Informatics, computer technology and management. Рубрика в журнале - Siberian Aerospace Journal
Torsion of prismatic orthotropic elastoplastic rods
Статья научная
Conservation laws were introduced into the theory of differential equations by E. Noether more than 100 years ago and are gradually becoming an important tool for the study of differential equations systems. Not only do they allow you to qualitatively investigate the equation, but, as the authors of this article show, they also enable you to find exact solutions to the boundary value problems. For the equations of the iso-tropic theory of elasticity, the conservation laws were first calculated by P. Olver. For the equations of the theory of plasticity in the two-dimensional case, the conservation laws were found by one of the authors of this article and used to solve the main boundary value problems of the plasticity equations. Later it turned out that the conservation laws can also be used to find the boundaries between elastic and plastic zones in twisted rods, bent beams, and deformable plates. The proposed work found conservation laws for equations describing the orthotropic elastic state of the twisted straight-line rod. It is assumed that the remaining current depends linearly on the voltage tensor component. In the workit was also found an endless series of laws of preservation, which allows you to find an elastic-plastic boundary, which arises when twisting the orthotropic rod.
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Using of the contour method to solving the problem of optimal traffic distribution in the network
Статья научная
The purpose of this work is to create a method for solving the problem of optimal traffic distribution in a network using the contour data analysis method. In the first section of the work, the principle of converting any available network to a contour form is explained, and the case is considered both for networks without loss and for networks with losses. The second section shows in a general way the method of bringing the network in contour form to a system of non-linear inequalities, by solving which one can obtain a certain distribution of traffic in the system. In the final section, using the M/M/1/N queuing system as an example, the solution of the problem of optimal traffic distribution according to the loss minimization criterion is shown. The initial data for the task were the incidence matrix, service intensity and buffer dimension for communication channels. A feature of the proposed algorithm is the search for a contour matrix, for the compilation of which it is proposed to use loss edges as elements of the spanning tree of the graph, which allows you to immediately determine the contour matrix using the concept of a fundamental cycle of a graph. This approach to optimal traffic distribution reduces the number of variables used compared to the known methods based on loopless routes, and also does not require their preliminary search, since they are determined from the dimension of the incidence matrix of the simulated network graph.
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Using signals of navigation satellites in the monitoring of the Earth covers
Статья научная
The features and capabilities of remote sensing of earth covers by means of signals of navigation satellites are presented. The methods of reflectometry of the surfaces of earth covers and radioscopy of forest canopy are described. The options for using the signals of GLONASS, GPS systems are considered. Test measurements of interference diagrams were carried out on 5 test platforms from heterogeneous soil surfaces: salt marshes and asphalt; water surfaces of saline and freshwater bodies in summer, including ice cover of small thickness in the period of autumn freeze-up. The method of radioscopy helped obtain the data on the spatial and temporal characteristics of attenuated signals of the GLONASS and GPS satellites in the pine forest. Estimates of the linear attenuation coefficients of the signals passing through a forest canopy with a coordinate reference were made. The results obtained are the basis for the development of methods and technologies for continuous monitoring of the characteristics and state of earth covers by means of signals of navigation satellites for solving a wide range of applied tasks.
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Volume temperature control at automated high-frequency processing of polymer and composite materials
Статья научная
The purpose of this work is to develop and justify a method for volumetric temperature control of a polymer and composite material in automated high-frequency processing. The developed method is implemented by in-troducing thermocouples into the prism-shaped or cube-shaped sample body according to a certain pattern of their location throughout the volume. This technique is cost-effective and easy to implement compared to expen-sive and specialized equipment with complex design, as well as to the cost of thermocouples having a simple de-sign. Methods to achieve the purpose of the research of the contact method of volumetric temperature of a polymer or composite sample control are development and outlining thermocouples throughout the volume so as to iden-tify the most accurate temperature spectrum of the polymer or composite sample during automated high-frequency processing. Another method to achieve this purpose is the method of finding out how it will affect the measurements accuracy of the heating sample temperature from the introduction of thermocouples by making holes in it for installation. For this, a finite-difference mathematical calculation of the dependence of the sample temperature on the number of holes for thermocouples in it was performed in the MSC Patran Sinda software package. The calculation results were summarized and presented on graphic data. Further, a general mathemat-ical calculation was performed according to the formulas for the process of heat and mass conductivity calcula-tion, the results of which were table and graphic data. At the end of the finite-difference and general mathematical calculation, a comparative analysis of the ob-tained error of temperature measurement from the introduction of thermocouples into the body of the sample was performed. Based on this analysis, the developed method is applicable for further research on automated high-frequency processing of polymer and composite materials, since the errors obtained do not exceed the permissi-ble 3 %.
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m-aperiodic words on three-letter alphabet
Статья научная
The work is devoted to the study of sets of aperiodic words over a finite alphabet. The set of aperiodic words can be considered as a dictionary of some finite formal language. The existence of infinite words in two-letter or three-letter alphabets that do not contain subwords that are third powers or, respectively, squares of other words was first discovered more than a hundred years ago. S.I. Adyan in 2010 constructed an example of an infinite sequence of irreducible words, each of which is the beginning of the next and does not contain word squares in a two-letter alphabet. S.E. Arshon established the existence of an n-digit asymmetric repetition-free sequence for an alphabet of at least three letters. In the monograph by S.I. Adyan proved that in an alphabet of two symbols there exist infinite 3-aperiodic sequences. In the works of other authors, generalizations of aperiodicity were considered, when not only the powers of some subwords were excluded. In the monograph by A.Yu. Olshansky proved the infinity of the set of 6-aperiodic words in a two-letter alphabet and obtained an estimate for the number of such words of any given length. The author previously considered the case of a three-letter alphabet only in the case of 6-aperiodic words. In this article, we prove the infinity of the set of m-aperiodic words in the three-letter alphabet at m 4 and obtain an estimate for the set of such words. The results can be applied when encoding information in space communications.
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