Pub Date : 2022-01-01DOI: 10.21638/11701/spbu10.2022.407
V. Pavlovsky
Currently, when solving problems of heat and mass transfer, linear constitutive equations are used - in hydrodynamics, the viscous stress tensor is proportional to the strain rate tensor (Newton's rheological ratio), in heat transfer, the heat flux density is linearly related to the temperature gradient (Fourier's heat conduction law), in mass transfer, the diffusion flux density proportional to the concentration gradient (Fick's law). When writing these linear governing equations, proportionality coefficients are used, which are called the viscosity coefficient, thermal conductivity coefficient and diffusion coefficient, respectively. Such constitutive equations are widely used to describe the processes of heat and mass transfer in a laminar flow regime. For turbulent flows, these equations are unsuitable, it is necessary to introduce into consideration the empirical turbulent coefficients of viscosity μt, thermal conductivity λt and diffusion Dt. However, to describe turbulent flows, it is possible to go in another way - to modify the linear constitutive relations by giving them a nonlinear power-law form. Two-parameter power-law generalizations of Newton's, Fourier's and Fick's formulas for shear stress, heat flux density and diffusion, which, depending on the value of the exponents, can be used to describe the processes of heat and mass transfer both in laminar and turbulent fluid flow. Also, this generalization can be used to describe the behavior of power-law fluids and flows of polymer solutions exhibiting the Toms effect.
{"title":"Power generalization of the linear constitutive equations of heat and mass transfer and the variants of writing the equations of momentum transfer, heat and diffusion arising from them","authors":"V. Pavlovsky","doi":"10.21638/11701/spbu10.2022.407","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.407","url":null,"abstract":"Currently, when solving problems of heat and mass transfer, linear constitutive equations are used - in hydrodynamics, the viscous stress tensor is proportional to the strain rate tensor (Newton's rheological ratio), in heat transfer, the heat flux density is linearly related to the temperature gradient (Fourier's heat conduction law), in mass transfer, the diffusion flux density proportional to the concentration gradient (Fick's law). When writing these linear governing equations, proportionality coefficients are used, which are called the viscosity coefficient, thermal conductivity coefficient and diffusion coefficient, respectively. Such constitutive equations are widely used to describe the processes of heat and mass transfer in a laminar flow regime. For turbulent flows, these equations are unsuitable, it is necessary to introduce into consideration the empirical turbulent coefficients of viscosity μt, thermal conductivity λt and diffusion Dt. However, to describe turbulent flows, it is possible to go in another way - to modify the linear constitutive relations by giving them a nonlinear power-law form. Two-parameter power-law generalizations of Newton's, Fourier's and Fick's formulas for shear stress, heat flux density and diffusion, which, depending on the value of the exponents, can be used to describe the processes of heat and mass transfer both in laminar and turbulent fluid flow. Also, this generalization can be used to describe the behavior of power-law fluids and flows of polymer solutions exhibiting the Toms effect.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74017718","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 : 2022-01-01DOI: 10.21638/11701/spbu10.2022.411
G. Kropachev, T. Kulevoy, Alexei L. Sitnikov, E. Khabibullina, S. Vinogradov
The project DARIA (neutron source dedicated to applied research and industrial applications) directed to the development of compact neutron generators for universities, scientific centers and industry. In framework of the DARIA project, the 3 MeV, 162.5 MHz and 100mA pulse proton Radio Frequency Quadrupole (RFQ) is under development at National Research Centre "Kurchatov Institute". In this article the main aspects of the beam dynamics design of this RFQ are described, namely the choice of RFQ parameters, the optimization of the transport and the transmission. Results of beam dynamic simulation in RFQ are presented.
{"title":"Beam dynamics of the project DARIA RFQ","authors":"G. Kropachev, T. Kulevoy, Alexei L. Sitnikov, E. Khabibullina, S. Vinogradov","doi":"10.21638/11701/spbu10.2022.411","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.411","url":null,"abstract":"The project DARIA (neutron source dedicated to applied research and industrial applications) directed to the development of compact neutron generators for universities, scientific centers and industry. In framework of the DARIA project, the 3 MeV, 162.5 MHz and 100mA pulse proton Radio Frequency Quadrupole (RFQ) is under development at National Research Centre \"Kurchatov Institute\". In this article the main aspects of the beam dynamics design of this RFQ are described, namely the choice of RFQ parameters, the optimization of the transport and the transmission. Results of beam dynamic simulation in RFQ are presented.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90327403","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 : 2022-01-01DOI: 10.21638/11701/spbu10.2022.113
V. Tregubov, N. K. Egorova
This article presents results from an experimental study of the frequency properties of a sitting person. This analysis shows that in order to define the structure and parameters of a human body model, it is necessary to find the only solution to the problem of determining the model parameters. Otherwise, this model cannot be used to build vibration protection systems, which is its main purpose. This problem was solved for a two-mass human model. To do this, the total model mass and although the amplitude-frequency response and input frequency impedance for both solids in the model structure are needed to be known. In addition to this, the influence of multi-articular muscles on the frequency characteristics of a human body is found using mechanical models with an arbitrary number of degrees of freedom. In particular, the possibility of the existence additional antiresonance frequencies on the upper mass is shown.
{"title":"Determining the structure and parameters of the human model subjected to vibration","authors":"V. Tregubov, N. K. Egorova","doi":"10.21638/11701/spbu10.2022.113","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.113","url":null,"abstract":"This article presents results from an experimental study of the frequency properties of a sitting person. This analysis shows that in order to define the structure and parameters of a human body model, it is necessary to find the only solution to the problem of determining the model parameters. Otherwise, this model cannot be used to build vibration protection systems, which is its main purpose. This problem was solved for a two-mass human model. To do this, the total model mass and although the amplitude-frequency response and input frequency impedance for both solids in the model structure are needed to be known. In addition to this, the influence of multi-articular muscles on the frequency characteristics of a human body is found using mechanical models with an arbitrary number of degrees of freedom. In particular, the possibility of the existence additional antiresonance frequencies on the upper mass is shown.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91064299","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 : 2022-01-01DOI: 10.21638/11701/spbu10.2022.306
Cheikh Yatma Diop, M. Kaparkova, V. Kukhtin, A. Makarov, I. Rodin, S. Sytchevsky, Alexey A. Firsov
The study investigates possible disturbances of the Earth’s geomagnetic field associated with ferromagnetic structures of clinical buildings. An original methodology has been applied for 3D field mapping of hospital areas in the Senegalese Radiotherapy (RT) Centre. The RT unit will be located in a bunker with thick steel walls to ensure safety of patients and staff. Steel reinforcement will provide the shielding effect lowering the field level in the therapy room. A detailed numerical model has been created to simulate an expected field map in the RT bunker. The model reflects the actual geometry and reinforcement pattern of the building as well as adopted national standards for hypomagnetic field environment. The field maps generated with the EM codes KLONDIKE and KOMPOT form a basis for validation in comparative computations with the other codes (COMSOL Multiphysics, etc).
{"title":"Numerical models for analysis and adjustment of magnetic field in medical centers. I. Simulation of geomagnetic field disturbances","authors":"Cheikh Yatma Diop, M. Kaparkova, V. Kukhtin, A. Makarov, I. Rodin, S. Sytchevsky, Alexey A. Firsov","doi":"10.21638/11701/spbu10.2022.306","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.306","url":null,"abstract":"The study investigates possible disturbances of the Earth’s geomagnetic field associated with ferromagnetic structures of clinical buildings. An original methodology has been applied for 3D field mapping of hospital areas in the Senegalese Radiotherapy (RT) Centre. The RT unit will be located in a bunker with thick steel walls to ensure safety of patients and staff. Steel reinforcement will provide the shielding effect lowering the field level in the therapy room. A detailed numerical model has been created to simulate an expected field map in the RT bunker. The model reflects the actual geometry and reinforcement pattern of the building as well as adopted national standards for hypomagnetic field environment. The field maps generated with the EM codes KLONDIKE and KOMPOT form a basis for validation in comparative computations with the other codes (COMSOL Multiphysics, etc).","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84581228","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 : 2021-06-01DOI: 10.21638/11701/spbu10.2021.207
Viktor Р. Iakushev, V. Bure, O. Mitrofanova, E. Mitrofanov
Еach model for forecasting agrometeorological risks based on the analysis of one-dimensional time series is effective for a certain range of initial information. In addition, the values of the initial observations can differ significantly for each specific case, respectively, the widespread use of one method for the analysis of arbitrary information can lead to significant inaccuracies. Thus, the problem of choosing a forecasting method for the initial set of agrometeorological data arises. In this regard, a universal adaptive probabilistic-statistical approach to predicting agrometeorological risks is proposed, which makes it possible to solve the problem of choosing a model. The article presents the results of the first stage of research carried out with the financial support of the Ministry of Education and Science of the Russian Federation a brief overview of the current state of research in this direction is presented, theoretical foundations for predicting agrometeorological risks for a possible onset of drought and frost have been developed, including the task of generating initial information, a description of basic forecasting models, and also a direct description of the proposed approach with a presentation of the general structure of an intelligent system, on the basis of which the corresponding algorithm can be developed and automated as directions for further work.
{"title":"Theoretical foundations of probabilistic and statistical forecasting of agrometeorological risks","authors":"Viktor Р. Iakushev, V. Bure, O. Mitrofanova, E. Mitrofanov","doi":"10.21638/11701/spbu10.2021.207","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2021.207","url":null,"abstract":"Еach model for forecasting agrometeorological risks based on the analysis of one-dimensional time series is effective for a certain range of initial information. In addition, the values of the initial observations can differ significantly for each specific case, respectively, the widespread use of one method for the analysis of arbitrary information can lead to significant inaccuracies. Thus, the problem of choosing a forecasting method for the initial set of agrometeorological data arises. In this regard, a universal adaptive probabilistic-statistical approach to predicting agrometeorological risks is proposed, which makes it possible to solve the problem of choosing a model. The article presents the results of the first stage of research carried out with the financial support of the Ministry of Education and Science of the Russian Federation a brief overview of the current state of research in this direction is presented, theoretical foundations for predicting agrometeorological risks for a possible onset of drought and frost have been developed, including the task of generating initial information, a description of basic forecasting models, and also a direct description of the proposed approach with a presentation of the general structure of an intelligent system, on the basis of which the corresponding algorithm can be developed and automated as directions for further work.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73180939","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 : 2021-06-01DOI: 10.21638/11701/spbu10.2021.208
Irina V. Аlexandrova, Аlexey Р. Zhabko
In this article, explicit constructions of Lyapunov - Кrasovskii functionals are proposed for homogeneous systems with multiple constant delays and homogeneity degree of the right- hand sides strictly greater than one. The constructions are based on the Lyapunov functions suitable for the analysis of corresponding systems with all delays equal to zero. The letter systems are assumed to be asymptotically stable. It is proved that the proposed functionals satisfy the conditions of the Кrasovskii theorem, and hence it allows us to establish the asymptotic stability of the trivial solution for arbitrary values of delays. The functionals are applied to the estimation of the attraction region of the trivial solution.
{"title":"Lyapunov - Кrasovskii functionals for homogeneous systems with multiple delays","authors":"Irina V. Аlexandrova, Аlexey Р. Zhabko","doi":"10.21638/11701/spbu10.2021.208","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2021.208","url":null,"abstract":"In this article, explicit constructions of Lyapunov - Кrasovskii functionals are proposed for homogeneous systems with multiple constant delays and homogeneity degree of the right- hand sides strictly greater than one. The constructions are based on the Lyapunov functions suitable for the analysis of corresponding systems with all delays equal to zero. The letter systems are assumed to be asymptotically stable. It is proved that the proposed functionals satisfy the conditions of the Кrasovskii theorem, and hence it allows us to establish the asymptotic stability of the trivial solution for arbitrary values of delays. The functionals are applied to the estimation of the attraction region of the trivial solution.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82352469","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 : 2021-06-01DOI: 10.21638/11701/spbu10.2021.206
V. Tregubov, N. K. Egorova
It is known that the Кelvin-Voigt model does not describe stress relaxation, which is observed along with elastic properties in many polymers and biomaterials. In this regard, the standard linear body model is used to describe the properties of these materials. Studies of its properties were mainly limited to the study of its reaction to an instantaneously applied load, as well as to the determination of the time and nature of stress relaxation. Аt the same time, the frequency properties of the standard linear body remained unexplored. In this regard, an analysis of its frequency properties was carried out, which made it possible to study its behavior under vibration exposure. Оn the basis of the equation of motion, the amplitude-frequency response (АFC) was constructed, and its peculiarity was revealed, which consists in the fact that an increase in the damping coefficient leads to a decrease in the maximum value of the АFC only to a certain value greater than one. А further increase in the damping coefficient leads to an increase in the maximum frequency response up to infinity at a frequency that should also be considered resonant. Thus, the frequency response of a standard linear body always has a maximum. The subsequent increase in the damping coefficient leads to the tendency of the maximum frequency response to zero at infinity.
{"title":"Investigation of the frequency properties of a standard linear body","authors":"V. Tregubov, N. K. Egorova","doi":"10.21638/11701/spbu10.2021.206","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2021.206","url":null,"abstract":"It is known that the Кelvin-Voigt model does not describe stress relaxation, which is observed along with elastic properties in many polymers and biomaterials. In this regard, the standard linear body model is used to describe the properties of these materials. Studies of its properties were mainly limited to the study of its reaction to an instantaneously applied load, as well as to the determination of the time and nature of stress relaxation. Аt the same time, the frequency properties of the standard linear body remained unexplored. In this regard, an analysis of its frequency properties was carried out, which made it possible to study its behavior under vibration exposure. Оn the basis of the equation of motion, the amplitude-frequency response (АFC) was constructed, and its peculiarity was revealed, which consists in the fact that an increase in the damping coefficient leads to a decrease in the maximum value of the АFC only to a certain value greater than one. А further increase in the damping coefficient leads to an increase in the maximum frequency response up to infinity at a frequency that should also be considered resonant. Thus, the frequency response of a standard linear body always has a maximum. The subsequent increase in the damping coefficient leads to the tendency of the maximum frequency response to zero at infinity.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87185373","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 : 2021-06-01DOI: 10.21638/11701/spbu10.2021.204
O. Drivotin
Momentum is considered on the basis of the approach widely used in the calculus of variations and in the optimal control theory, where variation of a cost functional is investigated. In physical theory, it is the action functional. Action variation under Lie dragging can be expressed as a surface integral of some differential form. The momentum density flow is defined using this form. In this work, the momentum balance equation is obtained. This equation shows that the momentum field transforms into a momentum of a mass. Examples showing the momentum flow structure for a mass distribution representing a uniform thin layer are provided.
{"title":"Оn momentum flow density of the gravitational field","authors":"O. Drivotin","doi":"10.21638/11701/spbu10.2021.204","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2021.204","url":null,"abstract":"Momentum is considered on the basis of the approach widely used in the calculus of variations and in the optimal control theory, where variation of a cost functional is investigated. In physical theory, it is the action functional. Action variation under Lie dragging can be expressed as a surface integral of some differential form. The momentum density flow is defined using this form. In this work, the momentum balance equation is obtained. This equation shows that the momentum field transforms into a momentum of a mass. Examples showing the momentum flow structure for a mass distribution representing a uniform thin layer are provided.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88100664","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 : 2021-06-01DOI: 10.21638/11701/spbu10.2021.210
E. Kotina, D. Ovsyannikov
А new mathematical model for the optimization of discrete systems is constructed in the article. The program motion and the ensemble (beam) of perturbed motions are investigated. In this case, the authors consider the joint optimization of smooth and non-smooth functionals defined on the program and perturbed motions. The variation of the functional and the necessary optimality conditions are provided. The developed mathematical technique allows solving non-standard control and optimization problems in various fields of science and technology.
{"title":"Mathematical model of joint optimization of programmed and perturbed motions in discrete systems","authors":"E. Kotina, D. Ovsyannikov","doi":"10.21638/11701/spbu10.2021.210","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2021.210","url":null,"abstract":"А new mathematical model for the optimization of discrete systems is constructed in the article. The program motion and the ensemble (beam) of perturbed motions are investigated. In this case, the authors consider the joint optimization of smooth and non-smooth functionals defined on the program and perturbed motions. The variation of the functional and the necessary optimality conditions are provided. The developed mathematical technique allows solving non-standard control and optimization problems in various fields of science and technology.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80397757","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 : 2021-06-01DOI: 10.21638/11701/spbu10.2021.205
Аlexander V. Fominyh
The article analyses a linear nonstationary interval system of ordinary differential equations so that the elements of the matrix of the system are the intervals with the known lower and upper bounds. The system is defined on the known finite time interval. It is required to construct a trajectory, which brings this system from the given initial position to the given final state. The original problem is reduced to finding a solution of the differential inclusion of a special form with the fixed right endpoint. With the help of support functions, this problem is reduced to minimizing a functional in the space of piecewise continuous functions. Under a natural additional assumption, this functional is Gateaux differentiable. For the functional, Gateaux gradient is found, necessary and sufficient conditions for the minimum are obtained. Оn the basis of these conditions, the method of the steepest descent is applied to the original problem. Some examples illustrate the constructed algorithm realization.
{"title":"Method for finding a solution to a linear nonstationary interval ОDЕ system","authors":"Аlexander V. Fominyh","doi":"10.21638/11701/spbu10.2021.205","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2021.205","url":null,"abstract":"The article analyses a linear nonstationary interval system of ordinary differential equations so that the elements of the matrix of the system are the intervals with the known lower and upper bounds. The system is defined on the known finite time interval. It is required to construct a trajectory, which brings this system from the given initial position to the given final state. The original problem is reduced to finding a solution of the differential inclusion of a special form with the fixed right endpoint. With the help of support functions, this problem is reduced to minimizing a functional in the space of piecewise continuous functions. Under a natural additional assumption, this functional is Gateaux differentiable. For the functional, Gateaux gradient is found, necessary and sufficient conditions for the minimum are obtained. Оn the basis of these conditions, the method of the steepest descent is applied to the original problem. Some examples illustrate the constructed algorithm realization.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72710993","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：