssimazioni migliori possono ottenersi per sovrapposizione di polinomi di Chebyshev del primo tipo e grado dispari.

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Резйме Мы рассматриваем вертикалыу дефект проскалъзования, которыю внедрен в упручию слою, расположенныю над упрутим полупространством. Слою и полупространство имейт разлибные модули сдвича. В таком модели дислокации обыгно возникают при равномерном проскалъзовахии. Мы принимаем, гто дислокация представляет треЩину в однорном полупространстве, и исследуем, при каких условиях дислокация может рассматриватщся как трещина в слоистой среде. Наилугжее приближение может вытъ полугено с помощью суперпозиции полиномов Чебышева первого рода и нечетною степени.

     

Axioms for Euclidean Green's functions II

We give new (necessary and) sufficient conditions for Euclidean Green's functions to have analytic continuations to a relativistic field theory. These results extend and correct a previous paper.with an Appendix by Stephen SummersSupported in part by the National Science Foundation under Grant MPS 73-05037 A01.Alfred P. Sloan Foundation Fellow.     

Nonsteady perturbation theory for Green's functions

A simple method is proposed for uncoupling a complex chain of Green's function (GF) equations when the initial GF is coupled simultaneously with several higher-order GF. Uncoupling of the chain of equations of motion for the nuclear spin anticommutator Green's function provides an example of the use of this method.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 126–133, August, 1978.