Derivation Of Green Function Research Articles

Influence of disorder of inclusions on the electromagnetic coupling factors of piezocomposites

A new solution of a coupled boundary-value problem of electromagnetoelasticity in the generalized singular approximation of the method of periodic components is found for random structures of composites. The solution is based on the singular parts of the second derivatives of Green functions for homogeneous transversely isotropic piezoelectromagnetic media with an ellipsoidal grain of heterogeneity. A numerical analysis of the effect of the degree of disorder of unidirectional piezomagnetic ferrite fibers in the isotropy plane of a unidirectional fiber-reinforced PVF-matrix composite on the effective factors of electromagnetic coupling of the composite is presented.

Green functions with pulsating sources in a two-layer fluid of finite depth

The derivation of Green function in a two-layer fluid model has been treated in different ways. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating due to the free surface and the interface. This paper is concerned with the derivation of Green functions in the three dimensional case of a stationary source oscillating. The source point is located either in the upper or lower part of a two-layer fluid of finite depth. The derivation is carried out by the method of singularities. This method has an advantage in that it involves representing the potential as a sum of singularities or multipoles placed within any structures being present. Furthermore, experience shows that the systems of equations resulted from using a singularity method possess excellent convergence characteristics and only a few equations are needed to obtain accurate numerical results. Validation is done by showing that the derived two-layer Green function can be reduced to that of a single layer of finite depth or that the upper Green function coincides with that of the lower, for each case. The effect of the density on the internal waves is demonstrated. Also, it is shown how the surface and internal wave amplitudes are compared for both the wave modes. The fluid in this case is considered to be inviscid and incompressible and the flow is irrotational.

Derivation of Green function for disordered chain by integrating over commuting and anticommuting variables

The average Green function and density of states for a one-dimensional random chain are considered. A representation of the Green function in the form of a functional integral over commuting and anticommuting variables is used and the transfer matrix method is applied. The results coincide with those obtained by Halperin (1965) and by Thouless (1975) by different methods.