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## Publications

## Editor-in-Chief

**Nikiforov**

Vladimir O.

D.Sc., Prof.

Vladimir O.

D.Sc., Prof.

## Partners

**Summaries of the Issue**

### PHOTONICS AND OPTOINFORMATIСS

753

Application possibility of quantitative ellipsometry method for studies of optical anisotropy and structural heterogeneity of the skin in vivo is shown. To describe the polarization properties of the depolarizing optically-active biotissue medium, the Mueller matrix algebra is used. Based on comparative analysis of the technical options and their application in experiments with biotissue, a setup for recording of the polarization state of the backscattered radiation was developed. It is proposed to use the emitting channel of the LEF-3 ellipsometer in the optical scheme of the stand to have a uniform intensity distribution along the cross section of the input radiation beam, and also to form the polarization states necessary for the study. Radiation source wavelength selection in the spectral range (He-Ne laser, 632 nm) is justified, when scattering of radiation in turbid biological media predominates over absorption that makes it possible to estimate the structural parameters of the sample by the change of the output radiation polarization state. The receiving channel of the output polarization state analyzer was developed; it contains a video information block based on a color matrix sensor with a unified analysis field providing the possibility of further multispectral studying of the skin surface structure. The method of ellipsometric examination of the skin is proposed based on the distribution visualization of the polarization state parameters along the cross section of the output radiation beam and on its following analysis. An algorithm and software are developed with a Python language for image processing and calculation of the polarization characteristics of the sample. The distributions of the polarization characteristics of the skin sector containing scar structures are obtained in the backscattering mode of probing laser radiation.

### OPTICAL ENGINEERING

761

Subject of Research.The paper deals with mutlipulse inscription comparative results of the type IBragg gratings in the birefringent optical fiber with elliptical stress cladding and increased GeO2 concentration at different birefringence axes positions. Method. The gratings were inscribed by the phase mask method. The excimer laser Coherent COMPexPro 102F, working with the gas mixture KrF (248 nm), was used as the radiation source. The phase mask Ibsen Photonics with a period of1065.3 nm was used. Main Results.The results have shown that the multipusle inscription is more effective and has better dynamics when the plane containing the fiber axis and its slow birefringence axis is parallel to the writing radiation incidence plane containing the fiber axis. Practical Relevance. Theresearch results give the possibilityto make recommendations for the multipulse Bragg gratings inscription efficiency enhancement in the specialty birefringent fibers. The pre-inscription positioning of birefringence axes also makes it possible to reduce the polarization fading that is the noise source in phase interferometric sensors.

767

Subject of Research.The subject of research is the protective housing for the fiber-optic hydrophone that is a part of the working model of the ocean seismic bottom station. The fiber-optic hydrophone is built on the base of Mach-Zehnder interferometer. Its sensitive arm is wounded on the elastic mandrel. The mandrel material increases acoustic pressure sensitivity of the optical fiber. The developed housing is designed to protect the sensitive optical fiber from mechanical damage. The housing also passes the acoustic signals in water without attenuation in the work frequency range of the fiber-optic hydrophone up to 8 kHz. Method. The theoretical calculations, based on the Helmholtz resonator theory, and mathematical modeling by the finite element method in the ComsolMultiphysics environment were used to develop the protective housing with required parameters. Created models enabled the definition of the protective housing final construction that passes acoustic signals in the required frequency range. Main Results. As a result of mathematical modeling the final construction of the protective housing was chosen. The construction is based on the aluminum cylinder with the external radius equal to 30 mm, the height - 14 cm and the wall thickness - 1 mm and it contains 1900 holes with the radius equal to 1 mm. During the modeling the frequency response of the protective housing was obtained; this response demonstrated its acoustic transparency in water at frequencies up to 8 kHz. The chosen protective housing was fabricated and studied in the working model of the ocean seismic bottom station. Experiment results confirmed the acoustic transparency of the protective housing in the required frequency range. Practical Relevance. The results of this work might be used for the developing and creating of protective housings for fiber-optic hydrophones with the required frequency responses. The developed protective housing is used in the working model of the ocean seismic bottom station and it provides the mechanical protection of the optical fiber in the sensitive element of the fiber optic-hydrophone without distortion of its frequency response.

775

Subject of Research. We propose a method and technology of delivering optical radiation to biological single micro-objects at wavelength equal to 650 nm. The delivering optical radiation is implemented by a fiber optic system that is a standard optical fiber with a reduced diameter at the output end (cone optical fiber, or fiber optic taper). Method. The method essence appears as the creation of a fiber optic system for delivering optical radiation. A sampling method of fiber optic tapers by a fusion splicer for optical fibers is proposed in this paper. The process of protective coating formation, opaque to optical radiation exiting through the side surface of the fiber taper, is described. The end of the fiber optic taper is prepared to obtain a uniform intensity distribution of the outgoing optical radiation. The study of the divergence of optical radiation exiting from the taper end is carried out. Main Results. The proposed method has enabled creation of a fiber-optic taper with a waist diameter of 15±5 μm. The carried out study of optical radiation divergence has shown that the field diameter at a distance of not more than 200 μm to the micro-object is approximately 19 μm and does not exceed the taper waist diameter. Practical Relevance. Unlike other existing methods of delivering optical radiation, a fiber taper with a waist diameter of 15 ± 5 μm provides an impact not only on individual cells but also specific regions of cells with the size that exceeds the taper waist diameter. With the help of the manipulator, the end of the fiber taper can be placed into the required area without overlapping the object to the required distance directly in the environment where biological objects are located (cell cultures).

782

Subject of Research.We discuss the photodynamic therapy of onychomycosis (nail fungal disease). The paper presents device description and main technical characteristics of the efficient LED device for photodynamic therapy of onychomycosis. The relevance of presented study is associated with the high incidence of onychomycosis, the need to increase efficiency, comfort and reduce its treatment period. Method. The efficient LED with a wavelength equal to 656±10nm compatible with absorption wavelength of photosensitizer (radachlorin) was selected. The optical model of single LED was created. The light intensity distribution generated by twenty eight LEDs on the surface located at different distances from the source (LED board) was calculated. Main Results. On the basis of optical optimization calculation of light intensity distribution, the main parameters (dimensions, angles, shape) of the mirror reflector for LED radiation delivery were determined. The assembly parts were manufactured and breadboard model of modular LED device for photodynamic therapy of onychomycosis was assembled and tested. Engineering test has shown that to achieve therapeutic dose required for photodynamic therapy of onychomycosis in the square bounded by the rectangle 16х6 = 96cm2 (maximum area occupied by human foot toes), 20±2minutes will be necessary that is quite comfortable for the doctor and the patient.Practical Relevance. Afterengineering and clinical testing and certification the proposedLEDdevice can be applied in the state and private health care facilities of the Russian Federation for the photodynamic therapy of onychomycosis and other cases.

### AUTOMATIC CONTROL AND ROBOTICS

790

The paper deals with the trajectory control synthesis of a mobile robot movement in a nonstationary external environment, in particular, in the presence of external mobile objects in the robot working space, by differential geometry methods and stabilization methods for invariant manifolds in the space of control object outputs. For control algorithm development, the relative dynamics of the control object and the external mobile object is considered and the methods of differential-geometric transformation of the initial model to the task-oriented coordinates are formulated. The latter formulates the initial problem in terms of longitudinal motion, orthogonal and angular deviations, and the proportional differential control algorithms are created with direct compensation of nonlinearities. The main results are presented by the task-oriented model of spatial motion and corresponding nonlinear control algorithms. To illustrate the efficiency of the proposed method, the rigid body motion modeling along a linear trajectory in the presence of an external mobile object moving through a desired linear trajectory crossing the working space is given as an example. In the example, the plant traverses an external moving object along a circular path and returns to the original desired trajectory.

798

Subject of Research. We present the algorithm for tracking and classification of the operator's head movement according to the data obtained from an IMU (inertial measuring unit) installed in the helmet of virtual reality. We performed experimental testing of the developed algorithm and proposed the way of its application for control of mobile robot with six degrees of freedom. Method. The problem is solved by complex filtering of input signals from the gyroscope with the Kalman filter and the dead-zone filter. The definition of the operator's head movement pattern is based on determination coefficient calculation and its comparison with the threshold level. Main Results. We have developed an algorithm for unambiguous evaluation of the operator's head movement that can be interpreted by the control system as a control signal. Practical Relevance. Presented algorithms can be used in a wide range of systems, for example, for controlling mobile telepresence robots that have special suspension for camera guidance control and are controlled with the use of virtual reality helmet. The developed algorithm will be applied also in the implementation of mobile robotic platform, equipped with computer vision systems, navigation and augmented reality, that is planned to be created in the framework of practice-oriented research and development work at ITMO University.

### MATERIAL SCIENCE AND NANOTECHNOLOGIES

805

Subject of Research.The paper discusses the principles of information processing by nanomagnetic logic devices consisting in the magnetization manipulation of individual magnetic nanoparticles in a single-domain state and combined into a logical network. In a single-domain state, nanoparticles have uniaxial magnetic anisotropy that makes them a bistable system suitable for binary coding of information: the magnetization downwards corresponds to a logical "0", the magnetization upwards is "1". These two states are separated by an energy barrier with the height equal to the energy of the magnetic anisotropy. The logical network in question implies an entirely new way for performing of logical operations. The point at issue is about a network of nanomagnets connected by a dipole interaction and admitting the existence of intermediate frustrated states, analogous to quantum entanglement. Methods. Materials with sufficiently high magnetic anisotropy energy are required for nanomagnetic logic devices to ensure that thermal fluctuations do not lead to orientation loss of magnetic moment and the loss of information. As such, we proposed to use new nanomagnets based on the epsilon phase of iron oxide ε-Fe2O3 with giant magnetic anisotropy. Nanoparticles are produced by a combination of two methods: synthesis in reverse micelles and a sol-gel method. Elemental analysis of nanoparticles was carried out by mass spectrometry with inductively coupled plasma (Agilent Technologies, HP 4500). Photomicrographs were obtained by the JEOL JEM 2000EXII transmission microscope. The structure of nanoparticles is determined by X-ray diffraction on a Rigaku RINT2100 instrument. Study of the magnetic properties was carried out with the use of SQUID magnetometer Quantum Design, MPMS 5XL. Main Results. A new method for performing of logical operations is proposed that consists in the magnetization manipulation of individual nanoparticles not only with the aid of an external magnetic field, but also by varying the temperature of the ε-Fe2O3 nanoparticles under the conditions of a spin-reorientation transition. In the ε-Fe2O3 nanoparticles, a magnetoelectric interaction is discovered that opens new ways for solving the bit state reading problem in the devices under consideration. Experimental conditions for performing of logical operations in ordered arrays of ε-Fe2O3 nanoparticles are created. Practical Relevance. Temperature manipulation by the vector magnetization direction opens up new possibilities for creating devices for nano-magnetic logic and spintronics under conditions of strong anisotropy, when the magnetic fields required to switch the direction of magnetization (and, hence, the change in the bit state) become unacceptably large. The principles discussed in the paper are capable of providing a nondissipative processing of information in the energy limit close to Landauer's estimates, where thermodynamic aspects come to the fore.

812

Subject of Research. A new method of thermal imaging spectroscopy is presented giving the possibility to determine the chemical composition of defects formed as a result of the surface exposure by chemical, biochemical reagents, point contamination of the surface by biological organisms far from the operator in hard-to-reach places where there is no possibility for application of the known optical and spectroscopic equipment. Method. The surface study is performed by thermal imaging camera with simultaneous irradiation of the surface by laser radiation with a wavelength that coincides with the spectral absorption region of the defect substance. The presence of a defect on the surface is determined on the screen of the thermal imaging camera as a zone of contrast between the background temperature and the defect temperature. When the wavelength of the laser radiation coincides with the region of the characteristic absorption band in the absorption spectrum of the defect matter, it becomes possible to determine the chemical composition of the defect. Main Results. A mechatronic module for laser beam scanning over a surface is developed. Simultaneous measurement of the temperature field with the help of a thermal imager and feedback makes it possible to carry out work on the search for zones with the supposed presence of certain zones with definite chemical composition. Experimental results of the defects study are presented with different values of absorption coefficient applied on the heavyweight paper surface in the form of thick drop-shaped layers. A comparative analysis of the experimental and calculated values is carried out. The experiment scheme and the mechatronic complex structure are presented. Practical Relevance. The proposed method can be used to determine contamination spots on the surface of reservoirs, to search for material evidence on unfolded surfaces in forensic examination, to determine the sites of the surface contamination by biological objects during mycological examinations.

820

Subject of Research.We propose the method for simulation of infrared spectra of the most widespread medical substances (hydrogen peroxide, glycine, pyrazinamide, sodium oxybate, halothane). The aim of the study is to find out the possibility for replacement of experimental methods of medical substances spectra measurement with their quantum mechanical simulation. Method. Several quantum mechanical methods are used in the study: semi-empirical methods, the restricted Hartrey-Fock method, the Density Functional Theory method. The accuracy estimation of the results is carried out with the use of the Spectral Database for Organic Compounds (SDBS). Main Results. The spectra simulation of samples taken from the Vital and essential medicines notitia is carried out. The received results demonstrate the possibility of application of computer simulation methods together with experimental research. It is shown that the real spectrum in the examined infrared spectral region (from 500 to 4000 cm-1) can be received as a composition of spectra calculated with the use of different methods. The data, calculated with the use of semi-empirical method and the Density Functional Theory method, were more approximate to the experimental data. Practical Relevance. Obtained data may be of interest to specialists of pharmaceutical industry for the additional quality estimation of the produced medical substances.

826

Subject Research. The paper presents results of research on the thermal stability of the composite material (CM) "water glass–graphite microparticles" under temperature variation and the substance composition in the initial state at the intermediate stages of the heating process, and on the residue composition. Method. The study was carried out by the thermal analysis with the use of thermogravimetry method, when the sample mass change depending on the temperature is recorded. Thus, the condition is observed that samples drive off volatiles as a result of physical or chemical processes in the CM. We used methods of x-ray crystallography and electron microscopy. Main Results. "Water glass–graphite microparticles" composite material is studied by the thermoanalytical method. The physical processes occurring during the heating of CM are described. Composite material structure and component phases of the reaction products of microcomposition formation are defined by the x-ray diffraction analysis and electron microscopy. The stoichiometric coefficients of chemical reaction are obtained by the thermodynamic method. Practical Relevance. Composite material with the obtained characteristics can be used as a protective coating for building structures with the aim to increase fire resistance and reduce fire hazard.

834

Subject of Research.The paper deals with characteristics study of polymer composites based on commercially available polyvinyl chloride and biopolymer filler pectin in various weight ratios (1.5 and 10 mass%) for the usage as biodegradable packaging. Method. Biopolymer composite films were obtained by rolling at the temperature of 165-170 ℃and pre-mixing of all composition components with a paddle stirrer at a stirring speed of 6000 rpm for four minutes. The introduction of natural materials into the polymer matrix facilitates the decomposition of plastics during disposal, and the processing of composite polymeric materials for five and ten minutes by low-temperature plasma in argon: oxygen modifies the surface of the material, ensuring access of microorganisms for biodegradation. Samples of composites were studied by the methods of infrared Fourier spectroscopy and optical microscopy, depending on the content of the filler and etching time of the samples. Main Results. The effect of plasma-chemical treatment on the surface of polymeric composites has been experimentally proved; an increase in roughness, craters and other discontinuities may be explained by structural changes confirmed by infrared spectra. It is shown that composites containing 1% by weight of pectin are subjected to the greatest degree of material oxidation. Practical Relevance. The resulting biopolymer composites can be used as a package that decomposes during disposal and does not harm the environment. The introduction of a biodegradable component, natural polysaccharide of pectin, in small amounts does not change the chemical structure of the polymer material. Plasma-chemical treatment can be used as a method for surface treatment of industrial polymer materials before disposal.

### COMPUTER SCIENCE

841

Subject of Research.We study the ways of multipath distribution of copies of requests (packets) through the network and their redundant servicing by servers of a given cluster. The alternatives under consideration differ in the way of path selection for a packet in the network having routes with joint switching nodes (static or dynamic) and in the condition under which those copies exit early from the system as a result of their losses in the communication channels, the emergence of bit errors, the overflow of transmitting and receiving buffers of the network and computing equipment, or the combination of these reasons. Method. We consider the efficiency of redundant transmissions, defined as the probability of faultless and timely delivery of at least one redundant copy to the cluster and dependent on the intensity of the flow of incoming requests. Based on the alternatives described, a set of simulation models with parameters representing the requirements for the system under simulation is created with AnyLogic 7 simulation environment. The results of simulation experiments are being written to the Microsoft SQL Server 2008 database, undergo transformations, and then are exported into the application program developed in this study. Main Results. Organization of simulation experiments involving accumulating and processing of their results with the tools of the chosen database management system is proposed. After being handled, those results are used to form the basis for analysis of the obtained dependencies with third-party software applications, such as Microsoft Excel or the one implemented in this work, to determine the scope of efficiency of redundant transmissions and to automate the search for the optimal order of redundancy. The simulation results that confirm the efficiency of multipath distribution of copies of requests are presented. Practical Relevance.The proposed models and tools enable one to justify the choice and optimize project solutions to the problem of improving functional reliability of distributed computer systems with redundant transmission and servicing of requests.

850

The paper proposes solution for the problem of real time processing and analysis interface for Open Data containing geocontext markup inside location-based services (LBS) platform. Solution method is based on providing the ability to extend a platform by the addition that implements import and mapping of several Open Data sets. This addition also should perform calculation of additional data attributes and processing of set element by set statistical indicators and clustering methods. The plug-in for Geo2Tag LBS-platform was developed for the proposed method approval. The solution determines popularity of open WiFi hot spots with the use of VK social network data. The plug-in performs import and mapping of Saint Petersburg government Open Data set and VK posts archive related to particular city districts. The mapping is performed by calculation of additional data attribute related to posts distribution - median, arithmetical mean or cluster centers by k-means clustering method. For plug-in performance evaluation, a series of experiments was performed. Analysis of experiment results showed that plug-in work time firstly depends on Open Data downloading speed because the time of Open Data processing by plug-in is an order of magnitude less than the loading time. This fact demonstrates that plug-in can perform almost real-time analysis of remote Open Data source. Developed method can be applied not only for Geo2Tag LBS-platform but also for broad set of similar systems because the solution depends only on Open Data import subsystem implementation that can be implemented on any LBS-platform. The method also gives competitive advantage for LBS-platform because it gives the possibility to extend qualitative composition of platform data by imported Open Data analysis results wherein analysis methods can be defined not only by LBS-platform administrators but also by platform users who are also the developersdue to the fact that the method is based on user’s plug-in subsystems.

859

Subject of Research. The paper presents an overview of research in the area of experts’ collaboration for solving given problems. The capabilities of expert networks for collective information consumption and the creation of new knowledge are studied. Distinctive characteristics of modern expert networks are identified. The expert network building principles, expert search algorithms and query routing algorithms are described. A comparative analysis of expert networks of various types is given: general, specialized, scientific and educational ones.Main features of networks and basic functions are distinguished. Based on the analysis results, the requirements for modern expert networks of scientific and technological orientation are formulated. Method. Description and comparative analysis of related systems and technologies are used to identify expert network requirements. Main Results. The main scenarios for the expert networks utilization by experts and customers are identified. Expert network requirements are formulated that provide the effective use of the system in accordance with the scenarios. Practical Relevance. Application of the research results will help to develop expert network for collective work and efficient interaction of experts and their customers, so that the system meets requirements of the modern systems for expert collective work.

872

Subject of Research.The paper deals with effectiveness analysis of redundant service of requests time-critical to total gradual waiting in the queues of multi-tier clustering nodes. We search for design solutions on the organization of multi-stage redundant service of copies of requests in multi-tier cluster that makes it possible to increase the probability of timely servicing of requests critical to the total waiting time for all system levels (stages of maintenance). Method. We modeled the multi-stage redundant service of copies of requests in multi-tier cluster. The redundancy effectiveness is estimated by the probability of not exceeding the total phased waiting time in queues of nodes for all levels specified for the maximum allowable time. We selected the best options for the organization of redundant requests; the request is considered successful if at least for one accurately executed copy, total waiting time of the stages in the queues of the nodes at all levels of the cluster does not exceed the maximum allowable waiting value. Main Results. The experiments based on calculations carried out with the use of the proposed models on the three-tier cluster example gave the possibility to elucidate the dependence of probability of not exceeding the allowable total request time on the intensity of requests, the multiplicity of redundancy and the maximum allowable cumulative waiting time of requests in the queues of the nodes at all cluster levels. We have shown the existence of efficient redundant service of requests in multi-tier clusters, and the optimal multiplicity of redundancy of request copies depending on the system load and constraints on the allowable total time of staged waiting in the queues of the nodes in the clusters at all levels. Practical Relevance. The proposed models can be used to assess the reliability and timeliness of the service processes that are critical to request waiting time, as well as in the justification of selection of disciplines and service parameters in multi-tier computer systems, including real-time ones.

### MODLING AND SIMULATION

879

Subject of Research. We consider one of the actual problems of spectroscopy, that is, the separation of close spectral lines. Method. The problem is solved by a mathematical (computer) way, namely, by minimizing a functional of discrepancy between the measured and calculated spectra. In this case, the lines (components) are modeled by Gaussians and the problem is reduced to localization of their parameters. Main Results. To minimize the functional we propose the coordinate descent method modification with the use of decremental constraintstechnique. To smooth and differentiate noisy experimental spectral data, we suggest using splines. The software on MatLab is developed and a number of spectra are processed. Practical Relevance. The developed technique can be used to restore the fine structure of spectra and, thereby, to increase the resolving power of spectrometers.

890

Subject of Research. The paper deals with the possibility of the algorithm execution for the purpose of energy detection of hydro-acoustic communication synchronization signal and its software implementation in a multiprocessor system for processing of hydro-acoustic signals. The result of this algorithm is the detection of hydro-acoustic communication synchronization signal and the definition of its spatial channel for the further implementation of communication session. Method. The essence of the proposed solution lies in comparing the signal energy in a given frequency band with the signal energy outside the specified frequency band. The synchronization signal is emitted in the mode of hydro-acoustic communication before transmission of data block of signals. It gives the possibility to define the modem frequency range and the spatial channel to be connected to the modem, and calculate the ratio of Doppler distortion. The chosen energy algorithm for detection of hydro-acoustic communication signal is not critical to computational resources that are limited in real-time systems. Main Results. The algorithm is implemented for "KOMDIV 128 RIO" signal processor. To test the functionality of the developed software for detection of timing signal, a software simulator was created enabling the generation of hydro-acoustic communication signal at the input of the receiving elements. Testing with the simulator showed the possibility of syncronization signal detection. Practical Relevance. The considered algorithm of hydro-acoustic communication signal detection is implemented in the software of a multiprocessor system for processing of hydro-acoustic signals.

896

Subject of Research.The paper presents testing results of difference scheme with customizable dissipative properties in the case of the two-dimensional problems for both gas dynamics and gas-suspensions mechanics. Method. The second order difference scheme is created with splitting of physical processes into two phases. The first phase uses the central difference, the scalar version of the nonlinear artificial viscosity limiters and semi implicit approximation of the interphase interactions. Reconstructions of TVD type are used at the second phase. Main Results. Testing was performed for problems with strong discontinuities when the shock waves interact with suspended particles. For illustrative test problems, the scheme with customizable dissipative properties has demonstrated a good quality of numerical solutions at the level of the WENO5 scheme with the ability to resolve fine details of the flow in case of multiple interactions of shock waves, contact discontinuities and rarefaction waves. Possible oscillations of the numerical solution in the proposed scheme are suppressed by setting its dissipative properties. Practical Relevance. The scheme with customizable dissipative properties is the basis for the development of applied software package as a justification tool for the attainable level of technical solutions with the use of the gas suspensions flows.

903

Subject of Research. The non-platform inertial navigation system mathematical model is proposed. The non-platform inertial navigation system is an aircraft flight navigation parameters detector and a part of the airborne equipment. This model as a part of the simulation stand provides the modeling of the aircraft flight navigation parameters including the inaccuracies that may occur when a real non-platform inertial navigation system is active. Method. The flight navigation parameters calculation with the use of the proposed model is based on the calculation of simulated functioning parameters of the inertial system in horizontal plane. The initial data for calculation are the current programmed values of the flight navigation parameters and the aircraft orientation parameters without paying attention to the angular velocity and acceleration. The model initial data can be programmed with the simulation stand. The model contains the mathematical apparatus modeling inaccuracies that may occur when the inertial coordinates system tries to determine the aircraft location and its ground speed. Main Results. The proposed model provides the geodesic coordinates calculation and the ground speed when the orientation inaccuracies constant components are programmed including the gyroscope drift and the inertial system accelerometer inaccuracies. The modeling inertial system technical characteristics can determine the inaccuracy values, in particular, for the systems based on the ring laser gyroscopes. The model work-out results with the use of flight test data are given and the modeling inertial system inaccuracies evaluation is presented. Practical Relevance. The modeling realization of the non-platform inertial navigation system parameters as a part of the airborne equipment stand provides the information display system functioning work-out on the ground. At the analysis of basic design requirements for equipment development the inertial system model can be used for the preliminary functioning analysis of the non-platform inertial navigation system and the evaluation of the flight navigation parameters inaccuracies.

910

920

A numerical simulation of the shock wave reflection from a plane wall is carried out. Depending on the input parameters, a regular (two-wave configuration) or Mach (three-wave configuration) reflection is observed. A finite volume method and high-order difference schemes are used for discretization of the Euler equations describing the flow of an inviscid compressible gas. The application of weighted essentially non-oscillatory (WENO) schemes of high accuracy order realized in different forms on unstructured meshes is demonstrated. The calculated shock-wave configuration is compared with the data available in the literature. It is shown that the WENO-scheme of the fourth order accuracy in characteristic version gives the possibility to reproduce much more details than the scheme of the third order with the absence of solution oscillations characteristic of TDV (Total Variation Diminishing) schemes and component-wise WENO schemes. The criteria for the accuracy of numerical calculations related to the location of shock-wave structures are discussed. Recommendations on the practical application of high order difference schemes on unstructured grids are given.

929

GENERATION OF SPECTRAL DENSITY MATRICES FOR MULTICHANNEL CONTINUOUS SYSTEMS UNDER WHITE NOISE ACTION

938

Subject of Research. Wepropose an algorithm of spectral density matrix generation for an output of multichannel continuous systems under vector white noise action. The spectral density matrix is used for the following cases. In the first case, a separate channel of the system is considered. The channel is excited by a scalar white noise. In this case, the spectral density matrix is scalar. In the second case, the system is excited by a vector white noise with components of different intensities. Stochastic process of the selected output is of interest. In this case, the spectral density matrix of the output is scalar too and becomes the spectral density function. In the third case, the system is excited by a vector white noise with components of different intensities, like in the second case. But, spectral density matrix of vector output is considered. Method. The algorithm development is based on the use of Lyapunov matrix equation and Wiener-Kolmogorov-Khinchin integral. Scalarization of frequency representation of stochastic output vector is based on two methods. The first method is a per-channel generation of spectral density functions. The second method is a singular decomposition of the spectral density matrix of the output to form a majorant and a minorant of spectral densities in the output space of the system. Main Results. The constructive algorithm is obtained for studies of the system spectral properties both for the case of separate channels and for the case of vector "input-output" ratio. Thus, the results are invariant to the dimension of the input-output ratios. Practical Relevance. The results serve a useful purpose for the cases when multichannel systems operate under external actions undefinable by a finite-dimensional representation. The most illustrative application examples of the paper findings are the systems of stabilizing a plant spatial position under stochastic actions with white noise representation.

947

We consider a nonlinear autonomous controlled mechanical system with several degrees of freedom with a mathematical model in the form of a polynomial system of differential equations containing homogeneous linear forms with respect to phase variables and nonlinear homogeneous forms up to the fourth power with small coefficients. By replacing variables with multipliers–exponential functions of time–the system is transformed into a system with an autonomous linear part and non-autonomous variable coefficients for homogeneous nonlinear forms with a matrix having eigenvalues with negative real parts reduced in absolute value, as well as nonlinear forms with variable coefficients. A method is proposed for the formation of a sequence of linear differential inequalities for positive-definite Lyapunov functions with estimates of the system approximation to a stable equilibrium state.

### BRIEF PAPERS

952

This brief paper discusses identification problem of unknown time-varying parameters for a linear regression model. A new algorithm is proposed that guarantees–in case of a set of assumptions existence–an estimate of unknown parameters and their dynamical model with an asymptoticallyzero error. We analyze in details the case with two unknown parameters that enables to understand the main idea of the proposed approach. The efficiency of the algorithm considered in the paper is illustrated by computer modeling.

956

We study the propagation rate of the combustion front in a quartz cylindrical tube filled with a mixture of propane and air with volumetric ignition by a streamer discharge. The streamer discharge is ignited on the inner walls of the tube by quasioptical microwave radiation with an initiator placed in the tube. The measurements are performed for different lengths of the streamer discharge. The carried out studies showed that the streamer discharge, that creates a multitude of ignition points, provides practically instantaneous ignition of the mixture in the entire volume, where the streamers reach. The resulting combustion front has a speed typical for the deflagration to detonation transition. Measurements have shown that the front speed rises with discharge length increase, but it is nonlinear. The dependence of the speed on the excess fuel coefficient is also ambiguous. The results can be applied in the development of multipont volumetric ignition systems in internal combustion engines, gas turbine engines, low-emission combustion chambers, the combustion organization in a supersonic flow, and the combustion chambers detonation engines.