Motion of a piston under the influence of gas pressure in the presence of an initial temperature gradient

A study is made of the motion of a piston without initial velocity under the influence of gas pressure. Under the assumption that the temperature gradient is constant and fairly small, expressions are obtained for the distributions of the gas-dynamic parameters in the disturbed region between the piston and the leading edge of the sound wave propagating through the gas at rest.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 177–180, March–April, 1984.     

Synthesis,structures, and magnetic properties of crystals of dinuclear copper(II) and cobalt(II) complexes with 3-(3,5-dimethylpyrazol-1-yl)-6-R-1,2,4,5-tetrazines

Dinuclear complexes of Cu^II with 3-(3,5-dimethylpyrazol-1-yl)-6-(2-hydroxyethylami-no)-1,2,4,5-tetrazine (1) and CoII with 3-(3,5-dimethylpyrazol-1-yl)-6-(piperidin-1-yl)-1,2,4,5- tetrazine (2) were synthesized and structurally characterized, and the magnetic (SQUID) and resonance (EPR) properties of van der Waals crystals based on these complexes were studied. Unusual behavior of the effective magnetic moment μ_eff(T) is observed at T < 60 K. A nonmonotonic increase in μeff(?) for 1 (s~6 %) and a 20% reduction of μeff(?) for 2 have a common origin and are due to the influence of spin-orbital coupling on the character of the splitting between the t2g and eg levels of the central ion. Distortions of the coordination site “switch on” a positive (1) or negative (2) contribution of the orbital magnetic moment near 6 K. Irreversible temperature behavior of μeff(T) in the heating and cooling regimes in the vicinity of 60 K suggests that the character of structural distortions and the magnetic properties are related to ligand geometry. This factor plays a significant role in crystal engineering of magnetoactive structures with polynitrogen ligands.     

Observation of the chaotic spin-wave soliton trains in magnetic films

The transition from stationary to chaotic spin-wave soliton trains has been observed. The experiment utilized cw excitation of envelope solitons through self-modulation instability of spin waves. By increasing the spin-wave power, the secondary self-modulation instability succeeded the primary modulation instability, resulting in after-modulation of the soliton train amplitude. Further increase of the spin-wave power led to development of the higher-order instabilities, resulting in formation of the chaotic soliton train.     

Ferrite-ferroelectric phase shifters controlled by electric and magnetic fields

Planar phase shifters fabricated based on ferrite-ferroelectric layered structures are studied experimentally. The structures served as waveguides for spin-electromagnetic waves, whose phase shift was controlled by both electric and magnetic fields. The measurements were performed in the magnetic field range from 900 to 2100 Oe, which corresponds to operating frequencies from 4.0 to 8.5 GHz, with 5- to 20-μm-thick yttrium-iron garnet ferrite films and 200- to 500-μm-thick barium-strontium titanate ferroelectric plates. It is shown that the phase shift may exceed 180° and is a function of the magnetic and electric fields and also of the thickness of the ferrite and ferroelectric layers.     

Vector acoustic solitons from the coupling of long and short waves in a paramagnetic crystal

We investigate the propagation of a longitudinal-transverse elastic pulse in a statically deformed crystal containing paramagnetic impurities and placed in an external magnetic field. We derive a system of three nonlinear wave equations describing the interaction of the pulse with the paramagnetic impurities in the quasiresonance approximation in the Faraday geometry. We assume that the transverse components of the pulse, which cause quantum transitions, have carrier frequencies and are short-wave (acoustic), while the longitudinal component has no carrier frequency and is long-wave. We show that in the case of an equilibrium initial distribution of populations of quantum levels of paramagnetic impurities, the coupling between the longitudinal and transverse components is weak, the pulse is therefore strictly transverse, and its dynamics are described by the Manakov system. With a nonequilibrium initial distribution of populations, conditions of effective interaction between all components of the elastic pulse can be reached, and their nonlinear dynamics are described by a vector generalization of the Zakharov equations. In the case of a unidirectional propagation of the pulse, these equations reduce to the Yajima-Oikawa vector system. We show that the obtained system of equations and its version with an arbitrary number of short-wave components can be integrated using the inverse scattering transform. We construct infinite hierarchies of solutions of the Yajima-Oikawa vector system (including a solution on a nontrivial background). We consider stationary (complex-valued Garnier system) and self-similar reductions of that system, also admitting a representation in the form of compatibility conditions.     

Structure and properties of core-shell microparticles in paraffin-ultradispersed polytetrafluoroethylene systems

Microsized spherical core-shell particles consisting of hydrocarbon cores encapsulated into fluoropolymer shells are obtained in supercritical carbon dioxide. Paraffins serve as a core material, while the polymer shell is formed from ultradispersed polytetrafluoroethylene. The morphology and molecular structure in the bulk and on the surface of the particles and the influence of conditions of particle formation on the shell thickness and the thermal properties of the materials are studied. The materials are composites comprised of paraffin cores coated with shells of loosened globular fluoropolymer particles with sizes of 0.2–1.7 μm. The shells is built of low- and high-molecular-mass fractions consisting of CF₃(CF₂)nCF₃ molecular chains with different lengths. The shell thickness is governed by preparation conditions, exposure time, and the percentage of the polymer in the initial dispersion.     

Geometric proof of R?dseth’s formula for Frobenius numbers

Using a geometric interpretation of continued fractions, we give a new proof of R?dseth’s formula for Frobenius numbers.     

New class of extremely short electromagnetic solitons

A physical realization is presented for the integrable modified sine-Gordon equation. In this case, this equation describes the propagation of an extremely short vector electromagnetic pulse in the system of asymmetric quantum objects that have permanent dipole moments in the self-energy states. Using soliton solutions for ordinary and extraordinary components, new regimes of the dynamics of the pulse and medium that are specific only to asymmetric media have been found.     

Integrable models of the dynamics of longitudinal-transverse acoustic pulses in a paramagnetic crystal

We study the interaction between longitudinal-transverse acoustic pulses and a system of paramagnetic impurities with the effective spin S = 1 in a statically deformed crystal. We show that the dynamics of a pulse propagating at an arbitrary angle to the static-deformation direction and of the effective spins satisfy the modified reduced Maxwell-Bloch equations and, if the spectrum of the acoustic pulse overlaps the quantum transitions between spin sublevels, the modified sine-Gordon equation. These equations generalize the well-known models in the theory of the inverse scattering method and in the theory of self-induced transparency and also belong to the class of integrable equations. Analyzing soliton solutions shows that the pulse-medium interaction reveals some qualitatively new features in these models compared with the cases of purely transverse or purely longitudinal acoustic fields. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 2, pp. 228–247, May, 2007.     

Almost Chebyshëv subspaces in the spaces of compact operators

Translated fromSibirskii Matematicheskii Zhurnal, Vol. 36, No. 4, pp. 917–926, July–August, 1995.