Nonlinear properties of surface “screw” instability in symmetric semiconductor plates

For the first time we study the nonlinear properties of the surface screw instability (SSI) when waves are excited at both faces of a plate and the interaction between them must be taken into account. The nature of the SSI development and the stability of surface screw waves against modulation are examined. Diagrams of the regions where the SSI development is soft and explosive as well as the regions of modulated waves are given in the space of parameters characterizing the electro-hole plasma and external fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 30–34, April 1990.     

Theory of absorption and amplification spectra of a weak electromagnetic field by two-level quantum systems

A theory is developed of the absorption and amplification spectra of a weak (probe) electromagnetic field (EMF) by open two-level quantum systems in a strong quasiresonant EMF, assuming separability of the triplet spectrum components. The theory describes the intensity and the form of the spectral lines for arbitrary intensities and detunings of the strong EMF, and also the dependence of the parameters of the adiabatic relaxation on the frequency of the weak EMF. The influence of nonlinear dynamic effects (NDE) due to the dependence of the relaxation on the EMF parameters on the shape of the spectral lines is investigated. It is shown, in particular, that under certain conditions the NDE can lead to a nonlinear dynamic transformation of the dispersion of the sideband dispersion lines into Lorentzian lines and to a considerable increase of the absorption in the central region of the spectrum. Particular attention is paid to an investigation of the NDE on the characteristics of the central component of the spectrum. Methods and results of an investigation of the spectra in a basis of unperturbed wave functions in in a basis of dressed states are compared.Radiophysics Division, Lebedev Physics Institute. Translated from Preprint No. 117 of the Lebedev Physics Institute, Academy of Sciences of the USSR, Moscow, 1990.     

Disordered charge distributions and dielectric loss in extra dense flint glasses

The complex permittivities of some extra dense flint glasses (EDF glasses) have been studied. The dielectric features of the samples are dominated by their PbO content. Both refractive indices and dielectric losses exhibit a close relation to the concentration of Pb ions. The latter are located either at sites of the network atoms or filling the potential minima interstitially. They can be identified by their different relaxation mechanisms. The dispersion in the submillimeter wave and FIR area is characterized by a very broad distribution of comparably sharp resonant states. Thermal lens — or hysteresis effects can be excluded.     

Non-characteristic mixed problems for non-linear symmetric hyperbolic systems

In this paper the existence and uniqueness of solutions of the following initial boundary value problem for non-linear symmetric hyperbolic equations of the first order are shown, where M = I ⁺ ? S , has the same from as the Kreiss' condition, but S must be sufficiently small ( I ⁺ is the unit matrix in the space generated by eigenvectors of the matrix ? A · n? , corresponding to positive eigenvalues) and n? is a unit outward vector normal to the boundary. The main result of the paper is obtaining an a priori estimate for non-linear equations. This estimate is obtained for sufficiently small time and norms of given data functions. The existence of solutions is proved by the method of successive approximations, which can be used because at each step such properties as symmetry of matrices and the numbers of positive and negative eigenvalues of the matrix ? A · n? are assured. This can be done because we restrict our attention to such systems of equations for which these properties are satisfied for solutions from some neighbourhood of initial data u ₀. Therefore, using the fact that solutions in the class of continuous functions are sought, these properties can be satisfied for sufficiently small time. Moreover, some examples of initial boundary value problems for equations of hydrodynamics and magnetohydrodynamics are considered.     

On the dynamics of cosmological particle production

The time evolution of the particle number density and spectrum of massive scalar particles, coupled conformally to a classical Friedman-Robertson-Walker gravitational field is followed numerically. Not only for a pure radiation cosmos, but also for one with an inflationary interlude, the density of particles produced remains constant in time. This results in a constant equivalent temperature scale up to the Compton time of the massive particles, and opens the possibility that during a sufficiently long inflation the energy density of the particles produced can exceed that of the radiation background.     

Quantum field-theory models on fractal spacetime

Continuing the analysis of a previous paper, the present work applies rigorous renormalization group methods to the hierarchical models to establish the existence of field theories with non-Gaussian ultraviolet renormalization group fixed points in 4- dimensions.     

The van der Waerden Theorem and the Burnside Problem for semigroups

Ohne Zusammenfassung     

Crystal structures of dimethylsuccinate and dimethyloxalate: Carbonyl group orientation for C13 chemical shielding tensor studies

The crystal structures of dimethylsuccinate (DMS) and dimethyloxalate (DMO) have been determined to facilitate the determination of the C-13 chemical shielding tensors of the carbonyl carbon in esters. Crystals of DMS are monoclinic, space groupC2/c,Z=4,a=13.154(4),b=6.156(1),c=9.363(4)Å,=98.53(3)°. The structure was solved by direct methods and refined by leastsquares procedures to giveR=0.071 for 932 observed data. Crystals of DMO are monoclinic space group,P2₁/n,Z=2, witha=3.891(1),b=11.879(2),c=6.213(2) Å,=103.32(2)°. The structure is the same (within experimental error) as that reported by Dougill and Jeffrey (1953) and refined to giveR=0.074 for 395 observed data.