Pub Date : 2024-02-16DOI: 10.1134/s1990478923040154
S. N. Timergaliev
Abstract
We study the existence of solutions of a boundary value problem for a system of nonlinear second-order partial differential equations for the generalized displacements under given nonlinear boundary conditions that describes the equilibrium state of elastic nonshallow isotropic inhomogeneous shells of zero Gaussian curvature with free edges in the framework of the Timoshenko shear model. The research method is based on integral representations for generalized displacements containing arbitrary functions that allow the original boundary value problem to be reduced to a nonlinear operator equation for generalized displacements in the Sobolev space. The solvability of the operator equation is established using the contraction mapping principle.
{"title":"On the Existence of Solutions of Nonlinear Boundary Value Problems for Nonshallow Timoshenko-Type Shells with Free Edges","authors":"S. N. Timergaliev","doi":"10.1134/s1990478923040154","DOIUrl":"https://doi.org/10.1134/s1990478923040154","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study the existence of solutions of a boundary value problem for a system of nonlinear\u0000second-order partial differential equations for the generalized displacements under given nonlinear\u0000boundary conditions that describes the equilibrium state of elastic nonshallow isotropic\u0000inhomogeneous shells of zero Gaussian curvature with free edges in the framework of the\u0000Timoshenko shear model. The research method is based on integral representations for generalized\u0000displacements containing arbitrary functions that allow the original boundary value problem to be\u0000reduced to a nonlinear operator equation for generalized displacements in the Sobolev space. The\u0000solvability of the operator equation is established using the contraction mapping principle.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":0.58,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140882219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-16DOI: 10.1134/s1990478923040129
M. V. Neshchadim, A. A. Simonov
Abstract
We study the system of equations obtained on the basis of the relativistic Schrödinger equation and relating the potential, amplitude, and phase functions. Using the methods of the theory of consistency of systems of partial differential equations, we obtain completely integrable systems that relate only two functions of the above three. The systems found are related by Bäcklund transformations.
{"title":"Bäcklund Transformations of the Relativistic Schrödinger Equation","authors":"M. V. Neshchadim, A. A. Simonov","doi":"10.1134/s1990478923040129","DOIUrl":"https://doi.org/10.1134/s1990478923040129","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study the system of equations obtained on the basis of the relativistic\u0000Schrödinger equation and relating the potential, amplitude, and phase functions. Using\u0000the methods of the theory of consistency of systems of partial differential equations, we obtain\u0000completely integrable systems that relate only two functions of the above three. The systems\u0000found are related by Bäcklund transformations.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":0.58,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-16DOI: 10.1134/s1990478923040191
P. M. Nguyen, T. T. Le, L. H. Nguyen, M. V. Klibanov
Abstract
Our objective is to calculate the derivatives of data corrupted by noise. This is a challenging task as even small amounts of noise can result in significant errors in the computation. This is mainly due to the randomness of the noise, which can result in high-frequency fluctuations. To overcome this challenge, we suggest an approach that involves approximating the data by eliminating high-frequency terms from the Fourier expansion of the given data with respect to the polynomial-exponential basis. This truncation method helps to regularize the issue, while the use of the polynomial-exponential basis ensures accuracy in the computation. We demonstrate the effectiveness of our approach through numerical examples in one and two dimensions.
{"title":"Numerical Differentiation by the Polynomial-Exponential Basis","authors":"P. M. Nguyen, T. T. Le, L. H. Nguyen, M. V. Klibanov","doi":"10.1134/s1990478923040191","DOIUrl":"https://doi.org/10.1134/s1990478923040191","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Our objective is to calculate the derivatives of data corrupted by noise. This is\u0000a challenging task as even small amounts of noise can result in significant errors in the\u0000computation. This is mainly due to the randomness of the noise, which can result in\u0000high-frequency fluctuations. To overcome this challenge, we suggest an approach that involves\u0000approximating the data by eliminating high-frequency terms from the Fourier expansion of the\u0000given data with respect to the polynomial-exponential basis. This truncation method helps to\u0000regularize the issue, while the use of the polynomial-exponential basis ensures accuracy in the\u0000computation. We demonstrate the effectiveness of our approach through numerical examples in\u0000one and two dimensions.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":0.58,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140882148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-16DOI: 10.1134/s1990478923040117
A. Yu. Morozov, D. L. Reviznikov
Abstract
The paper deals with the numerical solution of fractional differential equations with interval parameters in terms of derivatives describing anomalous diffusion processes. Computational algorithms for solving initial–boundary value problems as well as the corresponding inverse problems for equations containing interval fractional derivatives with respect to time and space are presented. The algorithms are based on the previously developed and theoretically substantiated adaptive interpolation algorithm tested on a number of applied problems for modeling dynamical systems with interval parameters; this makes it possible to explicitly obtain parametric sets of states of dynamical systems. The efficiency and workability of the proposed algorithms are demonstrated in several problems.
{"title":"Algorithms for the Numerical Solution of Fractional Differential Equations with Interval Parameters","authors":"A. Yu. Morozov, D. L. Reviznikov","doi":"10.1134/s1990478923040117","DOIUrl":"https://doi.org/10.1134/s1990478923040117","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The paper deals with the numerical solution of fractional differential equations with\u0000interval parameters in terms of derivatives describing anomalous diffusion processes.\u0000Computational algorithms for solving initial–boundary value problems as well as the\u0000corresponding inverse problems for equations containing interval fractional derivatives with\u0000respect to time and space are presented. The algorithms are based on the previously developed\u0000and theoretically substantiated adaptive interpolation algorithm tested on a number of applied\u0000problems for modeling dynamical systems with interval parameters; this makes it possible to\u0000explicitly obtain parametric sets of states of dynamical systems. The efficiency and workability of\u0000the proposed algorithms are demonstrated in several problems.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":0.58,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-16DOI: 10.1134/s1990478923040142
V. P. Tanana, B. A. Markov
Abstract
The paper studies the problem of determining the error introduced by inaccuracy in determining the thickness of a protective heat-resistant coating of composite materials. The mathematical problem is the heat equation on an inhomogeneous half-line. The temperature on the outer side of the half-line ( ( x=0 )) is considered unknown over an infinite time interval. To find it, the temperature is measured at the interface of the media at the point ( x=x_0 ). An analytical study of the direct problem is carried out and enables a rigorous statement of the inverse problem and determining the functional spaces in which it is natural to solve the inverse problem. The main difficulty that the present paper aims at solving is obtaining an estimate for the error of the approximate solution. To estimate the conditional correctness modulus, the projection regularization method is used; this allows obtaining order-accurate estimates.
{"title":"On the Error in Determining the Protective Layer Boundary in the Inverse Heat Problem","authors":"V. P. Tanana, B. A. Markov","doi":"10.1134/s1990478923040142","DOIUrl":"https://doi.org/10.1134/s1990478923040142","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The paper studies the problem of determining the error introduced by inaccuracy in\u0000determining the thickness of a protective heat-resistant coating of composite materials. The\u0000mathematical problem is the heat equation on an inhomogeneous half-line. The temperature on\u0000the outer side of the half-line (\u0000<span>( x=0 )</span>) is considered unknown over an infinite time interval. To find it, the\u0000temperature is measured at the interface of the media at the point\u0000<span>( x=x_0 )</span>. An analytical study of the direct problem is carried out and enables a\u0000rigorous statement of the inverse problem and determining the functional spaces in which it is\u0000natural to solve the inverse problem. The main difficulty that the present paper aims at solving is\u0000obtaining an estimate for the error of the approximate solution. To estimate the conditional\u0000correctness modulus, the projection regularization method is used; this allows obtaining\u0000order-accurate estimates.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":0.58,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-16DOI: 10.1134/s199047892304004x
M. P. Galanin, V. V. Lukin, A. S. Rodin
Abstract
The Temetos platform is designed to conduct computational experiments at all stages of analysis and study of continuum mechanics models. A module has been developed to study the stress–strain state of a system of bodies with allowance for inelastic strains and contact interaction. It was used to analyze a fuel element that included up to 100 fuel pellets and a shell. The platform’s solvers are applied to astrophysics problems. Models of the formation of accretion disks in binary star systems that allow the interpretation of observation results are constructed.
{"title":"Temetos Software Platform and Its Applications in Problems of Continuum Mechanics","authors":"M. P. Galanin, V. V. Lukin, A. S. Rodin","doi":"10.1134/s199047892304004x","DOIUrl":"https://doi.org/10.1134/s199047892304004x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The Temetos platform is designed to conduct computational experiments at all stages of\u0000analysis and study of continuum mechanics models. A module has been developed to study the\u0000stress–strain state of a system of bodies with allowance for inelastic strains and contact\u0000interaction. It was used to analyze a fuel element that included up to 100 fuel pellets and a shell.\u0000The platform’s solvers are applied to astrophysics problems. Models of the formation of accretion\u0000disks in binary star systems that allow the interpretation of observation results are constructed.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":0.58,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-16DOI: 10.1134/s1990478923040087
E. S. Malygina, A. V. Kutsenko, S. A. Novoselov, N. S. Kolesnikov, A. O. Bakharev, I. S. Khilchuk, A. S. Shaporenko, N. N. Tokareva
Abstract
The paper provides an overview of the main approaches to the construction of post-quantum cryptographic systems that are currently used. The area of lattice-based cryptography is analyzed in detail. We give the description and characterization of some known lattice-based cryptosystems whose resilience is based on the complexity of the shortest vector problem, learning with errors problem, and their variations. The main approaches to solving the problems from lattice theory, on which attacks on the corresponding cryptosystems are based, are analyzed. In particular, some known theoretical estimates of time and memory complexity of lattice basis reduction and lattice sieving algorithms are presented.
{"title":"Post-Quantum Cryptosystems: Open Problems and Solutions. Lattice-Based Cryptosystems","authors":"E. S. Malygina, A. V. Kutsenko, S. A. Novoselov, N. S. Kolesnikov, A. O. Bakharev, I. S. Khilchuk, A. S. Shaporenko, N. N. Tokareva","doi":"10.1134/s1990478923040087","DOIUrl":"https://doi.org/10.1134/s1990478923040087","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The paper provides an overview of the main approaches to the construction of\u0000post-quantum cryptographic systems that are currently used. The area of lattice-based\u0000cryptography is analyzed in detail. We give the description and characterization of some known\u0000lattice-based cryptosystems whose resilience is based on the complexity of the shortest vector\u0000problem, learning with errors problem, and their variations. The main approaches to solving the\u0000problems from lattice theory, on which attacks on the corresponding cryptosystems are based, are\u0000analyzed. In particular, some known theoretical estimates of time and memory complexity of\u0000lattice basis reduction and lattice sieving algorithms are presented.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":0.58,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881790","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-16DOI: 10.1134/s1990478923040051
I. M. Kulikov
Abstract
The Rusanov solver for solving hydrodynamic equations is one of the most robust schemes in the class of Riemann solvers. For special relativistic hydrodynamics, the robustness condition of the scheme is the most important property, especially for sufficiently high values of the Lorentz factor. At the same time, the Rusanov solver is known to be very dissipative. It is proposed to use a piecewise parabolic representation of physical variables to reduce the dissipation of the Rusanov scheme. Using this approach has made it possible to obtain a scheme with the same dissipative properties as Roe-type schemes and the family of Harten–Lax–van Leer schemes. Using the problem of the decay of a relativistic hydrodynamic discontinuity, it is shown that the present author’s version of the Rusanov scheme is advantageous in terms of reproducing a contact discontinuity. The scheme is verified on classical problems of discontinuity decay and on the problem of the interaction of two relativistic jets in the three-dimensional formulation.
{"title":"Using Piecewise Parabolic Reconstruction of Physical Variables in the Rusanov Solver. I. The Special Relativistic Hydrodynamics Equations","authors":"I. M. Kulikov","doi":"10.1134/s1990478923040051","DOIUrl":"https://doi.org/10.1134/s1990478923040051","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The Rusanov solver for solving hydrodynamic equations is one of the most robust schemes\u0000in the class of Riemann solvers. For special relativistic hydrodynamics, the robustness condition of\u0000the scheme is the most important property, especially for sufficiently high values of the Lorentz\u0000factor. At the same time, the Rusanov solver is known to be very dissipative. It is proposed to use\u0000a piecewise parabolic representation of physical variables to reduce the dissipation of the Rusanov\u0000scheme. Using this approach has made it possible to obtain a scheme with the same dissipative\u0000properties as Roe-type schemes and the family of Harten–Lax–van Leer schemes. Using the\u0000problem of the decay of a relativistic hydrodynamic discontinuity, it is shown that the present\u0000author’s version of the Rusanov scheme is advantageous in terms of reproducing a contact\u0000discontinuity. The scheme is verified on classical problems of discontinuity decay and on the\u0000problem of the interaction of two relativistic jets in the three-dimensional formulation.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":0.58,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-16DOI: 10.1134/s1990478923040208
Y. Joundy, H. Rouah, A. Taik
Abstract
In this work, we study the influence of orientation on the stability conditions of the reaction front where the monomer is solid and the polymer is liquid. The mathematical model includes the heat equation, the concentration equation and the Navier–Stokes equation under the Boussinesq approximation. We use the method proposed by Zeldovich and Frank-Kamenetskii to perform asymptotic analysis. We then perform a stability analysis. The linearized problem is solved numerically using a multiquadric radial basis function method (MQ-RBF) to find the stability boundary. This will allow us to deduce the influence of each control parameter of the problem on this stability, in particular the angle of inclination of the experimental tube.
{"title":"Multiquadric RBF Method and Asymptotic Analysis to Study the Influence of Orientation on the Reaction Fronts Propagation","authors":"Y. Joundy, H. Rouah, A. Taik","doi":"10.1134/s1990478923040208","DOIUrl":"https://doi.org/10.1134/s1990478923040208","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> In this work, we study the influence of orientation on the stability conditions of the\u0000reaction front where the monomer is solid and the polymer is liquid. The mathematical model\u0000includes the heat equation, the concentration equation and the Navier–Stokes equation under the\u0000Boussinesq approximation. We use the method proposed by Zeldovich and Frank-Kamenetskii to\u0000perform asymptotic analysis. We then perform a stability analysis. The linearized problem is\u0000solved numerically using a multiquadric radial basis function method (MQ-RBF) to find the\u0000stability boundary. This will allow us to deduce the influence of each control parameter of the\u0000problem on this stability, in particular the angle of inclination of the experimental tube.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":0.58,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-16DOI: 10.1134/s1990478923040166
S. A. Vasyutkin, A. P. Chupakhin
Abstract
We consider the Navier–Stokes equations for the plane steady motion of a viscous incompressible fluid in an orthogonal coordinate system in which the fluid streamlines coincide with the coordinate lines of one of the families of the orthogonal coordinate system. In this coordinate system, the velocity vector has only the tangential component and the system of three Navier–Stokes equations is an overdetermined system for two functions—the tangential component of velocity and pressure. In the present paper, the system is brought to involution, and the consistency conditions are obtained, which are the equations for the curl of the velocity in this coordinate system. The coefficients of these equations include the curvatures of the coordinate lines and their derivatives up to the second order. The equations obtained are significantly more complicated than the curl equations in a channel of simple geometry.
{"title":"Curl Equation in Viscous Hydrodynamics in a Channel of Complex Geometry","authors":"S. A. Vasyutkin, A. P. Chupakhin","doi":"10.1134/s1990478923040166","DOIUrl":"https://doi.org/10.1134/s1990478923040166","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider the Navier–Stokes equations for the plane steady motion of a viscous\u0000incompressible fluid in an orthogonal coordinate system in which the fluid streamlines coincide\u0000with the coordinate lines of one of the families of the orthogonal coordinate system. In this\u0000coordinate system, the velocity vector has only the tangential component and the system of three\u0000Navier–Stokes equations is an overdetermined system for two functions—the tangential\u0000component of velocity and pressure. In the present paper, the system is brought to involution, and\u0000the consistency conditions are obtained, which are the equations for the curl of the velocity in this\u0000coordinate system. The coefficients of these equations include the curvatures of the coordinate\u0000lines and their derivatives up to the second order. The equations obtained are significantly more\u0000complicated than the curl equations in a channel of simple geometry.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":0.58,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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