Eigenvalues of the antiplane-shear crack problem for a power-law material

This paper discusses the problem of finding the eigenvalue spectrum in determining the stress and strain fields at the tip of an antiplane-shear crack in a power-law material. It is shown that the perturbation method provides an analytical dependence of the eigenvalue on the material nonlinearity parameter and the eigenvalue of the linear problem. Thus, it is possible to find the entire spectrum of eigenvalues and not only the eigenvalue of the Hutchinson-Rice-Rosengren problem. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 173–180, January–February, 2008.     

Theoretical study of hydrolysis mechanism of khellin

This paper describes khellin hydrolysis mechanism using semiemperical PM3 implemented in Gaussian 03 package. The calculations show that in the presence of an acidic media, an enolate molecular ion leads directly to ω-acetokhellinone while in the basic media it leads to khellinone.     

Circular dichroism spectra of langasite family crystals in the range of electronic transitions of structure defects

The absorption and circular dichroism spectra of langasite family crystals are studied. Wide bands in the range of 285–500 nm that are related to the structure lattice defects are found. For all the crystals, these bands are in approximately the same spectral region, have identical structures, and can be attributed to one type of defects formed by cation vacancies and excess oxygen atoms in the optically active positions.     

Specific features of the formation of submicron inclusion in Ti:sapphire

Specific features of the formation of submicron (70–300 nm) inclusions in Ti:sapphire (Al₂O₃:Ti) grown in a carbon-containing medium have been investigated. These inclusions are caused by deviation from the melt stoichiometry and are formed during the melt-crystal phase transition. These defects are submicropores containing excess aluminum and its suboxides; they can be destroyed by thermal loading of a crystal.     

Numerical study of the influence of boundary conditions on the dynamic behavior of a cylindrical shell conveying a fluid

We consider a finite element algorithm intended to study the dynamic behavior of an elastic cylindrical shell filled with an immovable or flowing fluid. To describe the fluid, we use the perturbed velocity potential whose equations with the corresponding boundary conditions are solved by the Bubnov-Galerkin method. To describe the shell, we use the variation principle, which includes the linearized Bernoulli equation for calculating the hydrodynamic pressure acting on the shell on the side of the fluid. Solving the problem is reduced to calculating and analyzing the eigenvalues of the coupled system of equations obtained as a result of combining the equations for the perturbed velocity potential and the shell displacements. We consider several test problems in which, along with the comparison of the computational results with the earlier published experimental, analytic, and numerical data, we also study the dynamic behavior of the “shell-fluid” system for various boundary conditions for the perturbed velocity potential.     

Averaging method in the motion stability problem for a rotating body suspended on a long rigid string

We use the averaging method to study the stability of the vertical rotation of a rigid body suspended on a long rigid string.     

Identification of nonstationary axisymmetric load distributed along a cylindrical shell

The paper outlines a procedure to identify the space-and time-dependent external nonstationary load acting on a closed circular cylindrical shell of medium thickness. Time-dependent deflections at several points of the shell are used as input data to solve the inverse problem. Examples of numerical identification of various nonstationary loads, including moving ones are presented. The relationship between the external load and the stress-strain state of the shell is described by the Volterra equation of the first kind. The identification problem is solved using Tikhonov's regularization method and Apartsin's h-regularization method __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 91–100, July 2008.     

Atomistic phenomena in dense fluid shock waves

The shock structure problem is one of the classical problems of fluid mechanics and at least for non-reacting dilute gases it has been considered essentially solved. Here we present a few recent findings, to show that this is not the case. There are still new physical effects to be discovered provided that the numerical technique is general enough to not rule them out a priori. While the results have been obtained for dense fluids, some of the effects might also be observable for shocks in dilute gases.