Pub Date : 2024-08-26DOI: 10.1134/s0040577924080087
M. A. Pogrebnyak
Abstract
The main result of this paper is a mathematical model that describes the dynamics of the motion of several cars in areas with different speed limits. As such areas, we can consider speed limit zones and speed bumps or uneven road surfaces. The model is a system of differential equations with a delayed argument. The dynamical properties of the model are studied by numerical methods. A computer program has been developed that uses the model to describe the motion of traffic flows in various road situations. The simulation results coincide with the observation data of real traffic flows.
{"title":"Modeling the traffic flow in areas with different speed limits","authors":"M. A. Pogrebnyak","doi":"10.1134/s0040577924080087","DOIUrl":"https://doi.org/10.1134/s0040577924080087","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The main result of this paper is a mathematical model that describes the dynamics of the motion of several cars in areas with different speed limits. As such areas, we can consider speed limit zones and speed bumps or uneven road surfaces. The model is a system of differential equations with a delayed argument. The dynamical properties of the model are studied by numerical methods. A computer program has been developed that uses the model to describe the motion of traffic flows in various road situations. The simulation results coincide with the observation data of real traffic flows. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-27DOI: 10.1134/s0040577924070067
D. A. Kulikov
Abstract
We continue studies of the nonlocal erosion equation that is used as a mathematical model of the formation of a spatially inhomogeneous relief on semiconductor surfaces. We show that such a relief can form as a result of local bifurcations in the case where the stability of the spatially homogeneous equilibrium state changes. We consider a periodic boundary-value problem and study its codimension-(2) bifurcations. For solutions describing an inhomogeneous relief, we obtain asymptotic formulas and study their stability. The analysis of the mathematical problem is based on modern methods of the theory of dynamical systems with an infinite-dimensional phase space, in particular, on the method of integral manifolds and on the theory of normal forms.
{"title":"Mechanism for the formation of an inhomogeneous nanorelief and bifurcations in a nonlocal erosion equation","authors":"D. A. Kulikov","doi":"10.1134/s0040577924070067","DOIUrl":"https://doi.org/10.1134/s0040577924070067","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We continue studies of the nonlocal erosion equation that is used as a mathematical model of the formation of a spatially inhomogeneous relief on semiconductor surfaces. We show that such a relief can form as a result of local bifurcations in the case where the stability of the spatially homogeneous equilibrium state changes. We consider a periodic boundary-value problem and study its codimension-<span>(2)</span> bifurcations. For solutions describing an inhomogeneous relief, we obtain asymptotic formulas and study their stability. The analysis of the mathematical problem is based on modern methods of the theory of dynamical systems with an infinite-dimensional phase space, in particular, on the method of integral manifolds and on the theory of normal forms. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-27DOI: 10.1134/s0040577924070092
N. N. Nefedov, A. O. Orlov
Abstract
The existence of stationary solutions of singularly perturbed systems of reaction–diffusion–advection equations is studied in the case of fast and slow reaction–diffusion–advection equations with nonlinearities containing the gradient of the squared sought function (KPZ nonlinearities). The asymptotic method of differential inequalities is used to prove the existence theorems. The boundary layer asymptotics of solutions are constructed in the case of Neumann and Dirichlet boundary conditions. The case of quasimonotone sources and systems without the quasimonotonicity requirement is also considered.
{"title":"Existence and stability of stationary solutions with boundary layers in a system of fast and slow reaction–diffusion–advection equations with KPZ nonlinearities","authors":"N. N. Nefedov, A. O. Orlov","doi":"10.1134/s0040577924070092","DOIUrl":"https://doi.org/10.1134/s0040577924070092","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The existence of stationary solutions of singularly perturbed systems of reaction–diffusion–advection equations is studied in the case of fast and slow reaction–diffusion–advection equations with nonlinearities containing the gradient of the squared sought function (KPZ nonlinearities). The asymptotic method of differential inequalities is used to prove the existence theorems. The boundary layer asymptotics of solutions are constructed in the case of Neumann and Dirichlet boundary conditions. The case of quasimonotone sources and systems without the quasimonotonicity requirement is also considered. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-27DOI: 10.1134/s0040577924070055
A. N. Kulikov
Abstract
We consider a system of autonomous nonlinear ordinary differential equations for which the existence conditions for an invariant manifold are satisfied in the case where this manifold is central. It is well known that the theorem on the existence of a central invariant manifold cannot be supplemented with the statement of its uniqueness. We obtain sufficient conditions that guarantee the uniqueness of the central invariant manifold.
{"title":"On the uniqueness problem for a central invariant manifold","authors":"A. N. Kulikov","doi":"10.1134/s0040577924070055","DOIUrl":"https://doi.org/10.1134/s0040577924070055","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider a system of autonomous nonlinear ordinary differential equations for which the existence conditions for an invariant manifold are satisfied in the case where this manifold is central. It is well known that the theorem on the existence of a central invariant manifold cannot be supplemented with the statement of its uniqueness. We obtain sufficient conditions that guarantee the uniqueness of the central invariant manifold. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-27DOI: 10.1134/s004057792407002x
M. A. Banschikova, O. M. Syusina
Abstract
We present the results of a study of nonlinearity in inverse problems of the orbital dynamics of Jupiter’s outer satellites, discovered in 2018–2022, and of potentially hazardous asteroids. The results show that for a more accurate study of orbital uncertainty, we must first find the minimum value of a nonlinearity indicator by varying the initial epoch within the measurable interval for different parametric spaces.
{"title":"Nonlinearity in the inverse problems of orbital dynamics using the example of potentially hazardous asteroids and outer satellites of Jupiter","authors":"M. A. Banschikova, O. M. Syusina","doi":"10.1134/s004057792407002x","DOIUrl":"https://doi.org/10.1134/s004057792407002x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We present the results of a study of nonlinearity in inverse problems of the orbital dynamics of Jupiter’s outer satellites, discovered in 2018–2022, and of potentially hazardous asteroids. The results show that for a more accurate study of orbital uncertainty, we must first find the minimum value of a nonlinearity indicator by varying the initial epoch within the measurable interval for different parametric spaces. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-27DOI: 10.1134/s0040577924070043
P. E. Bulatov, Han Cheng, Yuxuan Wei, V. T. Volkov, N. T. Levashova
Abstract
We consider a periodic problem for a singularly perturbed parabolic reaction–diffusion–advection equation of the Burgers type with the modulus advection; it has a solution in the form of a moving front. We formulate conditions for the existence of such a solution and construct its asymptotic approximation. We pose a control problem where the required front propagation law is implemented by a specially chosen boundary condition. We construct an asymptotic solution of the boundary control problem. Using the asymptotic method of differential inequalities, we estimate the accuracy of the solution of the control problem. We propose an original numerical algorithm for solving singularly perturbed problems involving the modulus advection.
{"title":"Boundary control problem for the reaction– advection– diffusion equation with a modulus discontinuity of advection","authors":"P. E. Bulatov, Han Cheng, Yuxuan Wei, V. T. Volkov, N. T. Levashova","doi":"10.1134/s0040577924070043","DOIUrl":"https://doi.org/10.1134/s0040577924070043","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider a periodic problem for a singularly perturbed parabolic reaction–diffusion–advection equation of the Burgers type with the modulus advection; it has a solution in the form of a moving front. We formulate conditions for the existence of such a solution and construct its asymptotic approximation. We pose a control problem where the required front propagation law is implemented by a specially chosen boundary condition. We construct an asymptotic solution of the boundary control problem. Using the asymptotic method of differential inequalities, we estimate the accuracy of the solution of the control problem. We propose an original numerical algorithm for solving singularly perturbed problems involving the modulus advection. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-27DOI: 10.1134/s0040577924070109
E. I. Nikulin, V. T. Volkov, A. G. Nikitin
Abstract
We obtain a contrast-structure type solution of a system of equations for the baretting effect that include a nonlinear singularly perturbed parabolic equation and an additional nonlocal integral relation. We prove the existence of the solution with an internal transition layer and construct the asymptotic approximation of this solution. We obtain estimates of the main physical model parameters, which coincide with experimental data and the estimates obtained previously by other methods.
{"title":"On contrast structures in a problem of the baretting effect theory","authors":"E. I. Nikulin, V. T. Volkov, A. G. Nikitin","doi":"10.1134/s0040577924070109","DOIUrl":"https://doi.org/10.1134/s0040577924070109","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We obtain a contrast-structure type solution of a system of equations for the baretting effect that include a nonlinear singularly perturbed parabolic equation and an additional nonlocal integral relation. We prove the existence of the solution with an internal transition layer and construct the asymptotic approximation of this solution. We obtain estimates of the main physical model parameters, which coincide with experimental data and the estimates obtained previously by other methods. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-27DOI: 10.1134/s0040577924070031
V. G. Bardakov, T. A. Kozlovskaya, D. V. Talalaev
Abstract
We study (n)-valued quandles and (n)-corack bialgebras. These structures are closely related to topological field theories in dimensions (2) and (3), to the set-theoretic Yang–Baxter equation, and to the (n)-valued groups, which have attracted considerable attention or researchers. We elaborate the basic methods of this theory, find an analogue of the so-called coset construction known in the theory of (n)-valued groups, and construct (n)-valued quandles using (n)-multiquandles. In contrast to the case of (n)-valued groups, this construction turns out to be quite rich in algebraic and topological applications. We study the properties of (n)-corack bialgebras, which play a role similar to that of bialgebras in group theory.
Abstract We study (n)-valued quandles and (n)-corack bialgebras.这些结构与维数为 (2) 和 (3) 的拓扑场论、集合论杨-巴克斯特方程以及 (n)-valued 群密切相关，已经引起了研究者们的极大关注。我们详细阐述了这一理论的基本方法，找到了在(n)值群理论中已知的所谓coset构造的类似物，并用(n)-multiquandles构造了(n)-valued quandles。与（n）值群的情况不同，这种构造在代数学和拓扑学上的应用相当丰富。我们研究了 (n)-corack 双桥的性质，它的作用类似于群论中的双桥。
{"title":"$$n$$ -valued quandles and associated bialgebras","authors":"V. G. Bardakov, T. A. Kozlovskaya, D. V. Talalaev","doi":"10.1134/s0040577924070031","DOIUrl":"https://doi.org/10.1134/s0040577924070031","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study <span>(n)</span>-valued quandles and <span>(n)</span>-corack bialgebras. These structures are closely related to topological field theories in dimensions <span>(2)</span> and <span>(3)</span>, to the set-theoretic Yang–Baxter equation, and to the <span>(n)</span>-valued groups, which have attracted considerable attention or researchers. We elaborate the basic methods of this theory, find an analogue of the so-called coset construction known in the theory of <span>(n)</span>-valued groups, and construct <span>(n)</span>-valued quandles using <span>(n)</span>-multiquandles. In contrast to the case of <span>(n)</span>-valued groups, this construction turns out to be quite rich in algebraic and topological applications. We study the properties of <span>(n)</span>-corack bialgebras, which play a role similar to that of bialgebras in group theory. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-27DOI: 10.1134/s0040577924070018
S. Anastassiou
Abstract
We study the local structure of vector fields on (mathbb{R}^3) that preserve the Martinet (1)-form (alpha=(1+x)dypm z,dz). We classify their singularities up to diffeomorphisms that preserve the form (alpha), as well as their transverse unfoldings. We are thus able to provide a fairly complete list of the bifurcations such vector fields undergo.
{"title":"Singularities of 3D vector fields preserving the Martinet form","authors":"S. Anastassiou","doi":"10.1134/s0040577924070018","DOIUrl":"https://doi.org/10.1134/s0040577924070018","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study the local structure of vector fields on <span>(mathbb{R}^3)</span> that preserve the Martinet <span>(1)</span>-form <span>(alpha=(1+x)dypm z,dz)</span>. We classify their singularities up to diffeomorphisms that preserve the form <span>(alpha)</span>, as well as their transverse unfoldings. We are thus able to provide a fairly complete list of the bifurcations such vector fields undergo. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-27DOI: 10.1134/s0040577924070122
A. O. Smirnov, I. V. Anisimov
Abstract
We consider methods for constructing finite-gap solutions of the real classical modified Korteweg–de Vries equation and elliptic finite-gap potentials of the Dirac operator. The Miura transformation is used in both methods to relate solutions of the Korteweg–de Vries and modified Korteweg–de Vries equations. We present examples.
{"title":"Finite-gap solutions of the real modified Korteweg–de Vries equation","authors":"A. O. Smirnov, I. V. Anisimov","doi":"10.1134/s0040577924070122","DOIUrl":"https://doi.org/10.1134/s0040577924070122","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider methods for constructing finite-gap solutions of the real classical modified Korteweg–de Vries equation and elliptic finite-gap potentials of the Dirac operator. The Miura transformation is used in both methods to relate solutions of the Korteweg–de Vries and modified Korteweg–de Vries equations. We present examples. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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