2010. № 40

Methods and tutorials

Tretiyakova O. N.

The description of 3D-modeling a computer practical work by using IT- technologies is stated in article.

Keywords: IT- technology, Internet, distance education in physics, computer 3D-modeling, the software, computer information base, a computer physics practical work

Mathematics. Physics. Mechanics

Katulev A. N., Kuznetsov A. U.

The new method for analyze of stability of nonlinear autonomous dynamical system without introduction function of Lyapunov is elaborated. The reliability of the method is proved theoretically, and its useful is confirmed by results of research the stability of concrete nonlinear autonomous systems of second- and fifth-order.

Keywords: stability; nonlinear; autonomous dynamical system; method; bifurcation set

Erofeyev V. I., Malkhanov A. O., Morozov A. N.

The effect of magnetic field on the formation of localized waves in nonlinear elastic conductive medium. An evolution equation for describing the propagation of a wave beam in the medium, coinciding with the well-known in the theory of nonlinear wave equation Khokhlov-Zabolotskaya-Kuznetsov. The dependence of the parameters of the beam on the external magnetic field.

Keywords: magnetic field, nonlinear elastic, magnetoelastic

Erofeyev V. I., Morozov A. N., Nikitina E. A.

The purpose of this study is to develop a mathematical model, which in a single scheme, and based on principles of continuum mechanics allows you to record the evolution equations of damage accumulation taking into account the geometrical and physical nonlinearities of the process. To solve this problem we propose a new approach based on the relationship of dynamic equations and the equations of material damage it.

Keywords: damage the material, elastic wave velocity dispersion, attenuation, no

Belov A. A., Igumnov L. A., Karelin I. S., Litvinchuk S. Y.

The results of analyzing the dynamic state of visco-elastic bodies using the boundary element method (BEM) in combination with the convolution quadrature and Dourbin methods are presented. The analysis of visco-elastic boundary problems in 3-D formulation in explicit time is constructed without using stepped procedures. A model of a porous medium with a two-phase internal structure introduced by Byo is examined. The results of analyzing the dynamic state of finite porous-elastic bodies using BEM are given. Numerical experiments are presented.

Keywords: boundary integral equations, boundary element, visco-elasticity, pore-elasticity

Vasilevsky D. V., Simahin E. A., Spirin G. G.

It is suggested to use the “action” (integral analogy of electrostatic field energy) to calculate the effective heat conductivity of elementary cell. The suggested approach is applied to the calculation of heat conductivity of disperse materials, the characteristic, necessary in design of heat performance of space vehicles. The maximum divergence of calculation results in the comparison with the numerical ones does not surpass 10%.

Keywords: Heat conductivity; “action”; elementary cell; disperse environment; temperature field

Tretiyakova O. N., Svetushkov N. N.

The problem of simulation of thermal processes in laser irradiation on the surface of various materials is discussed, in which uses a new approach based on the solution of integral equations of heat transfer. For aims of describing the physical characteristics and geometry of the model authors use the principles of the cluster model, implemented in the software package CLUSTER2D. Article describes the features of software to create thermophysical model for numerical calculations. This approach helps to avoid oscillations in the resulting numerical solutions, which arise when applying the finite-difference and finite-element methods.

Keywords: partial differential equation;, numerical methods; thermal processes; the geometry of the object; the instability of algorithm;, programming environment; computer modeling

Shilin I. A., Vestyak V. A.

We have derived some integrals representations of Legendre function by using so-called Poisson transform, which maps any homogeneous and infinitely differentiable function on the cone into a corresponding function on the two-sheeted hyperboloid. Above representations are applied in Fourier method or the method of separation of variables in the initial-boundary value problems of Dirichlet and Neumann problem for Poisson equation in a dihedral angle. These problems, in turn, are directly related to the nonlinear flow problem, the lifting force, and vibrations of an airplane wing.

Keywords: Legendre functions, group representations, Lorentz group, Poisson transform

Aviation technics and technology

Zay Y., Kyaw Z.

The present work defines the basic aerodynamic characteristics of typical aerospace vehicle during hypersonic flight in rarefied atmosphere, obtained with the Monte-Carlo method based on the hypothesis of locality. The present results are the aerodynamics characteristics of aerospace vehicle by Monte-Carlo method in free molecular flow at different values of Reynolds number and temperature factor. The results can be used for aerospace vehicle design project.

Keywords: aerodynamic characteristics; Monte-Carlo method; free molecular flow; Reynolds number

Gavrilov D. G., Mamonov S. V., Martirosov M. I., Rabinsky L. N.

Results of tests investigations of steel samples tension without coating and with applied protective coatings of different types are under consideration. The same consideration is provided for four points twist.

Keywords: coatings, test, tension diagram, mechanical properties, powder paint, lacquers, rule of mixtures, multiply coatings

Aerospace propulsion engineering

Komarov V. V., Ponomarev A. A., Ponomarev N. B.

The so-called restricted shock flow separation (RSS) was revealed experimentally in a high-area-ratio model nozzle having a truncated ideal contour and a 45° back exit cone intended initially for facilitating ground tests of rocket engines with such nozzles. Transitions from the usually observed free shock flow separation (FSS) to RSS and vice versa in this nozzle with the exit cone of different exit diameter during increasing and decreasing the chamber pressure are analyzed. To this effect both static pressures and their pulsations were measured on the nozzle surface, and also surface oil pictures in the flow separation region are employed.

Keywords: gas dynamics, nozzle, flow separation, shock waves

Navigation systems

Zaharov A. A.

The pre-production model of an integrating wave solid-state gyroscope with differentiation (WSG-IGD) has found out the following feature of change of the measured values (Ωизм) to constant angular speed set to the sample Ω [radian/second]. Function Ωизм(t) contains not sinusoidal periodic component, to the greatest which first harmonic correspond amplitude Ωим1≈0,0066 Ω and circular frequency ω≈1,09Ω . By the analysis it is established that feature is caused by a methodical periodic error of measurement of a corner of orientation of a standing wave in the resonator. Using this feature, the way of experimental definition of scale factor (K) WSG-IGD is developed and tested. On the given sample the measured factor has made K=0.2773. Recommendations about application of ways of definition of scale factor WSG-IGD are considered.

Keywords: a way, the scale factor integrating a wave solid-state gyroscope, an integrating wave solid-state gyroscope with digital differentiation, drift, a corner of position of a standing wave, angular speed

Zaharov A. A.

The mathematical description of characteristics of the converter of two-polar voltage in frequency (CTVF) in the conditions of an entrance background hindrance is considered. Mathematical model CTVF is constructed at use of characteristics of unipolar converters. On wasps-novanii of this model population mathematical expectations (МE) target frequency CTVF (depending on a constant component of entrance voltage) and extreme values of a deviation of this frequency from МE are received. It is spent linearization expressions МE for small entrance signals.

Keywords: mathematical model, the converter of two-polar voltage in frequency, the converter of unipolar voltage in frequency, small entrance voltage, work in the conditions of a background hindrance, residual (or target) frequency, the likelihood information, average frequency, a population mean, values of deviations, the gauge of the angular speed, dynamically adjusted gyroscope

Zaharov A. A.

The description of characteristics of the converter of two-polar voltage in frequency (CTVF) is considered at small voltage in the conditions of an entrance background hindrance, a random error of start and temperature changes. On the basis before the developed model "ideal" CTVF it is defined linearization population mathematical expectations (МE) frequency CTVF (depending on a small constant component of entrance voltage). Functional dependence specified МE from temperature CTVF is Thus received. For algorithmic correction of errors of the converter methods of measurement of parametres of zero zone CTVF are offered at its joint work with a two-scale gyroscopic measuring instrument of angular speed.

Keywords: model, the converter of two-polar voltage in frequency, small entrance voltage, work in the conditions of a background hindrance, temperature changes, a start random error, average residual (target) frequency, the gyroscopic gauge of angular speed of the compensatory type, dynamically adjusted gyroscope, a population mean

Technical cybernetics. Information technology. Computer facilities

Kartashov D. A., Medetov N. A., Smirnov D. I., Orlov R. S., Ivashchenko O. V.

Calculation efficiency of results double-wave X-ray reflectometry for multilayered structures on GPU with application of platform NVIDIA CUDA is considered. For the first time effective implementation of calculations on interpretation of the data relative double-wave X-ray reflectometry on the basis of technology CUDA is offered. In this paper comparison calculation speed of mathematical model on GPU NVidia GeForce 8500 GT with speed of calculation on the basis of the CPU Intel Core 2 Duo E6400 is spent. Experiments have shown, that calculations time of parameters for multilayered structures on GPU is reduced more than 10 times in comparison with calculation on the CPU.

Keywords: Double-wave X-ray reflectometry, multilayered structures, efficiency of calculations, the CUDA technology on GPU

Akimov E. V., Kuznetsov M. N.

This paper deals with the stochastic mathematical models of components and operational aspects of wireless sensor networks (WSN), designed to evaluation the reliability of the network using the theory of markovian processes. These models can also be used to solve other problems associated with the design and analysis of WSN.

Keywords: Wireless Sensor Network, reliability, radio channel, multiply medium access, “hidden node” effect

Radio engineering. Electronics. Telecommunication systems

Bogdanov A. S., Shevtsov V. A.

The article reveals a new way to determine the location and management in modern mobile radio networks, based on the integrated use of mobile radio communication network and deployed within its range of local radio-navigation network.

Keywords: radio communication; the mobile; a site; management; GSM; UMTS; radio navigation; cellular; algorithm; handover

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