Stress concentration around a circular hole in a transversely isotropic spherical shell

Analytical expressions for the stresses near a circular hole in a transversely isotropic shallow spherical shell under uniform pressure are derived. The form of the solution depends on the range of change in the compliance to transverse shear. The influence of the relative radius of the hole and the compliance to transverse shear on the stress concentration is analyzed.__________Translated from Prikladnaya Mekhanika, Vol. 40, No. 12, pp. 99–106, December 2004.     

Scattering on univalent graphs from theL-function point of view

The scattering process on multiloop infinite (p+1)-valent graphs is studied. These graphs are discrete spaces of a constant negative curvature, being quotients of a p-adic hyperbolic plane over free-acting discrete subgroups of the projective group PGL(2,Q _p). They are, in fact, identical to p-adic multiloop surfaces. A finite subgraph containing all loops is called the reduced graph T_red; the L-function is associated with this finite subgraph. For an infinite graph, we introduce the notion of spherical functions. They are eigenfunctions of a discrete Laplace operator acting on the graph. In scattering processes, we define the s-matrix and the scattering amplitudes c_i, imposing the restriction c_i=A_ret(u)/A_adv (u) = const for all vertices u T_supp. A_ret and A_adv are retarded and advanced branches of a solution to the eigenfunction problem and T_supp is a support domain for scattering centers. Taking the product over all c_i, we obtain the determinant of the scattering matrix, which is expressed as a ratio of two L-functions: C L(₊)/L(_–). Here the L-function is the Ihara-Selberg function depending only on the form of T_red, being the eigenvalue of the Laplacian. We present a proof of the Hashimoto-Bass theorem, the expressing L-function L(u) of any finite graph via the determinant of a local operator (u) acting on this graph. Numerous examples of L-function calculations are presented.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 103, No. 3, pp. 489–506, June, 1995.     

Mechanisms of resonant laser ionization

An experimental investigation and numerical simulation of resonant laser breakdown are performed. As a result, quantitative agreement between the experimental data on the parameters of a dense resonant plasma (the electron density and the electron temperature) and the results of calculations in the range of detunings of the laser radiation from resonance Δλ>2–2.5 nm, in which the spatial instability of the intense resonant laser beam and the absorption of radiation are minimal, is obtained for the first time. It is shown that the previously proposed mechanism of resonant breakdown associated with laser-induced associative ionization introduces only a small correction to the final extent of ionization of the resonant plasma and scarcely alters its temperature. The influence of quantum stimulated inverse bremsstrahlung processes, which are usually described as collisions of the second kind in the resonance case, on the energy gain by electrons is analyzed for the first time in reference to specific experimental findings. The numerical calculations show that at detunings of the order of the Rabi frequency, the mechanism by which electrons gain energy through the resonant system does not reduce to collisions of the second kind and can significantly increase the density of the resonant plasma. However, in this range of detunings the laser beam is still strongly perturbed by instability processes, precluding a proper comparison of the theory with experiment. At large Δλ the classical and quantum cases differ from one another only slightly, and the values of N _e calculated for both mechanisms lie within the measurement error. Zh. éksp. Teor. Fiz. 111, 1274–1296 (April 1997)     

Stability of layered materials with zero in-plane strains

The equilibrium state of layered bodies under biaxial loading is analyzed for stability. It is assumed that the in-plane strains in the layers are zero. The three-dimensional linearized theory of stability and the piecewise-homogeneous material model are used. Two models of layered bodies are considered. Specific problems for layered bodies of different structure are solved. The critical load and wave number that cause instability of layered bodies are found     

Surface instability of orthotropic laminated materials under compression

The piecewise-homogeneous material model and the three-dimensional linearized theory of stability with the assumption of small subcritical strains are used to study the surface buckling of orthotropic and transtropic laminates. A plane problem is formulated, and characteristic equations are derived. A solution is found for a specific transtropic material with different orientations of the isotropy axis __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 7, pp. 64–72, July 2006.     

Allowing for the plastic properties of rock in stability problems for a stratified rock mass

The paper addresses the important issue of allowing for the inelastic properties of rock in stability problems for a stratified rock mass. A three-dimensional nonlinear problem statement is used. An exact method to study the surface instability of a regularly layered semi-infinite medium is developed. New numerical results are obtained __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 68–81, December 2007.     

Accuracy of asymptotic method for shallow spherical shells with holes

Donetsk University. Translated from Prikladnaya Mekhanika, Vol. 25, No. 1, pp. 83–88, January, 1989.     

Resonance luminescence of a nonuniformly heated dense vapor

The thermal luminescence spectra of a dense, nonuniformly heated resonance medium (sodium vapor) are investigated experimentally under conditions when the resonance corrections to the relative permittivity are not small compared to unity and the photon mean free path is comparable to the wavelength of the radiation. The shape of the recorded spectra agrees well with a previously developed general theory of resonance radiation transfer which predicts a strong asymmetry of the spectra. The prospects for performing more-sensitive measurements in order to make a quantitative check of the theoretically predicted anomalous intensity (an order of magnitude higher than in the standard theory of resonance radiation transfer) of the radiation from a dense nonuniform medium are discussed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 1, 15–19 (10 January 1997)