Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
https://journals.eco-vector.com/1991-8615
<p>Peer-review academic journal for Differential Equations and Mathematical Physics, Mechanics of Deformable Solids, Mathematical Modeling, Numerical Methods and Software Systems.<br /><strong>Publish</strong> quarterly since 1996 in Open Access with no APCs.<strong><br /></strong><strong>Editor-in-Chief</strong>: PhD, Professor <a class="SLink" href="http://www.mathnet.ru/php/person.phtml?option_lang=rus&personid=38375" target="_blank" rel="noopener">Vladimir P. Radchenko</a>.<br /><strong>Indexing</strong>: RSCI (Web of Science), eLibrary.ru, Cyberleninka, Google Scholar, OCLC WorldCat, BASE, OpenAIRE, RePEc, Socionet, СyberLeninka.ru, Math-Net.ru<br /><strong>ISSN</strong>: 1991-8615 (Print); <strong>ISSN</strong>: 2310-7081 (Online)</p>Samara State Technical Universityru-RUJournal of Samara State Technical University, Ser. Physical and Mathematical Sciences1991-8615<p align="justify">Authors who publish with this journal agree to the following terms:</p> <ol> <li>The journal applies the <a class="SLink" href="https://creativecommons.org/licenses/by/4.0/deed">CC BY 4.0</a> Licence to all content we publish. Under the <a class="SLink" href="https://creativecommons.org/licenses/by/4.0/deed">CC BY 4.0</a> Licence, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles in the journal, so long as the original authors and source are cited. No permission is required from the authors or the publisher.</li> <li>Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book, translate it into another language), with an acknowledgement of its initial publication in this journal.</li> <li>According to <a class="SLink" href="http://www.sherpa.ac.uk/romeo/index.php">SHERPA/RoMEO</a> classification this journal refers to the so-called "green" journals, i.e. permits authors to archive both pre-prints and post-prints of their papers. Authors are also permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process.</li> </ol>On a q-analogue of the Sturm–Liouville operator with discontinuity conditions
https://journals.eco-vector.com/1991-8615/article/view/108514
<p>n this paper, a <span id="MathJax-Element-2-Frame" class="MathJax" tabindex="0"></span><em><span id="MathJax-Span-4" class="math"><span id="MathJax-Span-5" class="mrow"><span id="MathJax-Span-6" class="mi">q</span></span></span></em>-analogue of the Sturm–Liouville problem with discontinuity condition on a finite interval is studied. It is proved that the <span id="MathJax-Element-3-Frame" class="MathJax" tabindex="0"></span><em><span id="MathJax-Span-7" class="math"><span id="MathJax-Span-8" class="mrow"><span id="MathJax-Span-9" class="mi">q</span></span></span></em>-Sturm–Liouville problem with discontinuity conditions is self-adjoint in <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>L</mi><mi>q</mi><mn>2</mn></msubsup><mo>(</mo><mn>0</mn><mo>,</mo><mi>π</mi><mo>)</mo></math>. The completeness theorem and the sampling theorem are proved.</p>Döne Karahan
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2022-09-302022-09-3026340741810.14498/vsgtu1934Uniform optimization of controlled systems with distributed parameters
https://journals.eco-vector.com/1991-8615/article/view/114785
<p>A constructive method is proposed for solving a spatiotemporal control problem in systems with distributed parabolic parameters under the conditions of the given accuracy of uniform approximation of the final state of a plant to the required spatial distribution of the controlled variable. The developed approach is based on the previously designed alternance method for constructing the parameterizable programmed control algorithms, which extended the results of the theory of nonlinear Chebyshev approximations to a wide range of optimization problems and uses the fundamental laws of the subject area. It is shown that in linear quadratic problem optimization the equations of optimal controllers with autonomous modal controls in the open domain of their definition and taking into account restrictions on the nature of the spatial distribution of the control actions specified by the conditions of technical implementation are reduced to linear feedback algorithms for the measured state of the plant with nonstationary transmission coefficients and the given dependence on the spatial arguments of the controlled value. The results obtained are extended to the problem of searching for time-invariant spatially distributed controls, considered as the desired design solutions for a plant.</p>Edgar Ya. Rapoport
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2022-09-302022-09-3026341944510.14498/vsgtu1943Questions of the existence and uniqueness of the solution of one class of nonlinear integral equations on the whole line
https://journals.eco-vector.com/1991-8615/article/view/106733
<div class="around-button">We consider a class of nonlinear integral equations with a stochastic and symmetric kernel on the whole line. With certain particular representations of the kernel and nonlinearity, equations of the mentioned type arise in many branches of mathematical natural science. In particular, such equations occur in the theory <span id="MathJax-Element-1-Frame" class="MathJax" tabindex="0"></span><em><span id="MathJax-Span-1" class="math"><span id="MathJax-Span-2" class="mrow"><span id="MathJax-Span-3" class="mi">p</span></span></span></em>-adic strings, in the kinetic theory of gases, in mathematical biology and in the theory of radiative transfer. Constructive existence theorems are proved for non-negative non-trivial and bounded solutions under various restrictions on the function describing the nonlinearity in the equation. Under additional restrictions on the kernel and on the nonlinearity, a uniqueness theorem is also proved in a certain class of bounded and non-negative functions that have a finite limit in <span id="MathJax-Element-2-Frame" class="MathJax" tabindex="0"></span><span id="MathJax-Span-4" class="math"><span id="MathJax-Span-5" class="mrow"><span id="MathJax-Span-6" class="mo">±</span><span id="MathJax-Span-7" class="mi">∞</span><span id="MathJax-Span-8" class="mo">.</span></span></span> At the end, specific applied examples of the kernel and non-linearity are given that satisfy to all restrictions of the proven statements.</div>Khachatur A. KhachatryanHaykanush S. Petrosyan
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2022-09-302022-09-3026344647910.14498/vsgtu1932Gadolin's problem on the assembly of a two-layer shaft by a shrink fit with a test of the connection for separation
https://journals.eco-vector.com/1991-8615/article/view/110978
<div class="around-button">The connection strength in the interference fit assembly of a two-layer shaft produced by the shrink fit operation is studied. The materials of the assembly parts are considered to be ideal elastoplastic, with yield stregth that are significantly depended on temperature. In the calculations, the conditions of plane deformed states are taken into account. Pull tests are performed by rotating the assembly around its axis, when pulling forces are generated in the form of centrifugal forces of inertia. It is shown that with an increase of the rotation speed, the tightness in the assemblies is decreased. Limitations of the possible angular speed are calculated under the assembly tightness disappearing.</div>Anatoly A. BureninAnastasia V. TkachevaSergey Viktorovich Firsov
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2022-09-302022-09-3026348049910.14498/vsgtu1928Prediction of individual deformation characteristics of structural elements by a “leader” product
https://journals.eco-vector.com/1991-8615/article/view/111588
<p>We propose a numerical method for predicting the individual deformation characteristics of structural elements by a “leader” product. The basis of this method is generalized one-parameter models. These models relate the integral characteristics of the stress state to the integral characteristics of the deformation state in the “generalized load – generalized displacement” coordinates. The scope of the method is structural elements of the same type, which are under identical conditions of external loading and are characterized by a large spread of deformation characteristics (generalized displacement). It is assumed that the operation of one structural element (prototype) begins some time earlier than the others. A hypothesis on the similarity of all realizations reduced to a single origin by a time shift in the “generalized displacement – time” coordinates is introduced. Using statistical information on the initial sections of “lagging” structural elements and the sample prototype, the statistical characteristics of the similarity parameter of the operated structural element are determined in relation to the “leader” product, and then its deformation characteristics are predicted.</p> <p>In the paper, we investigate friction units and structural elements (rods, threaded connections) under creep conditions. Based on statistical correlation analysis of the experimental information, a verification of the similarity hypothesis usabilty for all implementations of the structural elements studied is carried out. The method was illustrated by an example of predicting the wear of the friction units of the front landing gear of the aircraft depending on the number of take-off and landing cycles. The method was also illustrated with an example of how to calculate the elongation of rods made of a polyvinylchloride compound under uniaxial loading and axial displacement of the screwing area of a threaded joint under creep conditions.</p> <p>The experimental data for the generalized displacement of specific implementations are shown to not exceed the calculated limits of the confidence interval for mathematical expectation for all structural elements considered in prediction time intervals of one to four “basic” intervals, within which estimates of random parameters for specific structural elements were determined.</p>Vladimir P. RadchenkoElena Afanaseva
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2022-09-302022-09-3026350051910.14498/vsgtu1919Mathematical modeling of the effect of spacers on mass transfer in electromembrane systems
https://journals.eco-vector.com/1991-8615/article/view/109482
<p>The transfer of ions near ion-exchange membranes causes concentration polarization, which significantly complicates mass transfer in electromembrane systems. Spacers are used to neutralize the effect of concentration polarization and increase mass transfer. Spacers reduce the thickness of the boundary layer by increasing the mixing depth of the solution and creating a normal component of convective transport; ions can reach membranes faster, and the current increases, from a hydrodynamic point of view. However, spacers significantly increase the hydrodynamic resistance and consequently the cost of pumping the solution.</p> <p>For the first time, the main regularities of the transfer of salt ions in the desalination channel of an electrodialysis apparatus with spacers of various shapes and arrangements are determined, taking into account electroconvection, in overlimiting current modes. Namely, it is shown, using the current-voltage characteristic, that spacers of different shapes and locations are optimal at different stages of the desalination process.</p> <p>The paper presents the results of mathematical and simulation modeling of the salt ion transport process in electromembrane systems with spacers in overlimiting current modes. 2D direct numerical simulation was carried out for the coupled system of the Nernst–Planck–Poisson and Navier–Stokes equations without fitting parameters. The finite element method was used in combination with the method of successive approximations and segregation to solve boundary value problems for systems of nonlinear differential equations with partial derivatives. The novelty of the method lies in the fact that after discretization in time, the problem on each time layer is split into hydrodynamic and electrochemical problems, each of which is solved by the method of successive approximations until a complete mutual agreement.</p>Anna V. KovalenkoAminat M. UzdenovaAnna OvsyannikovaMakhamet Kh. UrtenovRamazan A. Bostanov
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2022-09-302022-09-3026352054310.14498/vsgtu1944General principle of maximum pressure in stationary flows of inviscid gas
https://journals.eco-vector.com/1991-8615/article/view/109730
<p>Within the framework of the Euler equations, the possibility of achieving extreme pressure values at the inner point of a stationary flow of a nonviscous gas is considered. The flow can be non-barotropic. The well-known (G.B. Sizykh, 2018) subsonic principle of maximum pressure (SPMP) cannot be applied in transonic and supersonic flow regions. Under the conditions of the classical principle of maximum pressure by C. Truesdell (1953), there is no restriction on the values of local Mach numbers, but it has a number of features that do not allow it to be used to verify numerical calculations in the same way as it can be done when using SPMP in subsonic regions. A previously unknown principle of maximum pressure is discovered: a function of derivative flow parameters is found, which must have a certain sign (different for minimum and for maximum pressure) at the point where the pressure reaches a strict or nonstrict local extremum. This principle of maximum pressure is called “general” (GPMP) because its conditions do not include barotropicity, restrictions on the values of local Mach numbers, and the assumption that the gas obeys the Mendeleev–Clapeyron equation. One of the consequences of GPMP is the conclusion that the requirement of barotropicity can be excluded from the conditions of Truesdell's principle of maximum pressure. It is proposed to use GPMP to verify numerical calculations of the ideal gas flow behind a detached shock wave formed in a supersonic flow around bodies and to verify numerical calculations of a viscous gas flow around bodies in regions remote from sources of vorticity, where the effect of viscosity can be neglected.</p>Grigory B. Sizykh
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2022-09-302022-09-3026354455510.14498/vsgtu1946The hp-version of the least-squares collocation method with integral collocation for solving a biharmonic equation
https://journals.eco-vector.com/1991-8615/article/view/108886
<p>A new algorithm for the numerical solution of the biharmonic equation is developed. It is based on the first implemented hp-version of the least-squares collocation method (hp-LSCM) with integral collocations for a fourth-order elliptic equation in combination with modern methods of accelerating iterative processes for solving systems of linear algebraic equations (SLAE). The hp-LSCM provides the possibilities to refine the grid (h-version) and increase the degree of polynomials to the arbitrary order (p-approach). The convergence of approximate solutions obtained by the implemented version of the method is analyzed using an example of a numerical simulation of the bending of a hinged isotropic plate. The high accuracy and the increased order of convergence using polynomials up to the tenth order in the hp-LSCM are shown.</p> <p>The effectiveness of the combined application of algorithms for accelerating iterative processes to solve SLAE that are combined with LSCM is investigated. In this paper, we consider the application of the following algorithms: preconditioning of SLAE matrices; the iteration acceleration algorithm based on Krylov subspaces; the prolongation operation on a multigrid complex; parallelization using OpenMP; a modified algorithm for solving local SLAEs. The latter is implemented with iterations over subdomains (which are cells) and makes it possible to more effectively solve overdetermined SLAEs in the LSCM in the case of solving a linear differential equation. The form of the matrices does not change at each iteration. Only the elements of the vectors of their right parts corresponding to the matching conditions are modified. The calculation time on a personal computer is reduced by more than 350 times with the combined use of all acceleration techniques compared to the case when only preconditioning was used.</p>Vasily P. ShapeevLuka S. BryndinVasily A. Belyaev
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2022-09-302022-09-3026355657210.14498/vsgtu1936Probabilistic models for the analysis of inverse extremal problems in combinatorics
https://journals.eco-vector.com/1991-8615/article/view/108999
<p>In an inverse extremal problem for a combinatorial scheme with a given value of the objective function of the form of a certain extreme value of its characteristic, a probabilistic model is developed that ensures that this value is obtained in its outcomes. Two types of such characteristics are considered, relating to each of the schemes or to a set of outcomes.</p> <p>The pre-asymptotic analysis of such a model is carried out by the author's enumerative method. It is based on the construction of an iterative random process with iterations of successive stages of a numbered non-repetitive enumeration and the formation of outcomes of the scheme. The iterative development of the process is represented by a probabilistic graph.</p> <p>The study of the outcomes of the scheme according to the model in the enumerative method is carried out in the following areas: visual numbering of the outcomes of the scheme, finding their number, establishing a one-to-one correspondence between the types and numbers of outcomes of the scheme, obtaining their probabilistic distribution (controlled by a random process of listing the outcomes of the scheme), and modeling them with this distribution.</p> <p>Along with the direct study of circuits in these areas, algorithms are proposed to obtain results for them by partially recalculating them from the results of a similar analysis of more general, previously studied circuits without restrictions or with less restrictions on the values of the characteristics under consideration.</p>Nataliya Yu. Enatskaya
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2022-09-302022-09-3026357159110.14498/vsgtu1947On the theory of fourth-rank hemitropic tensors in three-dimensional Euclidean spaces
https://journals.eco-vector.com/1991-8615/article/view/111114
<p>The paper is devoted to problems concerning the tensors with constant components, hemitropic tensors and pseudotensors that are of interest from the point of view of micropolar continuum mechanics. The properties and coordinate representations of tensors and pseudotensors with constant components are discussed. Based on an unconventional definition of a hemitropic fourth-rank tensor, a coordinate representations in terms of Kronecker deltas and metric tensors are given. A comparison of an arbitrary hemitropic fourth-rank tensor and a tensor with constant components are discussed. The coordinate representations for constitutive tensors and pseudotensors used in mathematical modeling of linear hemitropic micropolar continuums are given in terms of the metric tensor.The covariant constancy of fourth-rank pseudotensors with constant components and hemitropic tensors is considered and discussed.</p>Eugenii V. MurashkinYuri N. Radayev
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2022-09-302022-09-3026359260210.14498/vsgtu1941