Uniaxial tension of a plate with a circular hole at finite strain

Some kinematic characteristics of a geometrically nonlinear deformation process obtained experimentally at uniaxial tension of a plate with a circular hole are given. The plate is made of a highly elastic material. The geometric linearization method is used to determine the numerical characteristics of the deformation process under study.     

The modified horizontal derivative and some of its applications

To Gurii Ivanovich Marchuk on the occasion of his 70th birthday.     

Formation of the crystal structure of intermetallic compounds in mechanically activated Ni-Al and Ti-Al systems during self-propagating high-temperature synthesis

The dynamics of structural and phase transitions during heterogeneous reaction in mechanically activated mixtures has been investigated by X-ray diffraction, scanning electron microscopy, and dynamic synchrotron radiation diffraction. It is shown that the mechanisms of formation of the structure of reaction products are significantly different, depending on the temperature mode of the synthesis. Upon slow heating, the process is multistage and includes several intermediate crystalline phases. Upon fast heating, the transformation in the combustion wave occurs much faster, with only one intermediate phase observed.     

On conformal Killing symmetric tensor fields on Riemannian manifolds

A vector field on Riemannian manifold is called conformal Killing if it generates oneparameter group of conformal transformation. The class of conformal Killing symmetric tensor fields of an arbitrary rank is a natural generalization of the class of conformal Killing vector fields, and appears in different geometric and physical problems. In this paper, we prove that a trace-free conformal Killing tensor field is identically zero if it vanishes on some hypersurface. This statement is a basis of the theorem on decomposition of a symmetric tensor field on a compact manifold with boundary to a sum of three fields of special types. We also establish triviality of the space of trace-free conformal Killing tensor fields on some closed manifolds.     

Time-of-flight measurements in a molecular beam generated from a jet of condensing carbon dioxide

The technique is described and results are presented for time-of-flight (TOF) measurements of the number density of molecules using electron-beam fluorescence diagnostics of a cluster-containing molecular beam extracted from a jet of condensing CO₂. The possibility of using these methods to record the velocity distribution function of the molecules (monomers) in a cluster beam is substantiated. Methods for measuring the velocity of the clusters in a CO₂ cluster beam based on their fragmentation upon impact on a solid surface are proposed and implemented. The domains of applicability of these methods and their shortcomings and merits in comparison with the conventional methods are discussed. The proposed methods are used in measurements of the velocity and temperature of the gas and the velocity of the clusters in a jet of condensing CO₂. Zh. Tekh. Fiz. 68, 120–124 (August 1998)