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  • Author: J. Posta x
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Abstract

In this paper, we present a finite difference analysis of the consolidation problem for saturated porous media. In the classical model, the behaviour of the porous environment – fluid system is described by a set of equations for the unknown vector displacements of the matrix skeleton and the fluid pressure. For simplicity we consider a model problem with constant coefficients in a rectangular domain. A priori estimates for the difference solution of the problem are obtained and on their basis the convergence of two-level difference schemes is investigated.

Abstract

In this paper we consider the numerical approximation of the solution of the 2D unsteady Lame equations on a rectangular domain. The basic problems that appear, using both finite difference and finite element methods, are connected with the fact that these equations are strongly coupled. Thus it is natural to design computational algorithms in such a way that they allow one to consider boundary value problems only for uncoupled equations. To implement this general concept, some special (unconditionally stable) operator-splitting schemes are constructed. Its major peculiarity is that transition to the next time level is performed by solving separate elliptic problems for each component of the displacement vector. The previous results make it possible to design efficient numerical algorithms for elasticity equations.

Heteropolynuclear gold(I)-thallium(I) complexes of the type [TlLn][Au(C6F5)2] (L = py (2), 2,2’- bipy (3), 1,10-phen (4) or 4,4’-bipy and THF (5); n = 1, 2) have been obtained from reactions of the corresponding N-donor ligands with the precursor {Tl[Au(C6F5)2]}n (1). The crystal structures of complexes 3 - 5 have been determined by X-ray diffraction showing one- (3, 4) or three-dimensional (5) arrays. All complexes are photoluminescent in the solid state at RT and at 77 K. The strong visible emissions of complexes 2 - 5 are displayed over a wide range of wavelengths (460 - 620 nm) depending on the environment of the thallium(I) centres and on the nature of the N-donor ligand.