bluuebunny/crossref_metadata_2025 huggingface dataset:
Electromagnetic field of a relativistic electron vortex beam*
Authors: Lei Changyong , Dong Guangjiong
Published: May 2020

Electron vortex beams (EVBs) have potential applications in nanoscale magnetic probes of condensed matter and nanoparticle manipulation as well as radiation physics. Recently, a relativistic electron vortex beam (REVB) has been proposed [Phys. Rev. Lett.
107 174802 (2011)]. Compared with EVBs, except for orbital angular momentum, an REVB has intrinsic relativistic effect, i.e., spin angular momentum and spin–orbit coupling. We study the electromagnetic field of an REVB analytically. We show that the electromagnetic field can be separated into two parts, one is only related to orbital quantum number, and the other is related to spin–orbit coupling effect. Exploiting this separation property, the difference between the electromagnetic fields of the REVB in spin-up and spin-down states can be used as a demonstration of the relativistic quantum effect. The linear momentum and angular momentum of the generated electromagnetic field have been further studied and it is shown that the linear momentum is weakly dependent on the spin state; while the angular momentum is evidently dependent on the spin state and linearly increases with the topological charge of electron vortex beam. The electromagnetic and mechanical properties of the REVB could be useful for studying the interaction between REVBs and materials.
Logic of basic swarm reactions
Authors: Schumann Andrew
Published: May 2020

In the paper, there are defined continuous-valued logical functions defined on [0, 1] as natural reactions of swarm to several stimuli detected at one time step. In this model, the logical duality represented by squares or cubes of opposition is realizable by own swarm patterns based on lateral inhibition and lateral activation. Swarm reactions are considered not certain, but with a probability of their intensity in respect to the distance to an appropriate biologically active substance. At the same time, we can formalize cases when the swarm members are partly inhibited and partly activated. In other words, we assume that they can be less or more inhibited and less or more activated, etc. So, we can deal with a fuzzy mix of conjunction and disjunction at one time.
Information resources usability and split-testing features
Authors: Astachova I F , Makoviy K A , Khitskova Yu V , Burakova N A
Published: May 2020

The article discusses the features of split testing and usability testing. The stages of these two types of testing are proposed. To create a web resource convenient for the user and practical for the business, analytics helps. Ergonomics test (usability testing) is a type of software testing that is aimed at exploring the convenience for users of a web page, user interface or device. At the end of the usability testing, a split (A / B testing) is performed (or not). A / B testing involves setting up two different options for a web page or landing page and sending the same amount of traffic to each page option. Then, the number of conversions for each option is measured and the best is revealed. The best option generates the most conversions. The stages of these two types of testing are proposed. An application is described that allows usability testing of information resources. The developed application supports the function of analysing images according to the main colour schemes, collect statistics selected by the user and upload their PC to an Excel document, independently define areas for collecting statistics.
About the possibility of synchronization in dynamical systems
Authors: Gladkov S O , Bogdanova S B
Published: May 2020

The principle possibility of two metal pendulums synchronization oscillating in the parallel planes, the distance between the suspension points of which is fixed, is proved. This behavior is possible only due to the taking into account two physical factors. The first one is an effect of electromagnetic interaction between them. The second one is accounting the electromagnetic radiation of each pendulum, which leads to nonlinear attenuation. The system of nonlinear dynamical equations of the movement is obtained and its decision are numerically analyzed.
Verbal model of the process of resource distribution with the application of the extractive planning of an enterprise of criminally executive system
Authors: Shugaj O E
Published: May 2020

The article defines the goals and discusses the principles for the formation of control circuits for managing an MIS enterprise. The contours of operational and financial planning, the general scheme of extrapolatory planning of MIS enterprises are considered. A theoretical information contour has been developed for coordinating the distribution of resources based on the goals of the enterprise’s commercial activities.
Analytical study of temperature layer fields of pectin-containing raw material under controlled heat exposure
Authors: Alekseev G V , Moldovanov D V , Leu A G , Dmitrichenko M I
Published: May 2020

Shelf life and quality of raw materials depend on optimal conditions for long-term storage. The optimal storage time, is the longest period, at which the loss of quality and nutritional value of raw materials do not exceed the allowable limit, depends on the temperature and humidity conditions. Throughout the entire storage period, the constant temperature should be maintained as long as possible, since its fluctuations even within +5°C can seriously affect the storage duration. On the territory of the Russian Federation, the temperature of outdoor air changes during the day from about 5 to 15°C, reaching 30°C in some regions. The seasonal temperature also varies significantly. Optimal conditions for storing pectin-containing raw materials are temperature limits of 0−5°C. One of the modes of storage of raw materials is storage in a refrigerated state, when the temperature of the raw materials and the surrounding space is lowered to −10°C. Such conditions can be achieved by equipping storage facilities with artificial cooling. Using thermophysical methods, it is possible to objectively assess the optimal storage conditions for raw materials and predict storage periods.
On a property of curves given by the determining equations
Authors: Bilchenko G G
Published: May 2020

The motion of a mechanical system consisting of a carrier and a load is considered. The carrier, located all the time in a horizontal plane, can move translationally along a rectilinear trajectory. The carrier has a rectilinear channel through which the load can move. The load is considered further on as a material point. The load can move in the channel according to a predetermined motion law. The channel axis is located in a vertical plane passing through the trajectory of the carrier. The Coulomb dry friction model is applied for simulation the forces of resistance to the motion of the carrier from the side of the underlying plane. In the conditions of the carrier motion along horizontal plane without detachment, the carrier motion differential equations are a system of three linear second-order differential equations. The influence of the system parameters on the motion of the carrier from the rest state is studied in the point of view of determining functions. An important property of the determining expressions is proved: the existence of a single intersection point of the curves given by the determining equations, which corresponds to the zero angle of setting of the channel along which the load moves.
Development of solution for control problem based on cascade decomposition method
Authors: Bugaev Yu V , Litvinov D A
Published: May 2020

The problem of simplifying solution of linear dynamic systems with preset conditions at the edges and internal points of the segment is considered. In this regard a modification technique of the existing cascade decomposition method based on obtaining a general formula for the system state and control functions is described. Coefficients of this formula are identified in a recursive way. The formula is presented to obtain the cascade decomposition method and kernel functions of the intermediate step matrices being important for the last step function. Illustratively, a practice-oriented example proves the method advantages in convenience and speed comparing with the conventional method of cascade decomposition.
The development of the atherosclerosis diagnostic models under conditions of unbalanced classes
Authors: Demchenko M V , Kashirina I L
Published: May 2020

The main purpose of this study is to identify, using various methods of machine learning, the most effective markers of atherosclerosis and their main predictors, which can accurately determine the risk of this disease in the human body. In this study, various models and balancing techniques of the initial data set were used, which allowed us to develop the efficient classifiers according to the criteria of sensitivity, specificity and ROC AUC.
Computer simulations of the influence of atomic structure disorder on the hardness of Cu − Ag and Au − Ag alloys
Authors: Desta Okbamichael G , Bykova Maria I , Timoshenko Yury K
Published: May 2020

In this paper, computer simulations of the hardness of ordered and disordered alloys of Cu−Ag and Au−Ag were performed using the Sutton-Chen potential and the GULP software package within several models. In addition, Poisson ratios were estimated. When simulating a chemical disorder, a super-cell containing 108 atoms was built. Numerical experiments have shown that chemical disorder in the studied alloys leads to hardness degradation.
Mathematical simulation of a mass transfer in a cylindrical channel
Authors: Germider O V , Popov V N
Published: May 2020

A rarefied gas flow trough a long circular tube due to pressure and temperature gradients is studied on the basis of the S-model kinetic equation. The Maxwellian mirror-diffuse reflection model is used as the boundary condition on the channel walls. The mass flow rate is calculated as a function of the small pressure and temperature gradients. Similar results presented in the literature are compared. The thermomolecular pressure effect has been modeled and the coefficient of the thermomolecular pressure difference has been calculated at various values of the accommodation coefficient and in whole range of the Knudsen number.
The concept of structural-parametric synthesis and optimization of information systems in conditions of destructive impacts
Authors: Kochedykov S S , Yu Kobzistyy S
Published: May 2020

Currently, information systems have become an integral part of critical information infrastructure. In particular in the energy sector, developed and successfully operated information system in the management of technological, industrial and security measures. Systems in this class are subject to destructive impact and above all by cybercriminals seeking to infiltrate their database, block, or disable electronic equipment control and management. The main feature behind the concept of structural-parametric synthesis and optimization of information systems is that the systems of this class are objects for a formal description, which there is no unambiguous analytical dependencies. In addition, there are significant limitations on the choice of the optimization parameters that cannot be precisely determined at the stage of examination of the object of the synthesis, since they depend on the design solutions. Therefore, structural-parametric synthesis of the information systems cannot be reduced to the solution of the optimization math problems. Requires a special approach, which is able to resolve the difficulties due to the operational management of the course of the synthesis.
Algorithm of group movement of agents with directional antennas and the related game
Authors: Kuznetsov Alexander V
Published: May 2020

We describe one of the possible methods for organizing a control and communications system for agents such as unmanned aerial vehicles with directional antennae. A special kind of cellular automaton was proposed with an adjacency between cells changing every cycle to describe the group movement of agents forced to synchronize, as well as the corresponding game.
A computational experiment based on a nonlocal search algorithm using potential theory
Authors: Medvedev S N , Medvedeva O A
Published: May 2020

We consider a general method to derive an optimization algorithms based on potential theory. This theoretical approach is based on the randomization of an objective function and the computation of directional derivatives of the randomized functional. Using the gradient of the potential field we consider algorithm in terms of the means of the underlying movements in the space of random vectors. Effectively, this process combines the exploration power of random-search algorithms with the exploitation power of direct-search algorithms. At the end we offer the results of a computational expert.
Starting control of vibrations of points of a rectangular membrane
Authors: Tukhtasinov M T , Abdualimova G M
Published: May 2020

The problem of starting control of the vibration of points of a rectangular membrane with fixed boundaries is considered. The concept of implemented functions for these membrane points is introduced. For each function being implemented, valid controls are defined that form the control sets. The structure of the control set is studied. The problem is solved in the game setting, the initial player controls the initial position of the membrane, the second, the initial speed. The criterion of the quality of control is determined by the control standards with which the functional is built. The saddle point of the functional and the equilibrium situation of the game are found.
The use of the model of kinetics of ethylbenzene dehydrogenation to estimate the state variables and catalyst performance under unsteady conditions
Authors: Popov A P , Tikhomirov S G , Neizvestny O G , Kharlampidi Kh E
Published: May 2020

The article considers the application of the mathematical modeling method to describe the dynamics of the catalytic layer state variables of the styrene production reactor. This method was carried out using a kinetic approach for description of chemical transformations, which occurs in a multicomponent gas mixture. The main physical processes, affecting the decrease in catalytic activity during operation, are considered and the relationship between them is described. A method for increasing the efficiency of the catalytic system in terms of ACS (automated controlling system) synthesis is proposed. The mathematical formulation of the problem of creating a predictive program control system under unsteady conditions is completed. Mathematical software has been developed that allows us to evaluate activity and predict the dynamics of changes in such production efficiency indicators as ethylbenzene conversion and styrene selectivity. In that framework, the blocking of catalyst active centers, proceeding by the sequential mechanism of coke formation, is classified as a deactivating factor. The distribution patterns of carbon along the length of the reaction space at different times of the catalyst inter-reactivation period, depending on changes in the mixture component concentrations and the temperature condition, are revealed. Based on the production data, the calculation and approximation of raw materials conversion values and selectivity for the target product were carried out taking into account the accumulation of carbon on the layer surface, as well as the variation of process parameters such as temperature, pressure of the reaction mixture and partial pressures of the components.
Automated synthesis of band-pass filters with current to voltage conversion with given transfer gain in the Simone circuit designer
Authors: Ananev A V , Prikota A V , Gorovoy A V
Published: May 2020

The iterative method for automated synthesis of band-pass filters with current to voltage conversion with a given transfer gain is developed. The structure of the synthesis system of LC circuits with a given voltage transfer coefficient is presented. The implementation of the proposed method in SimOne Circuit Designer plugin is shown. Further ways for method development are suggested.
Numerical mathematical model for calculating ion density in the gas-discharge chamber of a radio-frequency ion thruster
Authors: Gordeev S V , Kanev S V , Khartov S A
Published: May 2020

The mathematical model for calculation of the ion density in the gas-discharge chamber of a radio-frequency ion thruster is developed. The model is based on the assumption of higher potential of the central plasma volume comparing to the chamber walls due to higher mobility of electrons. Firstly, the initial approximation for the plasma potential is set and parameters of the ion trajectories in quasistationary electric field are computed. Then, from the assumption of keeping the total ion flow for each trajectory, the ion density is computed as well as the next approximation for plasma potential. The computation is performed iteratively until the change in the ion density is less than the predefined small value. The model was verified by comparing the results of numerical simulation with the analytical solution for spherical volume. The high accuracy of the numerical model is shown. Also, the ion density in the discharge chamber of a radio-frequency ion thruster was calculated with the uniform distribution of neutral atom density and coefficient of ionization rate. It was shown that at such conditions the ion density has a maximum in central part of the discharge chamber and it decreases towards the walls.
Method of assessing the «usability» characteristic of the functioning quality of information protection systems
Authors: Kadnova A M , Khvostov V A , Drovnikova I G , Gulyaev O A
Published: May 2020

The article is devoted to solving the practical problem of assessing the quality characteristic of the information protection system –«usability». In the course of his/her work, the security administrator of the automated system, built in a secure execution, makes a number of technological operations restricted by regulatory and administrative documents. At this, the prompt of such operations is determined by the characteristics of the interfaces of the software modules of the information protection system (IPS). In this regard, the assessment of the quality characteristic of the IPS «usability» becomes relevant for the category of users - security administrators. A meaningful analysis of the activities of this category users of information systems showed that it is appropriate to assess the “usability” based on operational, temporal and probabilistic indicators. The methodological basis for assessing these indicators is an experimental measurement of the average execution time of each operation by a representative group of users, followed by an analytical prediction of the probability of their execution.
Usage of production-based expert system and neural network for signal recognition
Authors: Donskih D N , Barabanov V F
Published: May 2020

At the current paper the system of signal type automatic recognition for the problem of automated testing of radar stations based on collaborative usage of production system and neural network set is presented. The main approaches for solving the problem of automated recognition digital and analog modulation types are shortly outlined. Characteristics calculated based on time-domain and frequency-domain signal representation, typical for the radar impulses are considered. The structural schema of the software for automated classification of radar impulses is presented.
Model and algorithms of interaction of the snow avalanche with the stirrable and destructible obstructions
Authors: Kalach A V , Karpov S L , Soloviev A S , Karpov L D , Sitnikov A I
Published: May 2020

A model for studying the movement of avalanche-hazardous snow masses based on the method of smoothed particles is presented. This approach has been shown to be most appropriate in modelling environments prone to fragmentation. The impact of the snow avalanche on vehicles and the dependence of the affecting factors on the thickness of the snow cover and the terrain have been investigated. It has been found that with snow cover thickness up to 0.5 m, avalanche does not lead to loss of vehicle controllability. The results of the modelling at a qualitative level coincide with the real effects of the avalanche on the vehicle, which confirms the adequacy of the model developed.
Study of the influence of cross section sizes of the rod shock system on the efficiency of shock pulse energy transfer to the deformation center
Authors: Kirichek A V , Barinov S V , Yashin A V , Konstantinov A M
Published: May 2020

Using the finite element model of the shock system, the efficiency of the shock pulse energy transfer to the deformation zone under wave strain hardening is studied. It was established, that conducting research from the point of view of the efficiency of transferring the shock pulse energy to the deformation zone, and from the point of view of the design of the shock pulse generator, is advisable on shock systems in which the contacting ends of the striker and the waveguide have equal diameters. Studies showed that with ratios 1<L1/L2<10; 5<L1/d1<10, an increase in the fraction of the shock pulse energy transmitted to the deformation zone n exceeds 80% for the striker and waveguide with diameters of 30, 48, 60, 90 mm. According to the adopted optimization criteria, the geometrical dimensions of the striker and the waveguide are determined, which ensure the transfer of the largest amount of shock pulse energy to the deformation zone.
Research of radon transport processes in anisotropic media
Authors: Krizsky V N , Nafikova A R , Kozlova I A , Yurkov A K
Published: May 2020

The study of radon migration in geological environments is relevant for the search and contouring of oil and gas deposits, the search for uranium and thorium ores, environmental mapping when choosing sites for the construction of industrial and residential structures, and for predicting events in seismic activity zones. The paper considers a mathematical model of the three-dimensional problem of radon diffusion-advection in piecewise constant layered media with inclusions, taking into account the anisotropy of the diffusion properties of subregions of the geological environment. A combined method for solving the problem is described, based on a combination of the methods of Laplace integral transformations, integral representations with the construction of the Green function of the host layered medium, and Fredholm integral equations of the second kind arising at the boundaries of local inclusions. The results of a comparison of the data of computational and natural experiments for some special cases are presented. A mathematical model of the inverse geometric problem of search for the boundary of a local inclusion is presented.
The spectral theory of graphs at researches of fuzzy models of the determined regular structures of network information systems
Authors: Mezhuev A
Published: May 2020

Operation is devoted the decision of the task increase of structural stability and information efficiency of network information systems on the basis of mathematical apparatus of the theory of fuzzy sets and the spectral theory of graphs. For this purpose introduction of two variants fuzzy structural (channel and nodal) is offered to redundancy of the determined regular topology of network information systems. Functions of an accessory of separate structural elements to which in correspondence the modes of an information exchange which are representing itself as requirements to structural characteristics of system are defined. Analytical and imitative modeling for research of influence fuzzy redundancy on the main structural parameters of the determined topology and estimation of information efficiency of the received structures of network information systems is conducted. Results of modeling showed perspectivity of the offered approach at implementation of structural adaptation of systems to changing conditions of an information exchange.
Modeling of a continuous process of isoprene polymerization in the presence of titanium-based catalyst systems under polycentric conditions
Authors: Miftakhov E , Mustafina S , Petrenko V , Podvalnii E
Published: May 2020

In the research is represented the mathematical model of the periodic process of isoprene polymerization in the presence of titanium-containing catalyst systems. By the process of constructing of the mathematical model was taken into account the polycentric nature of the applied catalytic system. On purpose of organization of the possibility to describe a continuous process in a cascade of ideal mixing reactors, the mathematical model was supplemented by the corresponding hydrodynamic mechanism. For the resulting system of differential equations, a numerical solution method was programmatically implemented and was conducted a computational experiment to predict the main molecular characteristics of the resulting product.
Modern and future schemes of very-high cycle fatigue tests
Authors: Nikitin A , Stratula B , Volkov B
Published: May 2020

The development of a new piezoelectric fatigue machine operating in pure torsion is presented in this paper. The proposal for implementation of a testing machine to research on very-high cycle fatigue at biaxial bending is studied. Results of pure torsion tests on titanium alloy VT3-1 processed by forging and extrusion are shown. Evaluations of specimens shapes made of aluminum alloy D16T and titanium alloy VT3-1 were conducted as well as the possibility to conduct VHCF bi-axial bending tests was confirmed.
Uniqueness of solving the problem of transport and sedimentation of multicomponent suspensions in coastal systems
Authors: Sukhinov AI , Sukhinov AA , Sidoryakina VV
Published: May 2020

The present work is devoted to the study of three-dimensional model of transport and sedimentation of suspended matter in the coastal zone. The model takes into account the following processes: advective transport due to the movement of the aquatic environment, microturbulent diffusion and gravitational sedimentation of particles of the suspension, and changes in the geometry of the bottom caused by sedimentation of the suspension or the rise of bottom sediments. The aim of the work was to conduct an analytical study of the uniqueness of the initial-boundary-value problem corresponding to the constructed model. In accordance with the stated aim, an initial-boundary-value problem is considered for a parabolic type equation with lower derivatives in the domain for which a quadratic functional is constructed and the uniqueness of the solution is proved by the energy method.
Modelling of suspended particles motion in channel
Authors: Sukhinov Alexander I , Chistyakov Alexander E , Kuznetsova Inna Y , Protsenko Elena A
Published: May 2020

The paper considers the application of the scheme based on linear combination of the Upwind and Standard Leapfrog difference schemes with weight coefficients obtained by minimizing the approximation error. The proposed difference scheme has shown its effectiveness in solving diffusion-convection problems in the range of grid Peclet numbers 2 ≥ Pe ≥ 20, which allows us to apply this class of schemes for the numerical solution of computational Oceanology problems. The problem of soil dumping was considered as a practical example of application of the proposed schemes.
Mathematical modeling of hydrophysical processes for water with complex bottom geometry
Authors: Sukhinov A I , Chistyakov A E , Leontyev A L , Nikitina A V , Filina A A
Published: May 2020

The paper covers the development and research of computational structure for mathematical modelling of hydrobiological processes for water with complex bottom geometry, based on the modern information technologies and computational methods. The models used in modelling take into account following: microturbulent diffusion; gravitational settling of pollutants; plankton populations nonlinear interaction; the salinity impact, temperature. The scheme with weights was proposed for discretization of the developed model, that allowed significantly reduce the error and the computational time. Practical significance of the work is that the proposed model was software implemented; the limits and prospects of its use were defined. The experimental software was designed on the basis of a graphics accelerator for mathematical modelling of possible development scenarios of the waters with complex bottom geometry, taking into account the environment influence. Parallel implementation was performed using the decomposition methods for computationally labours diffusion-convection problems taking into account the CUDA architecture characteristics.
Development and approbation of the improved CART algorithm version
Authors: Demidova L A , Usachev P O
Published: May 2020

This article considers the classification problems using the decision trees. It suggests the improved CART algorithm version called clean CART (CCART). The key feature of this algorithm is the reducing of the hardware memory for the tree storing. The main ideas of the CCART algorithm software implementation have been presented. The experimental results of comparison of the original and the presented algorithms for constructing the decision trees confirm that the proposed CCART algorithm has the stated advantage. Therefore, the proposed CCART algorithm is recommended for use in the ensembles of classifiers construction.
Classification of cardiac arrhythmia using machine learning techniques
Authors: Firyulina M A , Kashirina I L
Published: May 2020

Cardiovascular disease is one of the leading causes of death worldwide. Currently, there is an increase in the percentage of people with various heart rhythm disorders. There are permanent (chronic), persistent and paroxysmal form of atrial fibrillation, and the most severe violation is the permanent form. Since the reasons for the development of a certain form of atrial fibrillation are not completely clear, this article presents an analysis of various characteristics that affect the formation of arrhythmias of these species. The most significant signs that can potentially be predictors of different forms of the disease have been identified. Four machine learning methods were used for the analysis: classification trees, logistic regression, random forest, and gradient boosting. The highest cross-validation accuracy was obtained using logistic regression.
On some class of nonlinear mean random values
Authors: Khatskevich V L
Published: May 2020

In this paper we study the properties of one class of nonlinear means, including a geometric mean, a harmonic mean, and also a power mean of random variables. The considered random variables are assumed to be positive and have finite mathematical expectations. The asymptotics and extremal properties, as well as algebraic properties and inequalities between means are also studied below.
Computer simulation of the sensory interaction of carbon nanotubes with various modifications in relation to alkali metal atoms
Authors: Boroznina Natalia , Zaporotskova Irina , Boroznin Sergey , Bakhracheva Yulia
Published: May 2020

The performed theoretical studies obtained by computer modeling and calculations performed by the semi-empirical method using the MNDO calculation scheme showed the possibility of creating sensitive chemically active probes, which are semiconductor sensor systems with boundary modification, which can act as the tip of the cantilever of the atomic force microscope. These studies allow us to predict that such a sensor based on a modified borocarbon nanotube will react to the presence of ultra-small amounts of substances, which opens up prospects for its use in the field of chemistry, biology, medicine, etc. The use of chemically modified nanotubes, including in atomic force microscopy, is the way to create probes with distinct chemical characteristics.
The development of V. V. Strygin’s ideas in numerical mathematics in the works of Samara mathematicians
Authors: Blatov I A , Dobrobog N V , Kitaeva E V
Published: May 2020

The article reviews the most important results in the field of numerical mathematics obtained by Professor V. V. Strygin’s disciples and the disciples of his disciples in 2000–2019 in the city of Samara. We present the results on spline interpolation of functions with a boundary layer, methods and algorithms for a posteriori adaptation of computational grids for singularly perturbed boundary value problems and the results on applied wavelet analysis based on spline wavelets.
Differential systems stability analysis based on matrix multiplicative criteria
Authors: Bulanov S G
Published: May 2020

This article proposes a method of stability analysis in the sense of Liapunov for systems of ordinary differential equations. The method is based on matrix multiplicative stability criteria obtained from transformations of numerical integration difference schemes. Criteria are formed in the form of necessary and sufficient conditions. A distinctive feature of the criteria is that they do not employ the methods of the qualitative theory of differential equations. Specifically, for the case of linear systems, the evaluation of characteristic numbers and characteristic indicators is not necessary. When analyzing the stability of nonlinear systems, the construction of Liapunov functions is not required. Matrix multiplicative form of the criteria allows computerization of stability analysis. The software implementation of the criteria is performed in real time and, based on its results, allows to make an unambiguous conclusion about the nature of stability of the system under study.
Analysis of the nature of features of heat and mass transfer in discrete bulk of food products
Authors: Voronenko B A , Leu A G , Abushinov E V , Yukhnik I P
Published: May 2020

Despite the importance of resolving issues related to predicting the formation of heat-moisture fields during storage of grain, seeds and bulk-stored roots and tubers and the changes in technological properties of food raw materials that depend on them, currently, the mathematical descriptions of these associated phenomena do not suffice. This is due to the complexity and poor knowledge of the storage processes for bulk-stored food products at both the micro and macro levels. Such masses are a system with distributed parameters. In this regard, the possibility of predicting the fields of heat and moisture content depends, on the one hand, on the completeness of the necessary information about the moisture and temperature of the components of the mass at the initial moment, and on the other hand, on the reliability of the mathematical model capable of describing the real processes of heat transfer in bulk based on this information, which is used to set boundary conditions and thermophysical constants. An analysis of the nature of the features of heat and mass transfer in a discrete bulk of food product can be carried out only on the basis of the developed analytical models. This is the subject of this paper.
The residual plastic strain distribution over elastic–viscous–plastic cylindrical shell length upon longitudinal impact on the face
Authors: Egorov M V
Published: May 2020

This work is devoted to the study of the distribution of residual plastic strains on outer and inner surface over the length of a cylindrical shell in the process of dynamic deformation generated by a longitudinal impact on its end face. As a mathematical model, the Timoschenko’s model was used to describe the dynamic deformation of elastic thin shells, modified for the case of plastic deformations using the Bingham’s model. As the boundary conditions, we selected a longitudinal impact applied at the end face of the shell with longitudinal strains constant in time. As a method for solving the resulting system of differential equations in partial derivatives of a hyperbolic type, the third–order ray method was implemented. The paper represents options for the numerical calculation of the distribution of residual plastic strains for various thicknesses, as well as the corresponding shell shape after unloading.
The cybernetic concept of multialternativity in the evolution of biological systems
Authors: Podvalny S L , Vasiljev E M
Published: May 2020

The article describes the results of mathematical simulation and quantitative analysis of the biological property of diversity. The purpose of this work is a methodological generalization of this wildlife property in the form of a cybernetic concept of multialternativity as an evolutionary strategy of functioning of complex systems. The process of mathematical simulation of evolutionary processes in a complex hierarchical ecosystem with the closed-loop trophic cycle is carried out on the basis of the differential equations of mass balance. Several substantive principles given in the conclusions formulate the concept of multialternativity, i.e., the principles of multilevelness, division of functions and discretization. The constructive nature of these principles opens the way to a practical realization of a strategy of multialternativity in the creation of complex control systems realizing various functions.
Mathematical modeling of axisymmetric flow of granular materials
Authors: Frolov A L , Frolova O A , Sumina R S , Sviridova E N
Published: May 2020

A mathematical model of the axisymmetric flow of cohesive granular materials is considered. A plastically compressible material is considered as a mathematical model. This material has an additional characteristic - its own rotation of particles. The existence of this characteristic leads to the asymmetry of the stress tensor and the presence of torque stresses. Asymmetric components of the stress tensor are balanced by normal pressure due to the presence of rolling friction. It is shown that the distinctive characteristic of the axisymmetric state is the layering of its flow. The condition for the flow of cohesive bulk material is obtained.
Experimental studies and multi-factor analysis of the fuel component distributions over the mixing head nozzles of the liquid rocket engine
Authors: Kretinin A V , Milenin A V , Popkov A N , Shmatov D P
Published: May 2020

A model device of the liquid rocket engine mixing head for experimental determination of hydraulic non-uniformity of fuel distribution is described. Schemes of hydraulic and gas-dynamic test benches are given. The results of the planned factor experiment to determine the array of flow rates through individual sprayers are presented. Neural network regression factor models were created to evaluate the criterion of non-uniformity. The influence of various factors on the parameters of non-uniformity is estimated
Mathematical modeling of rotating disk states
Authors: Semka E V , Artemov M A , Babkina Y N , Baranovskii E S , Shashkin A I
Published: May 2020

We consider the problem of a rapidly rotating disk in the elastic-plastic state. The piecewise linear plasticity condition in general form is chosen. It is believed that all plastic curves have the common point of intersection which corresponds to uniaxial tension. For external parameters, we obtain the conditions that determine the probability of inception of plastic zones. It is shown that plastic zones could incept in the center of the disk and/or on the boundary of it. The problem in the plastic zone is statically determinate. The case when the plastic zone occupies some central part (core) of the disk, where one regime of plastic condition is fulfilled, is considered. In order to estimate the stress state inside the elastic zone of the disk, equivalent stress which is equal to the chosen plasticity function is defined. In order to define the relationship between plastic deformations and stresses, the piecewise linear plastic potential being equal to the plasticity function is chosen. The plastic incompressible body is considered. The associated flow rule can be integrated so that the problem of getting displacements turns into quasistatic one. The problem of determining displacements in the plastic region leads to a first-order differential equation with respect to the radial component of the displacement vector. Therefore the continuity condition for displacements at the elastic-plastic boundary and the assumption that the displacements in the center of the disk are equal to zero leads to an overdetermined problem. So, only the continuity condition for displacements at the elasto-plastic boundary is accepted. It is assumed that plastic deformations at the elastic-plastic boundary are equal to zero. It is shown that displacements at the center of the disk are equal to zero automatically for all piecewise linear conditions of plasticity apart from the Tresca yield criterion. For the Schmidt–Ishlinskii yield criterion, all deformations at the center of the disk attain finite values. Meanwhile, for other piecewise linear conditions, plastic deformations at the center of the disk attain infinitely large values. This explains the discontinuity of displacements at the center of the disk for the Tresca yield criterion. The calculation results are presented as graphs of stresses, displacements, and deformations.
Modeling of dynamic branching of a longitudinal shear crack at an inclusion
Authors: Bogomolova T G , Verveyko N D , Shashkin A I , Bykova M I , Krupenko S E
Published: May 2020

Mathematical modeling of branching of the leading edge of a longitudinal shear crack on a porous inclusion is proposed. The leading edge of the crack is approximated by the δ-neighborhood of the plastic deformation of the material with the front of longitudinal or shear waves, at which the longitudinal or transverse velocities break when passing through the leading edge of the crack. Expressions are obtained and graphs of the relative intensity of the leading edges of the reflected cracks of longitudinal and transverse shear and the conditions for the generation of reflected cracks depending on the angle of intersection of the crack with inclusion and physical parameters of the material are constructed.
The analysis of the laminar-turbulent transition onset for the Poiseuille flow in the flat channel with the velocity profile periodic background perturbation
Authors: Kolodezhnov V N
Published: May 2020

The paper adopts an approach to predicting the laminar-turbulent transition onset, which is based on the hypothesis of a threshold “connection” of the transverse viscosity factor and the subsequent transverse velocity components “generation”. In the framework of this approach, certain empirical local transition conditions are proposed and imposed on the dimensionless invariant complexes that characterize the laminar flow under study. Based on these conditions, an analysis of the Poiseuille flow transition onset in the flat channel in the presence of the stationary velocity field periodic background perturbation is carried out. A comparison with the known experimental data is presented.
On the separation of two meteoroid fragments of different shapes
Authors: Lukashenko V T , Maksimov F A
Published: May 2020

Separation of two meteoroid bodies is studied using modelling method based on a system of grids and solving adjoint aerodynamic and ballistic problems. Bodies of the same mass but different shapes were considered. Calculations were done for different combinations of the cylindrical bodies with their cross sections having a shape of square, elongated rectangular and circle. Initially the bodies were placed near each other on the line perpendicular to the flight direction. The lowest value of separation velocity was obtained for the bodies with circular cross section; the separation velocity is significantly increased for the bodies with elongated rectangular cross section due to rotation. Stable aerodynamic position of the bodies with elongated cross sections occurs when the bodies fly with a large side perpendicular to the flight direction. The lateral velocity acquired by each body appears to be primary determined by its own geometry and show no dependency on the shape of a neighboring body.
Nonlinear effects at elastic deformation of cubic materials
Authors: Sokolova Marina , Khristich Dmitrii , Artyukh Ekaterina , Afanasova Olga
Published: May 2020

A variant of the relations of nonlinear elasticity is considered for anisotropic materials which are supposed to be crystals of cubic syngony with respect to the type of elastic symmetry. The proposed model takes into account the physical nonlinearity in the behavior of such materials under the condition of small deformations. Based on the representation of the elastic potential in the form of a tensor polynomial in third-order strains, relations for stresses with elastic constants of the second and third orders are obtained. On the basis of the concept of the elastic eigenstates of materials, in the case of a cubic material, representations for the elastic tensors of the fourth and sixth ranks in eigentensor bases are obtained. The proposed variant of constitutive relations takes into account the mutual influence of the processes occurring in various eigenspaces of cubic material.
Mechanical interaction of a reinforced concrete slab and a steel beam in bridge spans
Authors: Kozlov Vladimir A , Kozlov Alexey V
Published: May 2020

The paper aims to clarify the rules of calculation of steel-reinforced concrete bridge superstructures on the basis of generalization of modern scientific achievements in conjunction with the possibilities of computational software and computer technology in the field of calculations of multi-component sections without the need to use simplifying hypotheses that affect the accuracy of the calculation. An algorithm for calculating continuous multi-span beams of bridge structures with the possibility of taking into account the flexibility of the shear joint between concrete and steel structural elements is proposed, which increases the accuracy of determining the stress-strain state (SSS) of the structure. The results of the work can be used in the design of steel-concrete bridge superstructures. The significance of the work lies in the fact that the proposed analytical dependences in the joint use of modern computing power will clarify the calculation of steel-concrete bridges, thereby increasing the level of reliability of bridge structures, laid at the design stage.
Forced vibrations of beveled non-circular conical thin-walled structures of variable thickness
Authors: Kozlov Vladimir A , Chernikov Andrey V
Published: May 2020

The stress distribution in shells of variable thickness must be taken into account when designing various elements of general and transport engineering, aviation, rocket and space technology, structures. The paper presents one of the possible approaches to the dynamic calculation of a thin-walled non-circular conical structure rigidly fixed along a beveled end section. The resolving system of ordinary differential equations was obtained in the framework of the technical theory of shells using the variational Lagrange principle. The boundary-value problem of determining dynamic stresses in the structure under consideration under the influence of a harmonic load is solved numerically by the method of orthogonal sweeping of a system of linear ordinary differential equations of the first order. In contrast to the known works, a variable thickness of the structure along the length is considered.
Predicting the risk of road pavement premature destruction
Authors: Ermoshin N A
Published: May 2020

The paper reveals the ideas of assessing the road condition on the basis of risk theory, which allows predicting the rate of the road structure destruction and its actual life. The regularities of the influence of physicomechanical parameters of road construction materials, as well as the coefficient of variation of the required modulus of elasticity of the subgrade on the value of the equivalent modulus of elasticity and the rate of destruction of pavement are established.