Small free vibrations of an infinite cylindrical shell rotating on rollers

Small free vibrations of an infinitely long rotating cylindrical shell being in contact with rigid cylindrical rollers are considered. A system of linear differential equations for the vibrations of such a shell is derived. By using the Fourier transform of the solutions in the circumferential coordinate, a system of algebraic equations for approximately determining the vibration frequencies and mode shapes is obtained. It is shown that, for any number n of uniformly distributed rollers, the approximate values of the first n frequencies and mode shapes can be found explicitly. On the basis of the orthogonal sweep method, an algorithm for numerically solving the boundary value eigenvalue problem describing the vibrations of a rotating shell is developed. Analytical and numerical results are compared. The obtained approximate formulas for frequencies and the numerical algorithm can be used to design centrifugal concentrators for ore enrichment.     

Transition micromagnetic structures in asymmetric vortexlike domain walls (Static solutions and dynamic reconstructions)

The possible types of transition structures with a three-dimensional magnetization distribution over regions in the vortex asymmetric domain walls that exist in magnetically uniaxial soft magnetic films with in-plane anisotropy are studied by computer simulation in terms of a micromagnetic approach. It is shown that the possible structure types include both the type of vertical Bloch lines that was discussed earlier in other works and new types, namely, singular (Bloch) points and clusters consisting of vertical Bloch lines and Bloch points. The spatial configurations of the transition structures are calculated and their topological properties are found. The numerical simulation of the dynamics of closely spaced substructure regions reveals various scenarios of their interaction, including annihilation accompanied by energy release and the excitation of nonlinear waves.     

PPT-Inducing,Distillation-Prohibiting,and Entanglement-Binding Quantum Channels

We review the entanglement degradation in open quantum systems in the Choi–Jamio?kowski representation of linear maps. In addition to physical processes of entanglement dissociation and entanglement annihilation, we consider quantum dynamics transforming arbitrary input states into those that remain positive under partial transpose (PPT-inducing channels). Such evolutions form a convex subset of distillation-prohibiting channels. We clarify the relation between the above channels and entanglement-binding channels. We give an example of the distillation-prohibiting map Φ ? Φ, where Φ is not entanglement binding.     

Standard Envelopes of Commutative Triple Systems

Under certain constraints on the characteristic of a field , the commutative standard enveloping q-algebra >B of a commutative triple system A over is defined. It is proved that(1) if the algebra B is simple, then the system A is simple;(2) if the system A is simple, then B either is simple or decomposes into the direct sum of two isomorphic simple subalgebras (as of ideals).     

Spin polarized current controlled dynamics of domain walls in magnetic films with in-plane anisotropy

We study the dynamic properties of asymmetric vortex Bloch walls and classical 1D Néel walls controlled by a spin-polarized current in magnetic films with in-plane anisotropy. It is shown that fairly high velocities of domain walls (up to 100 m/s) can be obtained for the current density in the range j = 10⁶–10⁸ A/cm². The nonlinear dependence of the wall velocity on the film thickness and the linear dependence of the velocity on the current density and inverse damping parameter are found.     

Development of dual-polarization reflectometry facility for Uragan-2M torsatron

The dual-polarization reflectometry facility developed for torsatron U-2M uses the extraordinary wave in addition to the ordinary wave. This is possible because the magnetic field of U-2M is produced by external conductors, is independent of plasma parameters, and is therefore a known quantity. The plasma probing is carried out simultaneously in a large number of pairs of close frequencies, which makes it possible to use superheterodyne circuits and, hence, considerably improves noise protection of the system and accuracy of measurement of phase shifts. The use of the extraordinary wave considerably broadens the range of the densities being measured in the given frequency band of generators. To reconstruct the density profile of the plasma from the frequency dependence of the phase shift of probing waves, original iterative algorithms have been developed for solving integral equations that are stable to experimental errors.     

Superheating instability in a pulsed xenon discharge

It is shown that previously obtained conditions for superheating instability substantially vary if we take into account secondary xenon ionization. Instability completely vanishes if the density of heavy particles in the discharge is kept constant and whenever a discontinuous time variation of temperature T in a restricted region between 15 · 10³ ° K and 20 · 10³ ° K is possible for a constant effective pressure. The development of instability is studied numerically by a ranging method. Stationary temperature distributions possessing a high contrast as a local temperature passes through a given range of instability with constant pressure are presented.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 27–30, January–February, 1976.     

Pressure fluctuations and heating of a gas by the inflow of a supersonic jet into a cylindrical cavity

The formation of pressure fluctuations at the inflow of a jet into a cavity (or the so-called resonance tube) was first observed by Hartmann. Further investigations showed that at the same time there is a heating of the gas in the cavity [1, 2]. It was established in [1, 2] that at subsonic and slightly supersonic velocities (M < 2.0) the cavity air can be heated up to 500–700 °K. Further investigations [4, 6] showed that by using monatomic gases inside the cavity one can reach even higher temperatures (T 800–900 °K). The resonance tubes find an application as powerful sound sources. There is also a possibility of their use in thermochemistry, and for the plasma production [6], In the literature, there is an absence of data on the resonance tube characteristics for large Mach numbers. In the present work we investigate the resonance tubes for M = 3.2–4.0. These investigations have shown that pressure oscillations can occur at these Mach numbers with the peak-to-peak amplitude of P 0.4·P_o, where P_o is the total pressure in the inflowing jet. Depending on the clearance between the nozzle and the cavity, both low- and high-frequency oscillations can be set up. It is established that the most intense shock-wave heating of the gas takes place at high-frequency fluctuations, although their amplitude is smaller in comparison with the low-frequency ones. It is shown that the cold air inside the cavity can be heated by means of the fluctuations up to T 1600 °K or more.Translated from Izvestiya Akamemii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 104–111, September–October, 1977.     

General transverse vibrations equations for a circular cylindrical viscoelastic shell

Moscow Structural Engineering Institute. Translated from Prikladnaya Mekhanika, Vol. 26, No. 4, pp. 41–49, April, 1990.