# No 2 (2013)

**Year:**2013**Articles:**22**URL:**https://journals.rudn.ru/miph/issue/view/516

## Articles

### Variational Principles for a Diﬀerential Diﬀerence Quasilinear Operator

#### Abstract

The purpose of the present paper is to investigate the potentiality of the operator of diﬀerential diﬀerence equations and to construct the functional, if the given operator is a potential on a given set relatively to the some bilinear form. Method of construction of variational factor is suggested.

**Discrete and Continuous Models and Applied Computational Science**. 2013;(2):5-21

5-21

### Algebraic Methods for Reducibility of Regularly Perturbed Model Linear Periodic Systems of ODE

#### Abstract

Theorems of asymptotic reducibility of regularly perturbed linear model systems of ODE with a periodic matrix, including cases with multiple spectrum and the Jordan structure of the limiting matrix. The obtained result is an asymptotic analogue of Floque–Lyapunov theorem on the reducibility.

**Discrete and Continuous Models and Applied Computational Science**. 2013;(2):22-27

22-27

### Optimal Embeddings of Riesz Type Potentials

#### Abstract

We study Riesz potentials in n-dimensional Euclidean space. They are constructed on rearrangement-invariant spaces as convolutions with kernels with general form, their description of the class of kernels is based by means of some non-negative, decreasing function Φ. Generalized Riesz potentials include classical Riesz potentials spaces. Here we consider as a “base” space RIS Lorentz type space Λ p, 1 < p < ∞. During consideration of the question of ﬁnding conditions for embeddings of Riesz type potentials in RIS we used criteria stated by M.L. Goldman, where the operator of Hardy type and inequalities for operators of this type are playing the key role. For the case of Riesz potentials, 1 < p < ∞, the condition of optimal embedding in RIS is established. The case of Riesz type potentials based on space L p, 1 < p < ∞, considered by the authors M.L. Goldman and O.M. Guselnikova, corresponds with the result of this work.

**Discrete and Continuous Models and Applied Computational Science**. 2013;(2):28-37

28-37

### Analysis of M|G|1|r Queue with Batch Arrival and Hysteretic Overload Control

#### Abstract

The paper presents M|G|1|r queuing system analysis with batch arrival and hysteretic load control. We provide a system of equations for steady-state probability distribution and derive formulas for system characteristics that are of interest considering hysteretic load control mechanism in SIP-based signalling networks

**Discrete and Continuous Models and Applied Computational Science**. 2013;(2):38-44

38-44

### Structure of Solutions and Dynamic Chaos in Nonlinear Diﬀerential Equations

#### Abstract

The structure of solutions in nonlinear dissipative dynamical systems described by diﬀerential equations, including systems with chaotic behavior is considered. It is shown that the structure of the solutions in these systems is provided by either set of limit cycles, or tori, and is determined by the spectrum of Floquet Exponents. Important role in forming of structures play limit cycles having a complex but not complex conjugate Floquet Exponents. Examples of using the concept of the structure of solutions of nonlinear diﬀerential equations in the study of the formation of solitary traveling waves and the phenomenon of turbulence are presented.

**Discrete and Continuous Models and Applied Computational Science**. 2013;(2):45-63

45-63

### Numerical Simulation of Thermoelastic Waves Arising in Materials Under the Action of Diﬀerent Physical Factors

#### Abstract

In this work, a system of equations of one-dimensional thermoelasticity is presented, which takes into account the nonlinear dependence between stresses and deformation. Diﬀerent problems are considered, which correspond to diﬀerent external actions on the sample. The numerical simulation of thermoelastic waves arising in a metallic sample under a variable external pressure on the sample’s boundary is considered, when the maximum of the absolute value of pressure changes in the interval of observation or violation of the linear Hooke’s Law. The numerical investigation of the dynamics of these waves in two-layered structures is also performed. It is shown that the nonlinear dependence of stresses on deformation strongly aﬀects the form dynamics of the thermoelastic wave.

**Discrete and Continuous Models and Applied Computational Science**. 2013;(2):64-76

64-76

### Investigation of Thermoelastic Eﬀects in Metals in the Frame of the Modiﬁed Thermal Spike Model

#### Abstract

A numerical investigation of a thermoelastic waves arising in a nickel sample under the action of the uranium heavy ion high energy 700 MeV is made on the basis of a thermal spike model which is modiﬁed by adding to it move equations. It is shown that the arising maximal strength of the thermoelastic waves exceeds hundred times ultimate strength of a samples material on the axis of a track. The time dependence of the electron gas and ion lattice temperatures, of the thermoelastic waves strength are determined at a diﬀerent distance from center of track. The time dynamic change is also determined of the maximal region within which thermoelastic strength exceeds ultimate strength of a samples material. By moving away from the center of a track along the radius, the amplitude of the thermoelastic waves will decrease inversely proportional to the radius.

**Discrete and Continuous Models and Applied Computational Science**. 2013;(2):77-84

77-84

### Forest Wildﬁre Modelling and Prediction in Russia

#### Abstract

The wildﬁre (forest ﬁre) is a natural disaster that causes great economical losses in many regions of Russia. In the present work the joint sample of daily values of the number of forest ﬁre seats and the Nesterov meteorological index in Irkutsk region, seasons 1969–1988, are investigated. It appears that the evolution of forest ﬁre is well described by a vector autoregression process based model. The prediction of the future numbers of ﬁre seats can be performed using special computer algorithm, which is shown to produce accurate and reliable estimates up to 2 days ahead.

**Discrete and Continuous Models and Applied Computational Science**. 2013;(2):85-88

85-88

### Model with One Spatial Variable for Design of a Technical Device

#### Abstract

Model with one spatial cylindrical variable for optimization of a technical device is presented. Device is in the form of a multilayer cylindrical sample with a pulse source operating at cryogenic temperatures. The results of numerical experiments are shown.

**Discrete and Continuous Models and Applied Computational Science**. 2013;(2):89-93

89-93

### To the Problem of Closure of Diﬀerential Systems with Degenerating Diﬀusion

#### Abstract

It is built the Lagrange, Hamilton and Birkhoﬀ equations by properties of movement in the class of stochastic diﬀerential Ito equations in the presence of random perturbing forces from the class of processes with independent increments. The received results are illustrated on an example of movement of Earth’s satellite under the action of gravitation’s and aerodynamics forces.

**Discrete and Continuous Models and Applied Computational Science**. 2013;(2):94-104

94-104

### ASL Fingerspelling Recognition

#### Abstract

A method is proposed and software is developed for automatic recognition of gestures used in ASL ﬁngerspelling. Static gestures are captured using the new generation 3D sensor Asus Xtion Pro Live. Gesture recognition is achieved by extracting and further comparing the normalized geometric skeletons of the hand. Hand skeletons are compared using Dynamic Time Warping algorithm, which has polynomial complexity.

**Discrete and Continuous Models and Applied Computational Science**. 2013;(2):105-113

105-113

### Louis de Broglie’s Search of Physical Meaning of the Wave-Particle Duality

#### Abstract

Having opened in 1923, the fundamental principle of wave-particle duality of matter, which lies at the base of quantum mechanics, Louis de Broglie has long been engaged in search of the physical meaning of this principle. The article deals with certain questions of the theory of de Broglie, called the theory of double solutions, in which he attempts to relate the motion of the particle and associated with particle movement of matter waves. Attention is drawn to the discussion that has arisen after the de Broglie’s report on the V Solvay Congress 1927, to the diﬃculties of the theory and its historical signiﬁcance.

**Discrete and Continuous Models and Applied Computational Science**. 2013;(2):114-124

114-124

### The Chiral Cosmological Model with Dark Energy and Dark Matter

#### Abstract

Nonlinear sigma models with the potential of interactions (chiral cosmological models) are applied widely for description of various epochs of Universe evolution. For example, by considering an inﬂationary epoch, the essential progress in understanding of the essence of the phenomenon was achieved due to method of exact solutions construction for inﬂation. Obtained exact solutions are considered as background ones when cosmological perturbations are studied. However, the application of exact solutions construction method to modern Universe with dark energy and dark matter domination over radiation and baryonic matter, faces with considerable diﬃculties. Therefore one of the possibilities to overcome this diﬃculties is to investigate evolutionary behavior of kinetic interaction of the scalar ﬁelds, describing dark energy, considering the behavior of chiral metric components as a function of a scalar factor. In this way it becomes possible to describe both dark energy and dark matter based on special properties of sigma model inner space metric.

**Discrete and Continuous Models and Applied Computational Science**. 2013;(2):125-138

125-138

### Magnetic Wormholes and Regular Black Holes with Trapped Ghosts

#### Abstract

We construct explicit examples of globally regular static, spherically symmetric solutions in general relativity with scalar and electromagnetic ﬁelds which describe traversable wormholes (with ﬂat and AdS asymptotics) and regular black holes, in particular, black universes. A black universe is a nonsingular black hole where, beyond the horizon, there is an expanding, asymptotically isotropic universe. The scalar ﬁeld in our solutions is minimally coupled to gravity, has a nonzero self-interaction potential, while its kinetic energy is negative in a restricted strong-ﬁeld region of space–time and positive outside it. Thus in such conﬁgurations a “ghost” (as are called ﬁelds with negative kinetic energy) is trapped in a small part of space, and this may in principle explain why no ghosts are observed under usual conditions. The conﬁgurations obtained contain diﬀerent numbers of Killing horizons, from zero to four.

**Discrete and Continuous Models and Applied Computational Science**. 2013;(2):139-149

139-149

### Modiﬁcation of the Two-Dimensional Numerical Code for Gas-Dynamical Flows in Polar Coordinates

#### Abstract

The numerical method for solution of the gas-dynamical equations in strict divergent form has been modiﬁed. The two-dimensional numerical code for perfect non-stationary gas-dynamical ﬂows simulation on the polar grid is constructed. This code is based on the explicit quasimonotonic high resolution TVD-scheme.

**Discrete and Continuous Models and Applied Computational Science**. 2013;(2):150-158

150-158

### Tachyon Gas as a Candidate for Dark Matter

#### Abstract

In the physical geometry (i.e. in geometry, described completely by its world function) identical geometric objects have identical description in terms of the world function. As a result spacelike straight segment is a three-dimensional surface even in the space-time geometry of Minkowski. Tachyons have two unexpected properties: (1) a single tachyon cannot be detected and (2) the tachyon gas can be detected by its gravitational inﬂuence. Although molecules (tachyons) of the tachyon gas moves with superluninal velocities, the mean motion of these molecules appears to be underluminal. The tachyon gas properties diﬀers from those of usual gas. The pressure of the tachyon gas depends on the gravitational potential and does not depend on temperature. As a result the tachyon gas may form huge halos around galaxies. These halos have almost constant density, and this circumstance can explain the law of star velocities at the periphery of a galaxy. Properties of the tachyon gas admit one to consider it as a dark matter.

**Discrete and Continuous Models and Applied Computational Science**. 2013;(2):159-173

159-173

### Properties of DC and Low-Frequency AC Conductivities of Single Crystals LiCu 2O 2+δ

#### Abstract

The temperature dependences of DC and low-frequency AC conductivities of single crystals LiCu 2O 2 + δ in range from 4.5 K to 360 K were studied. The observed properties of conductivity indicated strong localization and inﬂuences of the spin, lattice and charge degrees of freedom on charge transport.

**Discrete and Continuous Models and Applied Computational Science**. 2013;(2):174-178

174-178

### Maintence of the Synchronism between a Particle and Electromagnetic Wave with the Help of Electrostatic Field

#### Abstract

It is shown analytically and numerically that eﬀective acceleration of the particle at the small distance at the regime of cyclotron autoresonance, supported with the help of synshronizied electrostatic ﬁeld, is possible. It is shown that in the accompanying reference frame moving with the electric drift velocity the new resonant eﬀects arise connected with the eﬀects of ﬁnite gyroradius. It is noted that in the case of the large enough electric drift velocity in the accompanying reference frame the averaging of the motion equations becomes invalid.

**Discrete and Continuous Models and Applied Computational Science**. 2013;(2):179-190

179-190

### Interference Refractometry of Terahertz Surface Plasmon-Polaritons Launched by a Free-Electron Laser

#### Abstract

The problem of terahertz (THz) surface plasmon-polaritons (SPP) refractometry, i.e. determination of their complex refractive index κ = κ′ + i ⋅ κ′′ employing interferometric measurements, is considered in the paper. It is stated that one can determine both parts of κ provided the interference pattern formed by a reference bulk wave and the wave produced by the SPP is recorded. The idea was tested for SPP generated by monochromatic radiation (wavelength 140 μm) of Novosibirsk THz free-electron laser on gold samples covered with diﬀerent thickness ZnS layers. Besides, intensity distribution of the SPP ﬁeld in air over the track has been registered instantly with an uncooled vanadium oxide microbolometer focal plane array consisting of 320×240 sensitive elements. The results obtained are in good agreement with the theory provided the covering layer thickness is equal or exceeds 2 μm.

**Discrete and Continuous Models and Applied Computational Science**. 2013;(2):191-200

191-200

### Light-Diode Holoellipsometer with Binary Modulation of Polarization Employing Light Scattering from Uniaxial Bi-Dimension Crystal

#### Abstract

A holoellipsometer with binary modulation of polarization employing almost normal light scattering by the sample representing itself an optically uniaxial crystal is presented. The device is actual for the tomometric tools which are widely used in nanotechnologies and medicine. The main equations of the holoellipsometry employing normal light scattering method are obtained.

**Discrete and Continuous Models and Applied Computational Science**. 2013;(2):201-209

201-209

### Nashi avtory

**Discrete and Continuous Models and Applied Computational Science**. 2013;(2):210-212

210-212

### Pravila oformleniya statey

**Discrete and Continuous Models and Applied Computational Science**. 2013;(2):213-213

213-213