Addition to the Aitken method for the extrapolation of the limit of slowly convergent sequences

The class of sequences and series in which the Aitken process accelerates the convergence is considerably extended. It is proved that a proper subsequence of a slowly convergent sequence satisfies the sufficient condition for accelerating the convergence of the Aitken transformation. Two numerical examples illustrate the highly accurate limit extrapolation.     

Adsorption of oxygen on low-index surfaces of the TiAl<Subscript>3</Subscript> alloy

Method of the projector augmented waves in the plane-wave basis within the generalized-gradient approximation for the exchange-correlation functional has been used to study oxygen adsorption on (001), (100), and (110) low-index surfaces of the TiAl₃ alloy. It has been established that the sites that are most energetically preferred for the adsorption of oxygen are hollow (H) positions on the (001) surface and bridge (B) positions on the (110) and (100) surfaces. Structural and electronic factors that define their energy preference have been discussed. Changes in the atomic and electronic structure of subsurface layers that occur as the oxygen concentration increases to three monolayers have been analyzed. It has been shown that the formation of chemical bonds of oxygen with both components of the alloy leads to the appearance of states that are split-off from the bottoms of their valence bands, which is accompanied by the formation of a forbidden gap at the Fermi level and by a weakening of the Ti–Al metallic bonds in the alloy. On the Al-terminated (001) and (110) surfaces, the oxidation of aluminum dominates over that of titanium. On the whole, the binding energy of oxygen on the low-index surfaces with a mixed termination is higher than that at the aluminum-terminated surface. The calculation of the diffusion of oxygen in the TiAl₃ alloy has shown that the lowest barriers correspond to the diffusion between tetrahedral positions in the (001) plane; the diffusion of oxygen in the [001] direction occurs through octahedral and tetrahedral positions. An increase in the concentration of aluminum in the alloy favors a reduction in the height of the energy barriers as compared to the corresponding barriers in the γ-TiAl alloy.     

Nonstationary deformation and failure of composite shells

We present the results of experimental studies of the strength of composite shells of cotton winding under the action of a lateral nonstationary load. We briefly describe devices generating pressure pulses of complicated space-time profile and the tools for measuring the parameters of the original object response to dynamic and pulse loadings. We study the influence of the action duration and the pressure application domain dimensions on the character of failure of empty and filled shells. We show that, at the shell stage of deformation, for the failure criterion one can take the moment at which the maximal circular strains attain some limit level (of the order of 2%). We propose some relations for estimating the maximal circular strain in terms of the shell characteristics and the load parameters.     

On attenuation in layered biot media and in effective models of them

Effective models of periodic layered porous Biot media possessing viscosity and relaxation are established and investigated. These models correspond to generalized Biot media with equations containing, as a rule, exponential kernels of relaxation and viscosity. Such kernels occur even if relaxation is absent in the initial medium. Inequalities that must be satisfield by the parameters of the kernels are established with the help of energy studies. Special cases in which the effective models possess no viscosity or no relaxation are stated. Bibliography: 7 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 250, 1998, pp. 244–262. Translated by L. A. Molotkov     

A corrected model of level-by-level analysis of three-layer irregular conical shells

An approach for level-by-level analysis is considered, and models for corrected investigation of stress-strain states in layers of generally irregular three-layer conical shells are developed on its basis. The models make it possible to take into account the features of a layer-inhomogeneous structure, the moment state of carrying layers, and the three-dimensional stressed state in the filler layer.     

A Conservative Version of the Method of Characteristics with a Floating Grid in Problems of Gas Dynamics

Doklady Physics - Test calculations of the motion and reflection of individual waves in a long tube have been performed applying newly developed and known schemes with a floating grid. Waves in the...     

Effective models of stratified media containing porous biot layers

Periodic stratified media in which either two porous Biot layer, or an elastic and a porous layers, or a fluid and a porous layer alternate are considered. The effective models of these media are constructed and investigated. In the case of alternating porous layers, the effective model is a generalized transversely isotropic Biot medium. In this medium, the density of the fluid phase and the mean density acquire tensor character. It is shown that the effective model of a porous-fluid medium is, on the one hand, a generalized transversely isotropic Biot medium of special type and, on the other hand, a generalization of the effective model of a stratified elastic-fluid medium.Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 239, 1997, pp. 140–163.This work was supported by the Russian Foundation for Basic Research under grant Nos. 96-01-00666 and 96-05-66207.