Pub Date : 2021-01-01DOI: 10.26907/2541-7746.2021.1.59-76
I. Nasyrov, D. Kogogin, A. Shindin, S. Grach, R. Zagretdinov, A. Beletsky, V. Emeljanov
The method of plotting a spatial distribution pattern of the total electron content (TEC) in the region of artificial airglow of the ionosphere in the red line of the optical spectrum ( λ = = 630 nm) was developed during the experiments on disturbances of the ionosphere by powerful radio emission of the SURA facility. To test the method, a measurement session on August 29, 2016 from 18:40 to 20:10 UTC, i.e., when the ionospheric and weather conditions varied slightly and allowed simultaneous optical measurements of the artificial airglow of the ionosphere from two spatially separated sites (Vasilsursk near the SURA facility and Magnitka lying ∼ 170 km East of the SURA facility), was selected. As a result of the simultaneous optical measurements, the area of artificial airglow was plotted in a three-dimensional projection and the spatial position of the disturbed region of the ionosphere stimulated by the powerful radio emission of the SURA facility was determined. The method of plotting a spatial pattern of the electron density distribution in the disturbed region of the ionosphere is based on a joint analysis of variations in the TEC on the radio paths “navigation satellite – ground receiving site” for a number of receiving stations of the global navigation satellite systems located within a radius of ∼ 160 km from the SURA facility. By using this method, the values of electron density variations for different spatial cross-sections of the disturbed region of the ionosphere can be obtained. The joint analysis of the experimental data carried out with the help of the method under consideration showed that in the field of the powerful radio wave a disturbed region with the complex structure formed along the magnetic field lines. Plasma inhomogeneities with an increased electron density occurred at the boundaries of the region with a reduced electron concentration. The difference ∆ N e /N e at the boundaries of the disturbed region, i.e., between the regions with increased and decreased electron density, might reach 10%. The size of the disturbed region is l ⊥ ≈ 45 ÷ 60 km across and l (cid:107) (cid:38) 70 km along the Earth’s magnetic field lines.
{"title":"The Method of Plotting a Spatial Distribution Pattern of the Total Electron Content in the Region of Artificial Airglow of the Ionosphere","authors":"I. Nasyrov, D. Kogogin, A. Shindin, S. Grach, R. Zagretdinov, A. Beletsky, V. Emeljanov","doi":"10.26907/2541-7746.2021.1.59-76","DOIUrl":"https://doi.org/10.26907/2541-7746.2021.1.59-76","url":null,"abstract":"The method of plotting a spatial distribution pattern of the total electron content (TEC) in the region of artificial airglow of the ionosphere in the red line of the optical spectrum ( λ = = 630 nm) was developed during the experiments on disturbances of the ionosphere by powerful radio emission of the SURA facility. To test the method, a measurement session on August 29, 2016 from 18:40 to 20:10 UTC, i.e., when the ionospheric and weather conditions varied slightly and allowed simultaneous optical measurements of the artificial airglow of the ionosphere from two spatially separated sites (Vasilsursk near the SURA facility and Magnitka lying ∼ 170 km East of the SURA facility), was selected. As a result of the simultaneous optical measurements, the area of artificial airglow was plotted in a three-dimensional projection and the spatial position of the disturbed region of the ionosphere stimulated by the powerful radio emission of the SURA facility was determined. The method of plotting a spatial pattern of the electron density distribution in the disturbed region of the ionosphere is based on a joint analysis of variations in the TEC on the radio paths “navigation satellite – ground receiving site” for a number of receiving stations of the global navigation satellite systems located within a radius of ∼ 160 km from the SURA facility. By using this method, the values of electron density variations for different spatial cross-sections of the disturbed region of the ionosphere can be obtained. The joint analysis of the experimental data carried out with the help of the method under consideration showed that in the field of the powerful radio wave a disturbed region with the complex structure formed along the magnetic field lines. Plasma inhomogeneities with an increased electron density occurred at the boundaries of the region with a reduced electron concentration. The difference ∆ N e /N e at the boundaries of the disturbed region, i.e., between the regions with increased and decreased electron density, might reach 10%. The size of the disturbed region is l ⊥ ≈ 45 ÷ 60 km across and l (cid:107) (cid:38) 70 km along the Earth’s magnetic field lines.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"27 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81736077","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 : 2021-01-01DOI: 10.26907/2541-7746.2021.1.21-30
E. V. Timoshchenko, V. A. Yurevich
Taking into account the foundations of the generalized two-level scheme, an analytical solution to the problem of the evolution of superradiance in a quasi-two-dimensional supercrystal formed by quantum dots is obtained under homogeneous lasing field assumption in the resonant medium of the quasicrystal. The calculation was performed for the physical parameters of a semiconductor structure with quantum-well effects in the presence of resonant nonlinearity and intraband relaxation. We use the generalized two-level scheme, which allows us to take into account the self-modulating spectral broadening of the light field due to the absorption of radiation in quasi-resonant transitions in the quantum mechanical material equations, which are solved together with the field coupling equations. A relation is formulated that is analo-gous to the law of conservation of the polar angle of the Bloch vector for the more general case of interaction under consideration, in which, along with the phase nonlinearity of the response, the spread rate of active dipoles within the spectral line width is taken into account (i.e., the finiteness of the phase relaxation time of elementary emitters). The use of the Bloch vector formalism in this case makes it possible to obtain an analytical solution of the original modification of the nonlinear system of equations for the semiconductor supercrystals response variables and to calculate the shape of the superradiance pulses. The calculations predict the pronounced asymmetry of the pulses emitted by the semiconductor supercrystals. The calculated estimates of the time dynamics of the superradiance process, taking into account the nonlinearities typical for the resonant response, can be used in the development of methods for obtaining and profiling optical pulses in the sub-picosecond range of durations in modern compact nanophotonics devices.
{"title":"On Solving the Problem of Quasi-Two-Dimensional Supercrystal Nonlinear Resonance Response","authors":"E. V. Timoshchenko, V. A. Yurevich","doi":"10.26907/2541-7746.2021.1.21-30","DOIUrl":"https://doi.org/10.26907/2541-7746.2021.1.21-30","url":null,"abstract":"Taking into account the foundations of the generalized two-level scheme, an analytical solution to the problem of the evolution of superradiance in a quasi-two-dimensional supercrystal formed by quantum dots is obtained under homogeneous lasing field assumption in the resonant medium of the quasicrystal. The calculation was performed for the physical parameters of a semiconductor structure with quantum-well effects in the presence of resonant nonlinearity and intraband relaxation. We use the generalized two-level scheme, which allows us to take into account the self-modulating spectral broadening of the light field due to the absorption of radiation in quasi-resonant transitions in the quantum mechanical material equations, which are solved together with the field coupling equations. A relation is formulated that is analo-gous to the law of conservation of the polar angle of the Bloch vector for the more general case of interaction under consideration, in which, along with the phase nonlinearity of the response, the spread rate of active dipoles within the spectral line width is taken into account (i.e., the finiteness of the phase relaxation time of elementary emitters). The use of the Bloch vector formalism in this case makes it possible to obtain an analytical solution of the original modification of the nonlinear system of equations for the semiconductor supercrystals response variables and to calculate the shape of the superradiance pulses. The calculations predict the pronounced asymmetry of the pulses emitted by the semiconductor supercrystals. The calculated estimates of the time dynamics of the superradiance process, taking into account the nonlinearities typical for the resonant response, can be used in the development of methods for obtaining and profiling optical pulses in the sub-picosecond range of durations in modern compact nanophotonics devices.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"111 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85688190","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 : 2021-01-01DOI: 10.26907/2541-7746.2021.1.77-89
R. Latypov, E. Stolov
{"title":"A New DCT Filters-Based Method to Improve the Resistance of Ternary Watermarks in Audio Files Against Attacks","authors":"R. Latypov, E. Stolov","doi":"10.26907/2541-7746.2021.1.77-89","DOIUrl":"https://doi.org/10.26907/2541-7746.2021.1.77-89","url":null,"abstract":"","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"29 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77049409","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 : 2021-01-01DOI: 10.26907/2541-7746.2021.3-4.291-303
V. I. Pan’zhenskii, A. O. Rastrepina
In this article, we propose a group model G of a real extension of the Lobachevsky plane H 2 × R . The group G is a Lie group of special-form matrices and a subgroup of the gene-ral linear group GL (3 , R ). It is proved that, on the group model of the real extension of the Lobachevsky plane, there is a unique left-invariant almost contact metric structure with the Riemannian metric of the direct product that is invariant with respect to the isometry group. The concept of a linear connection compatible with the distribution is introduced. All left-invariant linear connections for which the tensors of the almost contact metric structure ( η, ξ, ϕ, g ) are covariantly constant are found. Among the left-invariant differential 1-forms, a canonical form defining a contact structure on G is distinguished. The left-invariant contact metric connections are found. There is a unique left-invariant connection for which all tensors of the almost contact metric structure and the canonical contact form are covariantly constant. It is proved that this connection is compatible with the contact distribution in the sense that a single geodesic tangent to the contact distribution passes through each point in each contact direction. Parametric equations of geodesics of the given connection are found. It is also established that the Levi-Civita connection of the Riemannian metric of the direct product is not a connection compatible with the contact distribution.
{"title":"Contact and Almost Contact Structures on the Real Extension of the Lobachevsky Plane","authors":"V. I. Pan’zhenskii, A. O. Rastrepina","doi":"10.26907/2541-7746.2021.3-4.291-303","DOIUrl":"https://doi.org/10.26907/2541-7746.2021.3-4.291-303","url":null,"abstract":"In this article, we propose a group model G of a real extension of the Lobachevsky plane H 2 × R . The group G is a Lie group of special-form matrices and a subgroup of the gene-ral linear group GL (3 , R ). It is proved that, on the group model of the real extension of the Lobachevsky plane, there is a unique left-invariant almost contact metric structure with the Riemannian metric of the direct product that is invariant with respect to the isometry group. The concept of a linear connection compatible with the distribution is introduced. All left-invariant linear connections for which the tensors of the almost contact metric structure ( η, ξ, ϕ, g ) are covariantly constant are found. Among the left-invariant differential 1-forms, a canonical form defining a contact structure on G is distinguished. The left-invariant contact metric connections are found. There is a unique left-invariant connection for which all tensors of the almost contact metric structure and the canonical contact form are covariantly constant. It is proved that this connection is compatible with the contact distribution in the sense that a single geodesic tangent to the contact distribution passes through each point in each contact direction. Parametric equations of geodesics of the given connection are found. It is also established that the Levi-Civita connection of the Riemannian metric of the direct product is not a connection compatible with the contact distribution.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"84 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89888704","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 : 2021-01-01DOI: 10.26907/2541-7746.2021.3-4.250-260
V. L. Gnedenkova, M. Pavlova, E. Rung
This work is devoted to the study of the convergence of an implicit difference scheme for a one-dimensional initial-boundary problem that simulates the process of filtration consolidation with a limiting gradient. From a mathematical point of view, this model is a system of partial differential equations for the displacements of an elastic medium and fluid pressure. In addition, the equation for pressure is degenerate, with nonlinearity in the spatial operator, which generates a non-smooth solution. In this regard, the study of the convergence was carried out under minimal conditions on the smoothness of the initial data. It was based on obtai-ning a number of a priori estimates that allow, using the monotonicity method, to establish the convergence of piecewise constant completions of the difference solution to a generalized solution of the problem. The spatial operator was approximated using the method of summation identities.
{"title":"Convergence of an Implicit Difference Scheme for the Problem of Saturated Filtration Consolidation with a Limiting Gradient","authors":"V. L. Gnedenkova, M. Pavlova, E. Rung","doi":"10.26907/2541-7746.2021.3-4.250-260","DOIUrl":"https://doi.org/10.26907/2541-7746.2021.3-4.250-260","url":null,"abstract":"This work is devoted to the study of the convergence of an implicit difference scheme for a one-dimensional initial-boundary problem that simulates the process of filtration consolidation with a limiting gradient. From a mathematical point of view, this model is a system of partial differential equations for the displacements of an elastic medium and fluid pressure. In addition, the equation for pressure is degenerate, with nonlinearity in the spatial operator, which generates a non-smooth solution. In this regard, the study of the convergence was carried out under minimal conditions on the smoothness of the initial data. It was based on obtai-ning a number of a priori estimates that allow, using the monotonicity method, to establish the convergence of piecewise constant completions of the difference solution to a generalized solution of the problem. The spatial operator was approximated using the method of summation identities.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"169 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83675718","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 : 2021-01-01DOI: 10.26907/2541-7746.2021.2.117-127
T. Guseva
Some results of the numerical study of the impact of a cylindrical water jet (150–350 m/s) with the hemispherical head on a solid flat wall covered with a thin layer of water are presented. The numerical approach is based on the CIP-CUP method. The comparison is performed for the shock wave patterns, the zones with tensile stresses, and the wall load for a very thin layer (when the level of wall load and the load distribution are close to the jet impact on a dry wall) and for a relatively thick layer (when the load level decreases by more than 2 times and the load distribution is almost uniform). The tensile stress level indicates secondary cavitation. With an increase in the layer thickness, the size of the zone with tensile stresses increases and the stress level relatively slightly decreases. The effect of the jet velocity on the characteristics of the load and on the time dependencies of the maximum and average pressures for different layer thicknesses is considered in more detail. It is found that an increase in the jet velocity causes no significant change in the character of the wall load distribution, the change in the load level can be approximately estimated by the corresponding change in the water hammer pressure, and the size of the area with the maximum pressure increases. The maximum average pressure on the dry wall depending on the jet velocity is obtained, and it is well approximated by the water hammer pressure. With an increase in the layer thickness, the maximum average pressure on the wetted wall decreases from the water hammer pressure (which can be treated as a one-dimensional estimate in this case) the more, the lower the jet velocity. Thus, the influence of non-one-dimensional effects, which determines the damping effect of the layer, increases with a decrease in the jet velocity. Many thanks to Professor A.A. Aganin for helpful feedback on this study.
{"title":"Impact of a Liquid Jet on a Wetted Wall","authors":"T. Guseva","doi":"10.26907/2541-7746.2021.2.117-127","DOIUrl":"https://doi.org/10.26907/2541-7746.2021.2.117-127","url":null,"abstract":"Some results of the numerical study of the impact of a cylindrical water jet (150–350 m/s) with the hemispherical head on a solid flat wall covered with a thin layer of water are presented. The numerical approach is based on the CIP-CUP method. The comparison is performed for the shock wave patterns, the zones with tensile stresses, and the wall load for a very thin layer (when the level of wall load and the load distribution are close to the jet impact on a dry wall) and for a relatively thick layer (when the load level decreases by more than 2 times and the load distribution is almost uniform). The tensile stress level indicates secondary cavitation. With an increase in the layer thickness, the size of the zone with tensile stresses increases and the stress level relatively slightly decreases. The effect of the jet velocity on the characteristics of the load and on the time dependencies of the maximum and average pressures for different layer thicknesses is considered in more detail. It is found that an increase in the jet velocity causes no significant change in the character of the wall load distribution, the change in the load level can be approximately estimated by the corresponding change in the water hammer pressure, and the size of the area with the maximum pressure increases. The maximum average pressure on the dry wall depending on the jet velocity is obtained, and it is well approximated by the water hammer pressure. With an increase in the layer thickness, the maximum average pressure on the wetted wall decreases from the water hammer pressure (which can be treated as a one-dimensional estimate in this case) the more, the lower the jet velocity. Thus, the influence of non-one-dimensional effects, which determines the damping effect of the layer, increases with a decrease in the jet velocity. Many thanks to Professor A.A. Aganin for helpful feedback on this study.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"16 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78601655","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 : 2021-01-01DOI: 10.26907/2541-7746.2021.3-4.261-275
N. Zadorin
The article gives an estimate of the error of the classical formulas for the numerical diffe-rentiation of a function of one variable with large gradients in the exponential boundary layer. It is assumed that the function is decomposed in the form of the sum of the regular and singular components, which is valid for the solution of a boundary value problem for the ordinary second-order differential equation with a small parameter ε affecting the highest derivative. It is known that the application of the classical polynomial formulas of numerical differentiation to such a function in the case of a uniform mesh can lead to unacceptable errors. The article estimates the error of the formulas for numerical differentiation on the Bakhvalov mesh, which is condensed in the boundary layer region. Bakhvalov’s mesh is widely used to construct uniformly converging difference schemes; therefore, the error estimation of the numerical dif-ferentiation formulas on this mesh is of interest. The estimates of the error on the Bakhvalov mesh are obtained taking into account the uniformity in the small parameter for the classical difference formulas widely used to calculate the first, second, and third derivatives. The re-sults of numerical experiments are presented, which agree with the obtained error estimates. A numerical comparison of the obtained errors on the Bakhvalov and Shishkin meshes and on a uniform mesh is carried out.
{"title":"Analysis of Formulas for Numerical Differentiation of Functions with Large Gradients on a Bakhvalov Mesh","authors":"N. Zadorin","doi":"10.26907/2541-7746.2021.3-4.261-275","DOIUrl":"https://doi.org/10.26907/2541-7746.2021.3-4.261-275","url":null,"abstract":"The article gives an estimate of the error of the classical formulas for the numerical diffe-rentiation of a function of one variable with large gradients in the exponential boundary layer. It is assumed that the function is decomposed in the form of the sum of the regular and singular components, which is valid for the solution of a boundary value problem for the ordinary second-order differential equation with a small parameter ε affecting the highest derivative. It is known that the application of the classical polynomial formulas of numerical differentiation to such a function in the case of a uniform mesh can lead to unacceptable errors. The article estimates the error of the formulas for numerical differentiation on the Bakhvalov mesh, which is condensed in the boundary layer region. Bakhvalov’s mesh is widely used to construct uniformly converging difference schemes; therefore, the error estimation of the numerical dif-ferentiation formulas on this mesh is of interest. The estimates of the error on the Bakhvalov mesh are obtained taking into account the uniformity in the small parameter for the classical difference formulas widely used to calculate the first, second, and third derivatives. The re-sults of numerical experiments are presented, which agree with the obtained error estimates. A numerical comparison of the obtained errors on the Bakhvalov and Shishkin meshes and on a uniform mesh is carried out.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"18 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89301023","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 : 2021-01-01DOI: 10.26907/2541-7746.2021.2.167-180
A. Begun, L. V. Kovtanyuk
This paper is devoted to the study of deformation of a disk rotating with variable velocity (acceleration, deceleration, rotation at a constant rate) under consecutive accumulation of irreversible creep and plastic flow strains. The deformation processes of a hollow disk and a disk with an inclusion are studied. Under the assumption of a plane stress state within the framework of the flow theory, solutions of differential equations are obtained for calculating the fields of stresses, deformations, displacements, and velocities using finite difference schemes. In the case of an axisymmetric problem, the solution is obtained using the finite element method. The laws of viscoplastic flow area development are investigated. In a sufficiently thick disk, the radius of the elastoplastic boundary changes significantly along the thickness of the disk. The obtained solution is compared with the case of ideal elastoplasticity. Taking into account the viscosity leads to a deceleration of the flow. It is shown that the presence of angular acceleration during fast overclocking significantly affects the distribution of stress intensities.
{"title":"Irreversible Deformation of a Rotating Disc under Plasticity and Creep","authors":"A. Begun, L. V. Kovtanyuk","doi":"10.26907/2541-7746.2021.2.167-180","DOIUrl":"https://doi.org/10.26907/2541-7746.2021.2.167-180","url":null,"abstract":"This paper is devoted to the study of deformation of a disk rotating with variable velocity (acceleration, deceleration, rotation at a constant rate) under consecutive accumulation of irreversible creep and plastic flow strains. The deformation processes of a hollow disk and a disk with an inclusion are studied. Under the assumption of a plane stress state within the framework of the flow theory, solutions of differential equations are obtained for calculating the fields of stresses, deformations, displacements, and velocities using finite difference schemes. In the case of an axisymmetric problem, the solution is obtained using the finite element method. The laws of viscoplastic flow area development are investigated. In a sufficiently thick disk, the radius of the elastoplastic boundary changes significantly along the thickness of the disk. The obtained solution is compared with the case of ideal elastoplasticity. Taking into account the viscosity leads to a deceleration of the flow. It is shown that the presence of angular acceleration during fast overclocking significantly affects the distribution of stress intensities.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"10 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84263587","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：