Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva最新文献_第3页

Numerical solution of a singularly perturbed boundary value problem of supersonic flow transformed to the modified best argument 超声速流动奇摄动边值问题的数值解转化为修正最佳参数

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-09-30 DOI: 10.15507/2079-6900.24.202203.304-316

E. Tsapko

{"title":"Numerical solution of a singularly perturbed boundary value problem of supersonic flow transformed to the modified best argument","authors":"E. Tsapko","doi":"10.15507/2079-6900.24.202203.304-316","DOIUrl":"https://doi.org/10.15507/2079-6900.24.202203.304-316","url":null,"abstract":"When solving problems of aerodynamics, researchers often need to numerically solve singularly perturbed boundary value problems. In some cases, the problem can be reduced to solving a boundary value problem for an ordinary differential equation. Then it is possible to apply various numerical methods such as the grid method, the shooting method, as well as a number of projection methods, which, in turn, can form the basis of the finite element method. The grid method requires solving a system of algebraic equations, that are often nonlinear, which leads to an increase in the calculation time and to the difficulties in convergence of the approximate solution. According to the shooting method, the solution of boundary value problem is reduced to solving a certain set of Cauchy problems. When solving stiff Cauchy problems, implicit schemes are used as a rule, but in this case the same difficulties arise as for the grid method. The transformation of the problem to the best argument λ, calculated tangentially along the integral curve, makes it possible to increase the efficiency of explicit numerical methods. However, in cases where the growth rate of integral curves is close to exponential, the transformation to the best argument is not efficient enough. Then the best argument is modified in such a way as to smooth out this flaw. This paper investigates the application of modified best argument to the solution of the boundary value problem of an aerodynamic flow movement in case when the gas is injected at supersonic speed into a channel of variable cross-section.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126971896","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}

引用次数: 0

Resonance in bounded nonlinear pendulum-type systems 有界非线性摆型系统的共振

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-09-30 DOI: 10.15507/2079-6900.24.202203.289-296

E. Pelinovsky, Ioann Melnikov

{"title":"Resonance in bounded nonlinear pendulum-type systems","authors":"E. Pelinovsky, Ioann Melnikov","doi":"10.15507/2079-6900.24.202203.289-296","DOIUrl":"https://doi.org/10.15507/2079-6900.24.202203.289-296","url":null,"abstract":"Solving nonlinear differential equations with external forces is important for understanding resonant phenomena in the physics of oscillations. The article analyzes this problem basing on example of an ordinary second-order differential equation of the pendulum type, where the nonlinearity is described by a sinusoidal term. The phase plane of such an oscillator is constructed and its periodic trajectories are studied. It is illustrated that bounded nonlinearity matters only at intermediate amplitudes. The excitation of a nonlinear oscillator is carried out using a limited two–component force; the first its component corresponds to an oscillation at the resonant frequency of a linear oscillator, and the second is a limited function with a variable frequency. It is shown that with the appropriate choice of an external force, it is possible to obtain unlimited amplification of oscillations in a pendulum-type oscillator with amplitude linearly proportional to time. Spectral composition of the external force is investigated using short-time Fourier transform. It is demonstrated that in order to maintain the resonant mode, the frequency of the external force must continuously increase. Energy estimates of the external force and oscillator fluctuations depending on time are performed. The considered example is important for understanding resonant conditions in nonlinear problems.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127933227","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}

引用次数: 0

To the 70th anniversary of Shavkat Abdullaevich Ayupov 为沙夫卡特·阿卜杜拉耶维奇·阿尤波夫诞辰70周年干杯

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-09-30 DOI: 10.15507/2079-6900.24.202203.331-365

引用次数: 0

Determination of the average electro-thermophoretic force acting on a system of polarizable particles in an inhomogeneously heated fluid 在不均匀加热的流体中作用于极化粒子系统的平均电热电泳力的测定

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-06-30 DOI: 10.15507/2079-6900.24.202202.185-199

S. I. Martynov

{"title":"Determination of the average electro-thermophoretic force acting on a system of polarizable particles in an inhomogeneously heated fluid","authors":"S. I. Martynov","doi":"10.15507/2079-6900.24.202202.185-199","DOIUrl":"https://doi.org/10.15507/2079-6900.24.202202.185-199","url":null,"abstract":"The average force acting on the system of polarizing particles from the electric field in a non-uniformly heated dielectric liquid is determined. The case of pair interactions in the system is examined. To find the force acting on the particles, the interaction of two particles in a liquid is modelled in the presence of a given temperature gradient and the electric field strength far from the particles. The dependence of the particle permittivity on temperature is taken into account. The resulting expression for the force acting on two particles has such a power-law dependence on the distance between the particles, that allows to carry out the direct averaging procedure for a system of particles located in an infinite volume of liquid. When determining the average force, the probability density function of a continuous random variable is used, and the vector connecting the centers of particles plays the role of this variable. The differential equation for finding the probability density function is derived from two conditions. First, the pairs of particles are preserved in the space of all their possible configurations. Second, each pair of particles moves like a point with a speed equal to the speed of their relative motion. The resulting equation in the case under consideration has a set of solutions. Basing on the physical analysis of the problem, the choice of the probability density function is proposed, which allows one to determine the average electro-thermophoretic force acting in such a system with an accuracy up to the second degree of the volume concentration of particles.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"131 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133081891","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}

引用次数: 0

On the numerical solution of second-order stiff linear differential-algebraic equations 二阶刚性线性微分代数方程的数值解

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-06-30 DOI: 10.15507/2079-6900.24.202202.151-161

L. Solovarova, T. D. Phuong

{"title":"On the numerical solution of second-order stiff linear differential-algebraic equations","authors":"L. Solovarova, T. D. Phuong","doi":"10.15507/2079-6900.24.202202.151-161","DOIUrl":"https://doi.org/10.15507/2079-6900.24.202202.151-161","url":null,"abstract":"This article addresses systems of linear ordinary differential equations with an identically degenerate matrix in the main part. Such formulations of problems in literature are usually called differential-algebraic equations. In this work, attention is paid to the problems of the second order. Basing on the theory of matrix pencils and polynomials, sufficient conditions for existence and uniqueness of the equations’ solution are given. To solve them numerically, authors investigate a multistep method and its version based on a reformulated notation of the original problem. This representation makes it possible to construct methods whose coefficient matrices can be calculated at previous points. This approach has delivered good results in numerical solution of first-order differential-algebraic equations that contain stiff and rapidly oscillating components and have singular matrix pencil. The stability of proposed numerical algorithm is investigated for the well-known test equation. It is shown that this difference scheme has the first order of convergence. Numerical calculations of the model problem are presented.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121545771","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}

引用次数: 0

On an iterative method for solving optimal control problems for an elliptic type system 求解椭圆型系统最优控制问题的迭代方法

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-06-30 DOI: 10.15507/2079-6900.24.202202.162-174

M. E. Fairuzov, F. Lubyshev

{"title":"On an iterative method for solving optimal control problems for an elliptic type system","authors":"M. E. Fairuzov, F. Lubyshev","doi":"10.15507/2079-6900.24.202202.162-174","DOIUrl":"https://doi.org/10.15507/2079-6900.24.202202.162-174","url":null,"abstract":"An important class of applied problems is that of optimal control of some objects’ state. It is required to select control actions in such a way as to achieve desired effect. We deal with distributed systems, since their state is described by a partial differential equation. In this paper we study an iterative process for solving the problem of optimal control for an elliptic type system. Similar problem arises during the control of thermal processes. The quality of system state control is estimated by a given quality functional defined on the solution of the Dirichlet problem for an elliptic equation. One of the most important classes of thermal process control problems is temperature control, which means maintaining given temperature in the computational domain due to certain thermal effects. Here, a distributed internal heat source acts as a control. In the paper, we study statement correctness of the optimal control problem with a regularized functional. More precisely, we examine control problem for a system described by an elliptic type equation and formulate its optimality condition in the form of a system of equations for initial and conjugate states. An iterative method is proposed for solving the optimal control problem of an elliptic type system. Convergence of the iterative process is studied, and the rate of convergence is estimated.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114628500","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}

引用次数: 0

On the stability of Lotka-Volterra model with a delay 具有时滞的Lotka-Volterra模型的稳定性

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-06-30 DOI: 10.15507/2079-6900.24.202202.175-184

J. Khusanov, Azizbeck E. Kaxxorov

引用次数: 0

On perturbations of algebraic periodic automorphisms of a two-dimensional torus 二维环面代数周期自同构的摄动

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-06-30 DOI: 10.15507/2079-6900.24.202202.141-150

V. Grines, D. Mints, E. Chilina

{"title":"On perturbations of algebraic periodic automorphisms of a two-dimensional torus","authors":"V. Grines, D. Mints, E. Chilina","doi":"10.15507/2079-6900.24.202202.141-150","DOIUrl":"https://doi.org/10.15507/2079-6900.24.202202.141-150","url":null,"abstract":"According to the results of V. Z. Grines and A. N. Bezdenezhnykh, for each gradient-like diffeomorphism of a closed orientable surface M2 there exist a gradient-like flow and a periodic diffeomorphism of this surface such that the original diffeomorphism is a superposition of a diffeomorphism that is a shift per unit time of the flow and the periodic diffeomorphism. In the case when M2 is a two-dimensional torus, there is a topological classification of periodic maps. Moreover, it is known that there is only a finite number of topological conjugacy classes of periodic diffeomorphisms that are not homotopic to identity one. Each such class contains a representative that is a periodic algebraic automorphism of a two-dimensional torus. Periodic automorphisms of a two-dimensional torus are not structurally stable maps, and, in general, it is impossible to predict the dynamics of their arbitrarily small perturbations. However, in the case when a periodic diffeomorphism is algebraic, we constructed a one-parameter family of maps consisting of the initial periodic algebraic automorphism at zero parameter value and gradient-like diffeomorphisms of a twodimensional torus for all non-zero parameter values. Each diffeomorphism of the constructed one-parameter families inherits, in a certain sense, the dynamics of a periodic algebraic automorphism being perturbed.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128837276","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}

引用次数: 0

Mathematical study of medicine diffusion from swelling chitosan film 溶胀壳聚糖膜药物扩散的数学研究

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-06-30 DOI: 10.15507/2079-6900.24.202202.200-214

Alexey O. Syromyasov, A. Shurshina, Dmitry V. Galkin

{"title":"Mathematical study of medicine diffusion from swelling chitosan film","authors":"Alexey O. Syromyasov, A. Shurshina, Dmitry V. Galkin","doi":"10.15507/2079-6900.24.202202.200-214","DOIUrl":"https://doi.org/10.15507/2079-6900.24.202202.200-214","url":null,"abstract":"One of modern dosage forms is a medicine-saturated organic film: after putting this film onto a skin the medicine releases thus providing healing effect. Present article concerns films based on chitosan and containing amikacinum or cefazolinum. The most important characteristic of such film is rate of medicine release described by diffusion coefficient. To find it the film is placed in water and the average medicine concentration in the film is measured at different time moments. Two problems arise here. First, the film properties change because of its swelling. Second, diffusion is not the only process that takes place inside the film. To deal with these effects, authors suppose diffusion coefficient to be time-variable and complete the mathematical model with ODE describing detachment of medicine molecules from high-molecular matrix. All the equations in the model are solved analytically, so average medicine concentration in the film is known function of time. Thus, to solve stated inverse problem it is sufficient to find unknown scalar parameters of known functions using least-squares framework. Expressions arising in the solution are complicated so non-gradient methods are preferrable for optimization. Applying described procedure to experimental data leads to a good accuracy and the results may be explained from physicochemical point of view. In particular, the film swelling doesn’t influence release rate. In fact, the diffusion rate during first hours of experiment is large, and the main part of the medicine is released before swelling starts to play important role.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124078545","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}

引用次数: 0

Numerical study of the effect of surface recombination on nonlinear and phase distortions arising during the restoration of the optical signal shape 表面复合对光信号形状恢复过程中产生的非线性和相位畸变影响的数值研究

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-06-30 DOI: 10.15507/2079-6900.24.202202.215-227

V. Y. Grishaev, S. M. Muryumin, Evgeny V. Nikishin

{"title":"Numerical study of the effect of surface recombination on nonlinear and phase distortions arising during the restoration of the optical signal shape","authors":"V. Y. Grishaev, S. M. Muryumin, Evgeny V. Nikishin","doi":"10.15507/2079-6900.24.202202.215-227","DOIUrl":"https://doi.org/10.15507/2079-6900.24.202202.215-227","url":null,"abstract":"The photoconductivity kinetics of a resistor with homogeneous generation of electrons and holes in thickness is investigated. Calculations are carried out for an n-type semiconductor. The cases of linear and quadratic volumetric recombination are considered. The mathematical model of the process includes a non-linear parabolic partial differential equation. The cause of its non-linearity is quadratic recombination. Boundary conditions of the 3rd kind are used, thus allowing to examine the surface recombination of nonequilibrium charge carriers. This latter phenomenon makes it necessary to take into account the diffusion term when writing kinetic equations describing the distribution of electrons and holes. The model neglects the volumetric charge. In described circumstances it is possible to use the integration of the photocurrent flowing through the resistor to obtain the dependence of the light intensity on time for small optical pulse durations: T<max(τn,τp). Here T is the pulse duration, τn and τp are the lifetimes of electrons and holes, respectively. Nonlinear distortions in this case are mainly associated with the appearance of the second and the third harmonics of the Fourier series expansion of the function that determines the photocurrent dependence on time. To \"restore\" the optical pulse, the operation of differentiating the photocurrent can be used. Nonlinear and phase distortions are small when the condition T<max(τn,τp) is met. Proposed methods make it possible to expand the range of optical pulse durations (T) in which its \"recovery\" is possible. In the vicinity of the region defined by the equality T≈max(τn,τp), nonlinear and phase distortions are significant.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122283502","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}

引用次数: 0