Branching of equilibria of a system of micro/nanostrings at direct currents

Branching of equilibria of a system of three parallel conducting nano/microlayers, which is used to detect changes in the external and internal mechanical and electric characteristics (for example, conductivity, tension force, and gap between layers), has been investigated. A change in the physical parameters may cause asymmetric bending of the outer layers and deformation of the formerly neutral middle layer. By changing the current in one of the outer layers slowly, their initial symmetry (neutrality of the inner layer) can be restored and the change that occurred in the parameters can be determined.     

Fundamental problems of solid mechanics in high technologies

The paper provides an analytical review of some fundamental problems of solid mechanics in high technologies. The review relies partly on the invited report presented by the authors at the 10th All-Russian Congress on Theoretical and Applied Mechanics held in Nizhny Novgorod in 2011. Attention is focused on the problems involved in technologies of materials with a bulk fine-grained (nano) structure and in technologies used to control mechanical properties of surfaces and interfaces.     

The effect of dissipative and gyroscopic forces on the stability of a class of linear time-varying systems

It is shown that the effect of dissipative and gyroscopic forces on a certain class of potential linear time-varying system differs considerably from the effect of these forces on a time-invariant system. Examples are considered. In the first of these, the equations of motion of a disk, attached to a rotating weightless elastic shaft, are investigated, taking external friction into account. The results obtained are compared with the results obtained previously by others when considering this problem. In the second example, certain problems of the stability of rotation of a Lagrange top on a base subjected to vertical harmonic vibrations are investigated.     

Bäcklund transformations between four Lax-integrable 3D equations

Recently a classification of contactly-nonequivalent three-dimensional linearly degenerate equations of the second order was presented by E.V. Ferapontov and J. Moss. The equations are Lax-integrable. In our paper we prove that all these equations are connected with each other by appropriate Bäcklund transformations.     

A Bäcklund transformation between the four-dimensional Martínez Alonso–Shabat and Ferapontov–Khusnutdinova equations

We find a Bäcklund transformation between the four-dimensional Martínez Alonso–Shabat and Ferapontov–Khusnutdinova equations. We also discuss an integrable deformation of the Martínez Alonso–Shabat equation.     

Multinuclear compounds of s-elements with sterically hindered <Emphasis Type="Italic">о</Emphasis>-semiquinonates and catecholates

Alkali metals form mutinuclear compounds with redox-active singly and doubly reduced derivatives of sterically of hindered о-benzoquinones. Complexes [Na₆(Cat)₃(THF)₇]?4THF, [Na₅(Cat)₂(SQ)(THF)₅], [Na₄(SQ)₄(THF)₄]?THF?C₆H₁₄, [Na₄(3,5-SQ)₄(THF)₄], [K₄(SQ)₄(THF)₄]?4THF and [Li₃(SQ)₃(THF)₃]?THF (Cat is catecholate, SQ is semiquinonate) possessing high sensitivity to atmospheric oxygen were synthesized and their structures were determined. Magnetochemical measurements and quantum chemical calculations revealed that variation of the alkali metal and/or change in the structure of the polymetallic core significantly affect the energy of exchange interaction between the unpaired electrons of the paramagnetic ligands framing the polynuclear metal core formed by s-elements.     

Finite-element modeling of the heat mode of autoclave hardening of a three-layer panel

Results of finite-element modeling and experimental measurements of temperatures in the course of autoclave hardening of a three-layer panel of the wing of a T-50 aircraft, which is composed of upper and lower load-bearing panels made of carbon plastics and honeycomb from aluminum foil, are given. It is shown that the actual temperature values at various sections of the panel of wing differ from the theoretical ones by less than 90%.