Vol. 21, No 2, 2017 < Volumes
(ISSN 1428-6394)



hPawel Wojda and Sergey Leble General Dynamic Projecting of Maxwell Equations

A complete – system of Maxwell equations is splitting into independent subsystems by means of a special dynamic projecting technique. The technique relies upon a direct link between field components that determine correspondent subspaces. The explicit form of links and corresponding subspace evolution equations are obtained in conditions of certain symmetry, it is illustrated by examples of spherical and quasi-one-dimensional waves.


hIvan Karpov and Sergey Leble On Problem of Rossby and Poincar{\accent 19 e} Atmospheric Waves Separation and Spectra

We propose a new inverse problem formulation based on the hydrodynamics consideration of a gas/water fluid that results in planetary waves diagnostics. We analyze such a possibility beginning from a simplest version of geophysical hydrodynamics, written in the ????-plane model. The problem of diagnostics is solved approximately after expansion with respect to the transverse basis functions applying projecting to Rossby and Poincare waves in each transverse subspace that contains its superposition. The corresponding discrete version of the operators is built to be applied to the observation data.


hSergey Leble and Irina Vereshchagina Dynamic projection operator method in the theory of hyperbolic systems of partial differential equations with variable coefficients

We consider a generalization of the projection operator method for the case of the Cauchy problem in 1D space for systems of evolution differential equations of first order with variable coefficients. It is supposed that the dependence of coefficients on the only variable ???? is weak, that is described by the introduction of a small parameter. Such problem corresponds, for example, to the case of wave propagation in a weakly inhomogeneous medium. As an example, we specify the problem to adiabatic acoustics in waveguides with a variable cross-section. Projection operators are constructed for the Cauchy problem to fix unidirectional modes. The method of successive approximations (perturbation theory) is developed and based on the pseudodifferential operators theory. The application of projection operators adapted for the case under consideration allows deriving approximate evolution equations corresponding to the separated directed waves.


hValerian A. Yurov and Alla A. Yurova Inertial Oscillations Induced by Propagation of Vistula Lagoon Freshwater into the Baltic Sea

A mathematical model of the mechanism of the appearance of antisymmetric vortices during the propagation of freshwater into the seawater which is observed, in particular, at the exit from the Baltic Canal connecting the Vistula Lagoon and the Baltic Sea is constructed in the work. In particular it is shown that the main reason for the vortex formation in this case is the Coriolis force. The exact dependence of the circulation of velocity on time for the three simplest types of the “tongue” of the intrusion of freshwater is calculated analytically in the work as well.


hAnna Perelomova Nonlinear phenomena of small-scale sound in a gas with exponential stratification

The nonlinear dynamics of perturbations, quickly varying in space, with comparatively large characteristic wavenumbers k: k > 1/????, is considered. ???? is the scale of density and pressure reduction in unperturbed gas, as the coordinate increases (???? is the so-called height of the uniform equilibrium gas). Coupling nonlinear equations which govern the sound and the entropy mode in a weakly nonlinear flow are derived. They describe the dynamics of the gas in the leading order, with an accuracy up to the terms (k????)−1 . In the field of the dominative sound mode, other induced modes contain parts which propagate approximately with their own linear speeds and the speed of the dominative mode. The scheme of successive approximations of nonlinear links between perturbations in the progressive mode is established. The numerical calculations for some kinds of impulses confirm the theory.


hDmitrii Ampilogov Interaction of Orthogonal-Polarized Waves in 1D Metamaterial with Kerr Nonlinearity

The investigation of the wave propagation in a 1D metamaterial is continued in this paper. A nonlinear evolution equation of the wave interaction of two polarizations by means of the projection operator method is obtained and a particular solution in the case of slow-varying envelopes is found.


hBartosz Reichel and Mateusz Kuszner Projecting Procedure for Metamaterial Cylindrical Waveguide

In this paper a new way of derivation of an evolution equation for short pulses in a dielectric waveguide including one model of a metamaterial waveguide is shown. This derivation model relies upon projecting to an orthogonal basis. In our case such orthogonal basis for cylindrical waveguides is chosen as Bessel functions.


hAlexander A. Ivanov and Alexei I. Ivanov Diamond Side Resonances: Influence of Isotopic Substitution of Carbon

We discuss the side resonances of the optically detected magnetic resonance in a diamond crystal and propose a new approach to the calculation of the hyperfine interaction in a composed system consisting of a negatively charged nitrogen-vacancy ???? ???? − center and a nearby 13 ???? nuclear spin. The energy levels, rule selection and radiative transitions are obtained by a new method. The base of this method is the use of a complete set of commuting operators and entangled spin states. An estimation of the carbon hyperfine splitting parameters in the diamond ???? ???? − center from side-resonance frequencies is obtained in the frame of this method.


hSergey Kshevetsky and Aleksandr Shapilov Regularization of Coulomb Potential for Calculating Electron Density in Quantum Mechanical Systems

In this paper we show a simple and effective method for regularizing the Coulomb potential for numerical calculations of quantum mechanical problems, such as, for example, the solution of the Schrödinger equation, the expansion of charge density and others. The introduction explains why the regularization of the Coulomb potential is important. In the second part, the regularization method itself as well as its advantages and disadvantages will be described in detail. The third part demonstrates some numerical calculations for the Sulfur + Hydrogen system using the proposed method. In the final part, the obtained results are summed up.


hStepan Botman Numerical Calculation of 1D ZRP Chain Electrical Conductivity

In this paper we present a numerical procedure for calculation of electrical conductivity in a periodic lattice of one-dimensional zero range potentials with a case of dominant impurity scattering. The conductivity was previously obtained in an integral form via an approximate solution of the kinetic Kolmogorov equation. The proposed approach is based on the quadrature formula for certain type of integrals. The results are compared with the low temperature limit approximation.


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