Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences

The Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences is the periodical scientific edition published by Samara State Technical University since 1996.

For a long time the journal was an edition where the new scientific results of Russian scientific schools had been published. Now the journal is focused on both Russian and foreign scientists, working in the priority research areas of Samara State Technical University because the main purpose of the journal is an open dissemination of scientific knowledge among Russian and foreign scientists.

Since 2011 the journal is a quarterly printed edition (four issues a year); issue size — 200 p.; language of articles — Russian, English. The journal is published in printed and electronic version.

The editorial board takes and estimates the manuscripts irrespective of race, gender, nationality, heritage, citizenship, occupation, employment, residence, political, philosophic, religious and any other views of the author.

The contributed article should be a completed scientific research. It shouldn't have been published, or be in process of publication in other editions.

The manuscript should contain novel scientific results in the priority research areas of Samara State Technical University, including “Differential Equations and Mathematical Physics”, “Mechanics of Solids”, “Mathematical Modeling, Numerical Methods and Software Systems”.

The journal is published at the expense of publisher. All materials are publishing free of charge, the author's fee is not provided. All materials of the electronic version are freely available.

The target audience of the journal are the scientists working in the following areas:

  • “Differential Equations and Mathematical Physics”,
  • “Deformable Solid Body Mechanics”,
  • “Mathematical Modeling, Numerical Methods and Software Systems”.

The journal is included in the Russian Science Citation Index database on the Web of Science platform. The journal is included in VINITI abstracts databases. The issue details are publishing in ULRICH’S Periodical Directory. The journal articles are indexed in Scholar.Google.com, zbMATH, СyberLeninka.ru, Math-Net.ru. The journal is integrated in CrossRef and FundRef search systems.

Current Issue

Vol 27, No 4 (2023)

Differential Equations and Mathematical Physics

Inverse problem for an equation of mixed parabolic-hyperbolic type with a characteristic line of change
Durdiev D.K.
Abstract

This study investigates direct and inverse problems for a model equation of mixed parabolic-hyperbolic type. In the direct problem, an analogue of the Tricomi problem is considered for this equation with a characteristic line of type change. The unknown in the inverse problem is a variable coefficient of the lower-order term in the parabolic equation. To determine it relative to the solution defined in the parabolic part of the domain, an integral overdetermination condition is specified. Local theorems of unique solvability of the posed problems in terms of classical solutions are proven.

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2023;27(4):607-620
pages 607-620 views
A modified Cauchy problem for an inhomogeneous equation of degenerate hyperbolic type of the second kind
Urinov A.K., Okboev A.B.
Abstract

In this article, a modified Cauchy problem was studied for an inhomogeneous equation of degenerate hyperbolic type of the second kind in a characteristic triangle. It is known that degenerate hyperbolic equations have the singularity that the well-posedness of the Cauchy problem with initial data on the line of parabolic degeneracy does not always hold for them. Therefore, in such cases, it is necessary to consider the problem with initial conditions in a modified form. In this paper, modified Cauchy problems with initial conditions were formulated on the line of parabolic degeneracy for an inhomogeneous equation of degenerate hyperbolic type of the second kind. The considered problem is reduced to a modified Cauchy problem for a homogeneous equation and to a Cauchy problem for an inhomogeneous equation with zero initial conditions. The solutions of the modified Cauchy problem for a homogeneous equation are obtained from the general solution of the considered equation, and the explicit solutions of the modified Cauchy problem with homogeneous conditions for the equation of an inhomogeneous equation are found using the Riemann method. It is proved that the found solutions do indeed satisfy the equation and the initial conditions. The article uses the Riemann method and data from the theory of special functions, particularly the Gauss hypergeometric function, the Euler gamma function, and the Pochhammer symbol.

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2023;27(4):621-644
pages 621-644 views

Mechanics of Solids

Numerical simulation of the interaction of a deformable gas permeable fragment of a granular layer with a shock wave in a three-dimensional formation
Glazova E.G., Kochetkov A.V., Lisitsyn A.A., Modin I.A.
Abstract

The numerical method developed by the authors earlier for solving threedimensional problems of dynamic interaction of deformable bodies and media in Eulerian variables based on the high-precision Godunov scheme is applied to solve problems of interaction of a deformable gas-permeable fragment of a granular layer with shock waves. The modeling is based on a unified modified Godunov’s numerical method both for calculating gas motion and for calculating the dynamic deformation of elastic-plastic elements of a permeable granular layer. The increase in accuracy is achieved by merging the domains of influence of the numerical and differential problems. It is assumed that the sandy granular layer consists of a set of identical spherical deformable quartz particles representing a cubic packing. The space between the particles is filled with compressible gas medium (air). A symmetrical packaging element is highlighted in the form of a sequence of spherical particles. To demonstrate the numerical methodology, it is assumed that a multilayer granular medium in the direction of propagation of a planar shock wave
consists of three layers of particles in a square-section channel with rigid walls. The study is conducted following the methodology with explicit identification of moving Lagrangian contact surfaces using multigrid algorithms. The results of numerical studies of the shock wave propagation process in a granular layer taking into account the movement of its deformable elements are presented. It is shown that for the given task parameters, the influence of deformation processes is insignificant. The shock wave passing through the
layer forms a gas dynamic flow close to one-dimensional behind the barrier. The agreement of the results of the numerical solution with known experimental results regarding the parameters of the shock wave passing through the layer indicates the adequacy of the applied mathematical and numerical models.

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2023;27(4):644-658
pages 644-658 views
Thermomechanical states of gyrotropic micropolar solids
Murashkin E.V., Radayev Y.N.
Abstract

The paper is devoted to problems of modeling heat conduction processes in micropolar elastic solids, all thermomechanical states of which may be sensible to mirror reflections of three-dimensional space. A new variant of the heat conduction theory is developed in terms of the heat fluxes treated as pseudovectors of algebraic weight \(+1\) making their similar to the pseudovector of spinor displacements known from previous discussions. Constitutive pseudoinvariants (at least some of them) have odd negative weights (for example, thermal conductivity coefficient and specific heat). Having choosing elements of volume and area as natural known from the classical field theory formulations and considered as pseudoinvariants of weight \(-1\), the variant of theory is proposed. An absolute contravariant vector represents translational displacements and a contravariant pseudovector of weight \(+1\) does spinor displacements. As a result, heat flux, force stress tensor, mass density and specific heat can be treated as pseudotensor quantities of odd weights. The Helmholtz free energy per unit natural volume element is used as the thermodynamic potential with the functional arguments: temperature, symmetrical parts and accompanying vectors of the linear asymmetric strain tensor and wryness pseudotensor. The principle of absolute invariance of absolute thermodynamic temperature is proposed and discussed. A nonlinear heat conduction equation is obtained and linearized.

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2023;27(4):659-678
pages 659-678 views
Method for determining the parameters of an electrical signal for controlling forced steady-state vibrations of electroviscoelastic bodies. Mathematical relations
Sevodina N.V., Iurlova N.A., Oshmarin D.A.
Abstract

This paper presents a method for determining the magnitude of the electric potential generated on the electrodated surface of a piezoelectric element, which is part of a piece-wise homogeneous electroviscoelastic structure, necessary for the formation of a control action when actively controlling its dynamic behavior in the mode of forced steady-state vibrations in order to minimize the amplitude of vibrations at the selected resonant frequency. By mathematical transformations of the equations describing the intrinsic and forced vibrations of such electroviscoelastic bodies, the relations expressing the relationship between the values of the displacement of the nodes and the electric potential on the electroded surface of the piezoelectric element are derived. These formulas allow us to determine the magnitude of the potential that must be applied to the piezoelectric element in order to best dampen a given vibration mode of the structure. As a result of numerical experiments obtained by using the ANSYS finite element analysis software package, and the usability of the results of solving the problem of natural vibrations to find the optimal value of the potential characterizing the control electrical action aimed at damping the specified modes in the mode of forced steadystate vibrations is confirmed. The effectiveness of the obtained analytical dependencies is demonstrated by the example of a cantilevered viscoelastic plate with a piezoelectric element located on its surface. The proposed approach makes it possible to significantly reduce time and resource costs of the mathematical modeling of active control of forced steady-state oscillations of electroviscoelastic bodies, to determine the requirements for the hardware implementation of actuators and controllers of the control unit of
such smart-systems.

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2023;27(4):679-703
pages 679-703 views
Modeling of nonlinear torsional vibrations of a truncated conical rod
Khudoynazarov K.K.
Abstract

In the present study, a nonlinear mathematical model of non-stationary torsional vibrations of a truncated conical rod made of elastic material taking into account the nonlinear relationship between stresses and strains has been developed. A nonlinear equation for torsional vibrations of the truncated conical rod has been derived with respect to the main part of the torsional displacement of the axis of symmetry of the rod. It has been demonstrated that the obtained equation for nonlinear torsional vibrations of the truncated conical elastic rod coincides with known equations obtained by other authors in particular cases. Using the derived equation, the stress-strain state of an arbitrary cross-section of the conical rod can be uniquely determined based on spatial coordinates and time. The problem of non-stationary torsional vibrations of the truncated conical rod under the action of axial and surface dynamic loads has been numerically due to the constructed model, when the wide end of the rod is rigidly fixed and the narrow end is free.

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2023;27(4):704-722
pages 704-722 views

Mathematical Modeling, Numerical Methods and Software Complexes

Mathematical modeling of sunspot nucleation at the photospheric level of the Sun
Romanov D.V., Romanov K.V., Romanov V.A., Stepanov E.A., Lebedev A.A.
Abstract

In the present study, the initial stage of the generation of a group of sunspots at the photospheric level of the Sun is studied by computer simulation. The development of the nonlinear phase of the Parker instability of large-scale oscillations of magnetic fields in the middle layers of the convective zone is numerically modeled. The process of adiabatic cooling of a thin magnetic tube that floats from depths of the order of 100,000 km to the
photospheric level is studied. The results of the calculations make it possible to analyze in detail the change in the magnetogasdynamic parameters of the tube at different depths of the convective zone, and to obtain the values of the physical parameters of emerging sunspots that can be compared with observational data.
The paper investigates the physical mechanism of the time delay in the formation of the head part of the active region compared with the formation of the sprayed tail part. The problem of stability of nascent active regions is also being investigated. The physical parameters determining the stability of the formed active regions at various phases of the solar activity cycle are highlighted. The physical mechanism of generation of a powerful shock wave flux in the initial stage of the nucleation of the active region, which makes a significant contribution to the abnormal heating of the solar atmosphere recorded in the observational data, has been determined.

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2023;27(4):723-736
pages 723-736 views

Short Communications

A new common fixed point theorem on orthogonal metric spaces and an application
Touail Y., Jaid A., El Moutawakil D.
Abstract

In the present work, a common fixed point result for self-mappings on orthogonal complete metric spaces, which are not necessarily complete, is proved. Furthermore, as an application, we find the existence of solutions to two differential equations.

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2023;27(4):737-744
pages 737-744 views
One way of summing multidimensional series
Sabitov K.B.
Abstract

It is known that in analysis courses, multiple series are considered only at a conceptual level, and their simplest properties are provided. Two widely used methods for summing multiple Fourier series are the spherical and rectangular methods. The present study is devoted to a new method of proving the convergence of multidimensional series by reducing them to a one-dimensional series, allowing applicating known statements for one-dimensional series to multidimensional ones. Examples of justifying the convergence of numerical and functional series are provided as an illustration of this summing method.

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2023;27(4):745-752
pages 745-752 views
Estimation of the probability of collision of heterogeneous particles of composite powders during the formation of coatings by detonation method
Ganigin S.Y., Grechukhina M.S., Nechaev A.S.
Abstract

The study presents the results of an assessment of the probability of collision of heterogeneous particles of composite materials when obtaining coatings by detonation on the cumulative lining of perforation systems used in the opening of oil and gas reservoirs. Due to the different properties of the initial metal powders used to produce coatings, the interaction of their particles with each other in the gas-thermal flow can lead to premature chemical reactions, which will lead to a deterioration in the strength properties of the resulting coating. Therefore, a preliminary calculation of the probability of collision of metal powder particles makes it possible to conclude about their quantitative characteristics before obtaining a coating, as well as the possible transition of interacting particles into intermetallic phases, which subsequently affect the adhesion characteristics of the coating.

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2023;27(4):753-764
pages 753-764 views

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