Jumps of displacements and stresses as seismic sources in Biot's medium

Wave fields excited in a homogeneous isotropic Biot medium by point sources described in terms of discontinuities of displacements and stresses are determined. The results are represented in the form of relations involving Fourier-Bessel or Mellin integrals and in the form of Stokes-type formulas. The interrelations between these representations are established. Among all possible point sources exciting Biot's medium, the elementary sources, in terms of which any complicated linear source can be described, are selected. The special case where the wave fields in the two phases of the Biot medium are independent of one another is considered, and the corresponding sources in the Biot medium are compared with the known sources in elastic and fluid media.Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 239, 1997, pp. 164–196.This work was supported by the Russian Foundation for Basic Research under grant No. 96-05-65904.     

Computation of the deformation of a shell of double curvature under nonuniform heating

It is shown that nonuniform heating of a shell of double curvature during the development of creep deformations may exert significant influence on the distortion of its shape.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 33, 1991, pp. 45–48.     

Filippov type plasma focus as intense source of hard X-rays(Ex≃50 keV)

This paper evaluates the use of a plasma focus machine (Filippov type) as a pulsed intense source of hard X-rays. It is shown experimentally that discharging a capacitor bank of W=50 kJ in the new arrangement of the discharge parameters, one can deliver into the test cavity (volume of 6*10³ cm³) an average of Φ _x=8*10^-4 J/cm². The delivered energy fluence varies in the range of 2*10^-4 J/cm²⩽Φ_x⩽2.9*10^-3 J/cm², depending on the probe position. The X-ray energy spectra were established by the differential absorption method using thermo-luminescent detectors (time-integrated spectra) or plastic scintillators (time-resolved spectra). The average energy of X-ray photons is 40 keVx^av<50 keV (20 keV⩽E _x⩽170 keV) and remains quasi-constant during the main part of the pulse (~40 ns). The electron energy that can produce such bremsstrahlung radiation is in the range of 95 keV⩽E_e⩽170 keV. However, time-resolved experiments reveal that at each instant of time only one energy of electron beam occurs. The aforementioned radiation characteristics reveal new potentials for the plasma-focus machine for a variety of applications. Some insight into the physics behind production mechanism of quasi-monoenergetic relativistic-electron beams will be concurrently reviewed     

Temperature fields in laminar anisotropic shells

A numerical solution of the nonlinear heat-conduction problem is obtained for laminar anisotropic shells with temperature-dependent physicomechanical properties.Translated from Matematicheskie Metody i Fiziko-mekhanicheskie Polya, No. 26, pp. 98–101, 1987.     

Features of Structural Phase Transitions of Aluminum Hydroxides under Laser Processing

The results of the studies of laser processing of alkoxide aluminum hydroxides with micrometer and nanometer particle sizes are presented. It is shown that the pseudo-boehmite processing process and phase composition of formed oxides are controlled by particle packing, laser radiation propagation in powder, and specific energy deposition. The main phases formed upon laser heating are γ, α-Al₂O₃; the content of δ, θ-Al₂O₃ is low. The minimum corundum crystallite size is ～50 nm.     

Modeling of wave dispersion along cylindrical structures using the spectral method

Algorithm and code are presented that solve dispersion equations for cylindrically layered media consisting of an arbitrary number of elastic and fluid layers. The algorithm is based on the spectral method which discretizes the underlying wave equations with the help of spectral differentiation matrices and solves the corresponding equations as a generalized eigenvalue problem. For a given frequency the eigenvalues correspond to the wave numbers of different modes. The advantage of this technique is that it is easy to implement, especially for cases where traditional root-finding methods are strongly limited or hard to realize, i.e., for attenuative, anisotropic, and poroelastic media. The application of the new approach is illustrated using models of an elastic cylinder and a fluid-filled tube. The dispersion curves so produced are in good agreement with analytical results, which confirms the accuracy of the method. Particle displacement profiles of the fundamental mode in a free solid cylinder are computed for a range of frequencies.     

The effective model of a stratified solid-fluid medium as a special case of the Biot model

The Biot model is compared with the effective model of a stratified periodic elastic-fluid medium, and the parameters of the transversally isotropic Biot model that turn it into the effective model are found. In the course of this comparison, some intermediate models, which are generalizations of the effective model and particular cases of the Biot model, are considered. For all of the models, the wave fronts excited by a point source are determined. The distinguishing feature of wave fronts in the intermediate models is the occurrence of double loops on some of them. Bibliography: 15 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 230, 1995, pp. 172–195. Translated by L. Molotkov     

Synthesis and properties of pyrimidinylalkylphosphonic acids

Conclusions The salts of uracils react with the electrophilic phosphorus atom to give uracil phosphates, which function as phosphorylating agents toward compounds that contain a labile hydrogen atom.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 4, pp. 879–883, April, 1973.The authors wish to thank A. G. Abul'khanov for running the chromatographic separation of the reaction mixture.