Determining the intensity of solar flare ionizing radiation from data of the GPS/GLONASS navigation systems

The possibility of solar flare detection using data derived from the GPS/GLONASS navigation systems is demonstrated. Sudden increase of the total electron content (TEC) in the ionosphere is investigated on the basis of GPS data. The dependence of the TEC variations on solar ultraviolet and X-ray ionizing fluxes is analyzed. A technique of using the TEC variation rate to determine the effective intensity of solar ionizing radiation during a strong flare is proposed.     

MHD-based simulation of ionospheric perturbations generated in the atmospheric surface layer

The generation and propagation of acoustic gravity waves (AGWs) in a two-dimensional Earth atmosphere was numerically simulated on the basis of a magnetohydrodynamic model. Due to the divergent form of the equations and the conservativeness of the numerical method, strong perturbations, including discontinuous solutions, were considered and computed by applying a shock capturing algorithm. The results were compared with previous ones obtained using the Euler equations. The comparison results confirmed the generation of atmospheric AGWs by pulsed ground-based sources and supported the possibility of using simpler gasdynamic models for the given class of problems in a fairly wide range of governing parameters.     

The resonance stabilization of a class of unstable systems

The Lyapunov stability of the trivial solution of a non-linear system, which, in the first approximation, describes a multifrequency oscillatory process, is investigated. It is shown that a system that is unstable when account is taken of non-linear terms can be made asymptotically stable by tuning it to a fourth-order resonance. Sufficient conditions for asymptotic stability are obtained.     

On stability of autonomous systems with internal resonance : PMM vol. 39, n 6, 1975, pp. 974–984

When investigating the stability of the trivial solution of an autonomous system of ordinary differential equations in the critical case of n pairs of pure imaginary roots an essential role can be played by the presence of integral linear dependences between the system's frequencies or, in other words, by the internal resonance. Various special cases of this problem were examined in [1–6]. Our aims are: to obtain a special (normal) form of the differential equation system with internal resonance of most general form in it; to ascertain the conditions under which the presence of internal resonance does not permit the application stability investigation methods developed for resonance-free systems; to solve the stability problem in one of the most important cases of odd-order internal resonance, generalizing the preceding investigations. In the solution of the last problem the necessary and sufficient conditions are given for the stability of the model (simplified) system. Using Chetaev's theorem we show that as a rule the instability of the original system follows from the Instability of the model system. Cases of structurally-unstable instability (^*) for which the model system does not resolve the problem of stability are outlined. The results obtained are extended, in particular, to Hamiltonian systems.     

Acoustic-gravity waves in the Earth’s atmosphere generated by surface sources

The generation of acoustic-gravity waves and their propagation in the Earth’s atmosphere is analyzed numerically on the basis of a computer model of the stratified atmosphere with dissipation. Atmospheric and ionospheric wavelike disturbances from different surface sources such as earthquakes, explosions, seiches, temperature heating, and tsunamis are studied.     

Dimensional Resonances in Biatomic Nanostructures and the Characteristics of Their Holograms

A self-consistent problem of determining the field at the location of atoms in a nanostructural object and also at different observation points beyond a group of atoms (a small object) in the wave and near zones is solved on the basis of a system of compatible equations for the light-wave electric field strength and optical equations for linear dipole oscillators. We proved the existence of two dimensional resonances in the nanostructural object that consists of two identical atoms, with each having a single isolated resonance. We show that the properties of dimensional resonances depend strongly on small displacements of atoms with respect to one another. Formulas are obtained for effective polarizabilities of atoms in the small object. Optical plane holograms of the small object were obtained by interference of the coherent field of the dipoles of the small object and of the reference coherent wave in a certain plane of observation points far from the small object in the wave zone at frequencies corresponding to dimensional resonances.     

Transcontinental radio tomographic chain: First results of ionospheric imaging

The results of studying the structure of the ionospheric plasma distribution from data obtained at the transcontinental Russian radio tomographic chain, which is the world’s longest, are presented. The 4000 km long tomographic chain extends from the Svalbard Archipelago to Sochi. The unique feature of this upgraded radio tomographic system is that for the first time observations cover a wide sector of the ionosphere from high latitudes (polar cap and auroral region) to low latitudes. This allows us to study the transfer of perturbations in the system auroral-subauroral-midlatitude-low latitude ionosphere, and to analyze ionospheric electron density distributions in different latitudinal regions as a function of different external factors and solar-geophysical conditions. The first recent results speak for a complex structure of the ionospheric plasma, even in quiet geophysical conditions (K _p < 2.)     

Construction of stability regions in the three-body problem using parameter elimination

It is shown, using the example of an investigation of the stability of relative equilibrium positions (libration points) in the classical three-body problem and in several modifications of it, that in many cases it, is simpler and more informative to construct the stability region of equilibrium positions in the configuration space of the system rather than in the parameter space.