Classical equilibrium generalized hydrodynamic correlation Green's functions. II. Transverse autocorrelation Green's function

Moscow Institute of Electronic Engineering. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 83, No. 2, pp. 311–319, May, 1990.     

Green's functions for polynomials in the Laplacian

A Green's function is constructed for an arbitrary polynomial in theN-dimensional Laplacian operator, subject only to the condition that no root of the polynomial may be real and negative.     

Green's functions for elliptic and parabolic equations with random coefficients II

This paper is concerned with linear parabolic partial differential equations in divergence form and their discrete analogues. It is assumed that the coefficients of the equation are stationary random variables, random in both space and time. The Green's functions for the equations are then random variables. Regularity properties for expectation values of Green's functions are obtained. In particular, it is shown that the expectation value is a continuously differentiable function in the space variable whose derivatives are bounded by the corresponding derivatives of the Green's function for the heat equation. Similar results are obtained for the related finite difference equations. This paper generalises results of a previous paper which considered the case when the coefficients are constant in time but random in space.

     

Construction of equations for classical equilibrium correlation Green's functions on the basis of kinetic equations. II

Moscow Institute of Electronic Engineering. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 89, No. 1, pp. 132–150, October, 1991.     

Classical equilibrium generalized hydrodynamic correlation Green's functions. I

Moscow Institute of Electronic Engineering. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 82, No. 3, pp. 450–465, March, 1990.     

Classical equilibrium generalized hydrodynamic correlation Green's functions. IV

Moscow Institute of Electronic Engineering. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 86, No. 3, pp. 460–473, March, 1991.     

Method of anomalous Green's functions: Antiferromagnetism in the Hubbard model on a triangular lattice

A method is proposed for describing antiferromagnetic and ferromagnetic states on a triangular lattice in the formalism of anomalous temperature-dependent Green's functions, for which equations of Dyson-Gor'kov type are formulated. These equations are solved in the Hartree approximation, and self-consistency equations are obtained for the order parameters. Finally, the connection between the considered theory and experiment is discussed.deceasedSt. Petersburg Branch of the V. A. Steklov Mathematics Institute, Russian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 101, No. 2, pp. 294–303, November, 1994.     

Three-dimensional Green's functions in anisotropic magneto-electro-elastic bimaterials

In this paper, we derive three-dimensional Green's functions in anisotropic magneto-electro-elastic full space, half space, and bimaterials based on the extended Stroh formalism. While in the full space, the Green's functions are obtained in an explicit form, those in the half space and bimaterials are expressed as a sum of the full-space Green's function and a Mindlin- type complementary part, with the latter being evaluated in terms of a regular line integral over [0, p][0, \pi]. Despite the complexity involved, the current Green's function expressions are surprisingly simple. Furthermore, the piezoelectric, piezomagnetic, and purely elastic Green's functions can all be obtained from the current Green's functions by setting simply the appropriate material coefficients to zero. A special material case, to which the extended Stroh formalism cannot be applied directly, has also been identified.¶Simple numerical examples are presented for Green's functions in full space, half space, and bimaterials with fully coupled and uncoupled anisotropic magneto-electro-elastic material properties.For given material properties and fixed source and field points, the effect of magneto-electro-elastic coupling on the Green's function is discussed. In particular, we observed that magneto-electro-elastic coupling could significantly alter the magnitude of certain Green's displacement and stress components, with difference as high as 45% being noticed. This result is remarkable and should be of great interest in the material analysis and design.     

Variational problem of the theory of Green's potential. II

Necessary and sufficient conditions for the solvability of the problem of the minimum of the Green's energy on condensers are found. A number of properties of extremals are found.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 11, pp. 1475–1480, November, 1990.