# Mechanics

## Single Waves in a Gas-Liquid Bubble Mixture

Nonlinear wave processes in a two-phase medium (bubbly liquid) do not lose their relevance asan object of study due to their wide use in various fields of physics, engineering, chemical and petroleum industries. Last decades the jump in the development of computing has expanded the possibilities for the study of significantly nonlinear problems. The aim of this work was to obtain a stationary solution of equations describing the motion of a solitary wave in a gas-liquid mixture without taking into account dissipative processes.

## Mathematical Modeling of Deposits Accumulation on the Plastic Biliary Stent Surface for Predicting Its Occlusion

Endoprosthetics with plastic stents has been used to restore bile drainage through the percutaneous or endoscopic method since the late 1970s. The long-term results cannot be considered satisfactory due to the high incidence of jaundice recurrence which is caused by the occlusion of plastic stents with a biliary sludge (accumulation of cholesterol crystals, pigment crystals, bacteria and calcium salts). Cholesterol is considered to be the main component of biliary sludge that stimulates the reduction of the stent lumen. The average lifetime of stents is 3–6 months.

## Influence of Convolution Kernel and Beam-Hardening Effect on the Assessment of Trabecular Bone Mineral Density Using Quantitative Computed Tomography

Quantitative computed tomography along with densitometry is used to assess mineral density and strength of bone tissue. Raw data obtained by computed tomography are converted by software using convolution kernels. It is known that the use of convolution kernels can significantly change tissue density, which is measured in Hounsfield units. The beam-hardening effect is described in literature: when x-ray passes through an object, the absorption of lower-energy x-ray photons occurs.

## Unsteady Electromagnetic Elasticity of Piezoelectrics Considering Diffusion

The paper considers a model of the linear theory of deformation of elastic continuum with diffusion and piezoelectric effect taken into account, which describes the relationship between mechanical deformations, mass transfer, and the internal electric field. A one-dimensional model of electromagnetic diffusion in a rectangular Cartesian coordinate system is used.

## Asymptotic methods for obtained solutions in vicinities of wave fronts in viscoelastic rod at large time

Non-stationary longitudinal waves in viscoelastic rod at large time are considered. Equations for the wave fronts are derived by means of asymptotic methods. Solutions of these equations are obtained.

## Quaternion Models and Algorithms for Solving the General Problem of Optimal Reorientation of Spacecraft Orbit

The problem of optimal reorientation of the spacecraft orbit is considered in quaternion formulation. Control (vector of the acceleration of the jet thrust) is limited in magnitude. To solve the problem it is required to determine the optimal orientation of this vector in space. It is necessary to minimize the duration of the process of reorientation of the spacecraft orbit. To describe the motion of the center of mass of the spacecraft we used quaternion differential equation of the orientation of the spacecraft orbit. The problem was solved using the maximum principle of L. S.

## Investigation of Strength and Buckling of Orthotropic Conical Shells and Conical Panels

In the construction, thin-walled shell structures are used to cover the buildings of large areas, such as stadiums, hangars, circuses, airports. In this paper, the strength and buckling of closed conical shells as well as their panels are studied. The geometric nonlinearity and transverse shifts are taken into account. A mathematical model is used in the form of a functional of the total potential energy of deformation. Also expressions for deformations, forces and moments are given. The calculation program is implemented in the MatLab environment.

## Thin Film Thermocapillary Motion of Binary Alcohol-Containing Solution

Interphase convection is a widespread phenomenon that occurs in various branches of technology, including chemical technologies. The greatest interest in the case of thin liquid films is the Marangoni convection. Phase transitions significantly affect the convective flow, changing the coefficient of surface tension. In this paper, the behavior of a thin film of an alcohol-containing solution when it is heated is analytically studied.

## T-irreducible extension for unions of complete graphs

T-irreducible extension is one of kinds of optimal extensions of graphs. Constructions of optimal extensions are used in diagnosis of discrete systems and in cryptography. A graph H with n+1 vertices is called an extension of a graph G with n vertices if G can be embedded in every maximal subgraph of H. Any graph Ghas the trivial extension that is the join ng+of G with some outer vertex v. T-irreducible extensions are obtained from the trivial extension by removal of maximal number of edges in such a way that the extension property is preserved.

## Research into the time-depended transactional processes in viscoplastic fluids

The paper presents problem of transition from one steady-state conditions of viscoplastic fluid flow to another between parallel planes. The problem definition is given within the limits of five- parameter model, which permits to take up differences between behavior under stress and without stress and possible slippage along the solid walls. Hysteresis of deformation is considered by means of model of smooth transition from adhesion to slippage. The solution is determined by method of momentary eigenfunctions of Melamed-Grinberg.