Volume 6 Issue 3


Volume 6 Issue 3

Download one file 5


Bessonov A.S.,
Petrukhin E.A.

Virtual models of light backscattering in ring lasers 26

The simulation of light backscattering in a ring laser is considered. It is indicated that backscattering is the main source of laser gyro errors. A mathematical description of the backscattering processes based on the determination of the complex coupling parameters of counterpropagating waves is presented. A representation of complex coupling parameters in the form of vector diagrams is proposed. It is concluded that virtual models created in graphical programming environments are most convenient for users. These models combine information contained in mathematical models and in vector diagrams. With the help of computer animation, the complex coupling parameters phase changes of counterpropagating waves during the operation of the ring laser are displayed. The simulation results are presented in various text and graphic forms. The backscattering simulation results during the laser tuning to the generation of various modes, under the influence of temperature and in the antiphase motion of piezoelectric transducers are described. The created virtual models are intended for developers of measuring systems used in the production of ring lasers and laser gyros. The obtained results allow estimating the lock.

Keywords: ring laser, light backscattering, lock-in threshold, virtual model, mathematical model, vector diagram.


Gudko N.I.

Effective models and schemes of cyclic action digital devices 34

The work considersmodels and schemes of widespread digital devices of cyclic action. They includecoders and decoders of information transfer system, control units of processors, generators of codes, counters, distributors of impulses etc. Three models of devices for consecutive, parallel and ripple through information transfer are suggested and proved. The structure of the models is presented by a set of blocks with original operation algorithms and connections between their blocks. The blocks are implemented in the form of Moore machines (in case of consecutive transfer) and Mealy machines (in case of parallel and ripple through transfer). A technique for synthesizing devices based on these models with the use of canonic synthesis methods and ofHuffman transition tablesmodified by the authoris suggested. This allows implementing compactly devices of practically any complexity. Algorithms for transition from models with ripple through transfer to models with parallel and consecutive transfer are described. Examples of implementing models in the form of concrete schemes confirming their efficiency are considered.

Keywords: digital device of cyclic action, model, blocks, transitionstables, informationtransfer, counters, processing speed, economy of the number of gates.



Kryzhanovsky A.D.,
Pastushkov A.A.

A nonparametric method of reconstructing probability density according to the observations of a random variable

When investigating the statistical characteristics of a field formed by locally inhomogeneous regions, the problem of reconstructing the probability density function with several vertices on the basis of the results of experimental observations arises. In this case, it is very difficult to apply parametric methods for reconstructing the probability density. Therefore, to restore the probability density, it makes sense to use non-parametric methods of recovery. The Rosenblatt- Parzen method usually used for these purposes has low accuracy and convergence rate. The method proposed in the work of Chentsov N.N. has higher accuracy and convergence rate. However, for multi-vertex distributions its convergence rate is also low. Similar conclusions can be drawn regarding the method proposed in the work of Vapnik V.N. Thus, the problem of developing a technique for reconstructing the multi-vertex probability density on the basis of the results of experimental observations becomes very urgent. The article suggests a nonparametric method of reconstructing probability density according to the observations of a random variable. The method is regular in the sense of Tikhonov regularization and, as the analysis and solution of test problems show, it has sufficiently high accuracy and convergence rate.

Keywords: nonparametric methods, distribution function, probability density, sampling function, Whittaker series, quasisolution.



Berdnikov V.P.

Modified algorithm for determination of full stability areas in nonstationary nonlinear systems 27

The paper proposes a numerical algorithm for constructing Lyapunov spline functions for investigating the absolute stability of nonlinear nonstationary systems. In the case of asymptotic stability of the system, the implementation of the algorithm will lead to the construction of the Lyapunov function level set in the form of a piece-wise smooth (smooth, if additional conditions are met) closed surface of dimension equal to the dimension of the original system. It is shown that the modified algorithm significantly improves the stability boundary estimates obtained with frequency methods. Unlike the algorithm for constructing piecewise linear Lyapunov functions, the running time of the proposed algorithm for constructing the Lyapunov spline functions does not tend to infinity as the system approaches the stability boundary. This circumstance makes it possible to use a modified algorithm to determine the stability of systems that are close to the stability boundary. An estimate of the accuracy of determining the stability area using an example of a third-order system is shown. Specific recommendations on the algorithm initial conditions choice are given.

Keywords: differential inclusions, nonlinear nonstationary systems, absolute stability, Lyapunov functions, stability areas, Bezier splines, Bernstein polynomials.


Kovalenko A.N.,
Zhukov A.N.

Algebraic models of strip lines in a multilayer dielectric medium 25

The electrodynamic problem is reduced to an integral equation with respect to the current density on the strip conductor. It is solved by the projection method using the Chebyshev basis. A homogeneous system of linear algebraic equations (SLAE) is described with respect to the coefficients of the expansion of the longitudinal and transverse components of the current density in terms of Chebyshev polynomials with weight functions that take into account the specificity of the field at the edges of the strip conductors. On the basis of the condition that the determinant of this system is zero the constants of the natural waves propagation are determined by numerical methods. A procedure for improving the convergence of slowly convergent series for the matrix coefficients of SLAE is carried out. The problem of high-accuracy calculation of the functions represented in the form of infinite slowly convergent series, by means of which the matrix coefficients are determined, is solved. A universal formula independent of the number of layers for calculating the wave impedances of natural waves is obtained. The use of the Chebyshev basis and the improvement of the series convergence made it possible to develop an effective algorithm for calculating the basic electrodynamic parameters of the strip lines – the propagation constants and the wave impedances of the natural waves. The constructed algebraic models of strip lines allow computer simulation to obtain numerical results quickly and with high accuracy irrespectively of the number of dielectric layers and their parameters. On the basis of the developed algorithm we created a set of computer programs for calculating the propagation constants, the coefficients of the current density decomposition in terms of Chebyshev weighted polynomials and the wave impedances of screened strip lines of various types: a single and connected microstrip lines (with side and face communication); coplanar strip line; slit line and coplanar waveguide. These programs allow determining the electrodynamic parameters of the main wave and up to 50 waves of higher types. The results of a numerical analysis of the convergence of the developed algorithm for the calculation of natural waves are presented. This confirms the effectiveness of the constructed models. Numerical results obtained without the procedure for improving the convergence of series for matrix coefficients and results obtained by the projection method using the trigonometric basis are given.

Keywords: projection method; "Chebyshev" basis; eigenwaves; effective calculation algorithm; constant propagation; wave resistance; algebraic models; computer modelling.