The stressed state of piecewise-homogeneous bodies subject to nonsteady thermal fields

The study of the distribution of thermal fields and the thermal stresses they generate, and the influence of these factors on the strength of piecewise-homogeneous bodies was begun and developed in the work of Ya. S. Pidstrigach, Yu. M. Kolyano, and their students [5, 12, 13]. In the present paper we use the theory of generalized functions to reduce the two-dimensional quasistatic problem of thermal stresses for piecewisehomogeneous bodies to solving systems of integral equations. The kernels of these equations are chosen as the corresponding Green's functions. We obtain a single system of integral equations for the entire region under consideration. To solve the system we apply the method of boundary elements [2]. On the basis of the results obtained we carry out a study of the thermostressed state of a half-plane with rectangular inclusions. Translated fromMatematichni Metodi i Fiziko-mekhnichni Polya, Vol. 40, No. 1, 1997, pp. 53–58.     

Wave attenuation in an elastic medium

This article examines the propagation of viscoelastic (elastic) waves in a medium consisting of two layers of finite thickness. It is found that there is a mechanical effect manifest in the monotonic dependence of the damping factor on the parameters of the system. These dependences have distinct maxima and minima, thus making it possible to optimize the damping properties of systems by varying their geometric parameters.Translated from Dinamicheskie, Sistemy, No. 4, pp. 57–62, 1985.     

Acoustic effect of pulsed high-energy proton beams

Experimental data on the generation of acoustic radiation in solid targets by pulsed high-energy proton beams are outlined. The features of ultrasound generation in solids by beams of heavy charged particles are analyzed, and the possibility of using the acoustic effect of heavy charged particles to investigate the interaction between radiation and condensed media and to determine particle energies is shown.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 95–99, August, 1991.     

Measurement of the transverse Doppler shift using a stored relativistic7Li+ ion beam

We have performed for the first time precision spectroscopy on a coasting fast⁷Li⁺ ion beam in a storage ring. The ion beam moving with 6.4% speed of light was first electron cooled and then merged with two counterpropagating laser beams acting on two different hyperfine transitions sharing a common upper level (λ-system). One laser was frequency locked to thea ₃ ¹²⁷J₂ hfs frequency component established as a secondary frequency standard at 514 nm. The second laser was tuned over theλ-resonance, which was recorded relative to¹²⁷J₂ hfs components. This experiment is sensitive to the time dilation in fast moving frames and will lead to new limits for the verification of special relatively. The present status of the experiment and perspectives in accuracy are discussed.     

Inversion of the density gradient and the diffusion “gate” in isothermal mixing of gases

The stable quasistationary mixing of ternary gas mixtures in a system of two chambers connected by a capillary is described by a theoretical model which predicts the density distribution of the mixture along the length of the diffusion channel. It is demonstrated that inversion of the density gradient can occur due to a nonlinear concentration distribution of the heavy component in a diffusion “gate” effect. The results obtained using this model are compared with the experimental data. Zh. Tekh. Fiz. 68, 14–17 (May 1998)     

Magnetostatic analog of Love surface elastic waves

The possibility of the existence of a magnetostatic analog of Love surface elastic waves is predicted. They appear in situations where the conditions for the existence of magnetostatic volume waves hold in the upper layer of a ferromagnetic bilayer, but not in the lower layer. Zh. Tekh. Fiz. 68, 85–90 (October 1998)     

Existence of fixed points for mappings of finite sets

We show that the existence theorem for zeros of a vector field (fixed points of a mapping) holds in the case of a “convex” finite set X and a “continuous” vector field (a self-mapping) directed inwards into the convex hull co X of X. The main goal is to give correct definitions of the notions of “continuity” and “convexity”. We formalize both these notions using a reflexive and symmetric binary relation on X, i.e., using a proximity relation. Continuity (we shall say smoothness) is formulated with respect to any proximity relation, and an additional requirement on the proximity (we shall call it the acyclicity condition) transforms X into a “convex” set. If these two requirements are satisfied, then the vector field has a zero (i.e., a fixed point).     

A local characterization of the johnson scheme

Within the Johnson schemeI(m, d) we find the graphK(m, d) ofd-subsets of anm-set, two such adjacent when disjoint. Among all connected graphs,K(m, d) is characterized by the isomorphism type of its vertex neighborhoods providedm is sufficiently large compared tod. Partial support provided by NSF (USA), SERC (UK), ZWO (NL).