Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva最新文献_第2页

On a class of self-affine sets on the plane given by six homotheties 在六个同理给出的平面上的一类自仿射集合

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2023-03-30 DOI: 10.15507/2079-6900.25.202301.519-530

A. V. Bagaev

引用次数: 0

Continuous global optimization of multivariable functions based on Sergeev and Kvasov diagonal approach 基于Sergeev和Kvasov对角法的多变量函数连续全局优化

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-12-31 DOI: 10.15507/2079-6900.24.202204.399-418

Vladislav V. Zabotin, Pavel A. Chernyshevskij

{"title":"Continuous global optimization of multivariable functions based on Sergeev and Kvasov diagonal approach","authors":"Vladislav V. Zabotin, Pavel A. Chernyshevskij","doi":"10.15507/2079-6900.24.202204.399-418","DOIUrl":"https://doi.org/10.15507/2079-6900.24.202204.399-418","url":null,"abstract":"Abstract. One of modern global optimization algorithms is method of Strongin and Piyavskii modified by Sergeev and Kvasov diagonal approach. In recent paper we propose an extension of this approach to continuous multivariable functions defined on the multidimensional parallelepiped. It is known that Sergeev and Kvasov method applies only to a Lipschitz continuous function though it effectively extends one-dimensional algorithm to multidimensional case. So authors modify We modify mentioned method to a continuous functions using introduced by Vanderbei ε-Lipschitz property that generalizes conventional Lipschitz inequality. Vanderbei proved that a real valued function is uniformly continuous on a convex domain if and only if it is ε-Lipschitz. Because multidimensional parallelepiped is a convex compact set, we demand objective function to be only continuous on a search domain. We describe extended Strongin’s and Piyavskii’s methods in the Sergeev and Kvasov modification and prove the sufficient conditions for the convergence. As an example of proposed method’s application, at the end of this article we show numerical optimization results of different continuous but not Lipschitz functions using three known partition strategies: “partition on 2”, “partition on 2N” and “effective”. For the first two of them we present formulas for computing a new iteration point and for recalculating the ε-Lipschitz constant estimate. We also show algorithm modification that allows to find a new search point on any algorithm’s step.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124765360","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

Method for calculating radiative energy transfer in the “back and forth” approximation “前后”近似下辐射能量传递的计算方法

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-12-31 DOI: 10.15507/2079-6900.24.202204.436-451

Alexander Ju. Krukovskiy, M. Ladonkina, Yuri A. Poveshchenko, I. Popov

{"title":"Method for calculating radiative energy transfer in the “back and forth” approximation","authors":"Alexander Ju. Krukovskiy, M. Ladonkina, Yuri A. Poveshchenko, I. Popov","doi":"10.15507/2079-6900.24.202204.436-451","DOIUrl":"https://doi.org/10.15507/2079-6900.24.202204.436-451","url":null,"abstract":"Abstract. This paper presents a method for calculating the radiative energy transfer in the back and forth approximation for the case of cylindrically symmetric currents. The key element of the method is the scheme for calculating radiative heat transfer in a medium with opacity that strongly varies in space and time. The paper discusses the possibility of improving accuracy of solving a difference equations’ system by making the approximation of absorption coefficients more accurate. The numerical technique proposed for multi-parameter computing experiments makes it possible to obtain the radiation energy density as a quadrature of plasma opacity and emissivity. In two-temperature model of gas dynamics and magnetohydrodynamics, this determines the contribution of radiative heat transfer into the energy balance of the plasma electronic component. Numerical comparison of the proposed method with some diffusion methods was implemented via test examples simulating spatial inhomogeneity of the radiation field. It is shown that the calculations performed according to the methodology considered in this paper, give a qualitatively correct match with the analytical solution of the problem, in contrast to calculations performed by the method of diffuse approximation. The obvious advantage of the back and forth approximation is that integrality is inherent in its structure.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134342802","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

Analysis of methods for modeling human daily thermometry data 人体日测温数据建模方法分析

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-12-31 DOI: 10.15507/2079-6900.24.202204.469-484

Marina A. Shugurova, A. Tsyganov, Yu. V. Tsyganova

{"title":"Analysis of methods for modeling human daily thermometry data","authors":"Marina A. Shugurova, A. Tsyganov, Yu. V. Tsyganova","doi":"10.15507/2079-6900.24.202204.469-484","DOIUrl":"https://doi.org/10.15507/2079-6900.24.202204.469-484","url":null,"abstract":"Abstract. Mathematical and computer modeling of daily thermometry allows to study processes of human thermal homeostasis more deeply. In practice, thermometry data is obtained using a digital thermometer, which autonomously reads the temperature of human skin in certain time intervals. The aim of present work is to analyse the methods of modeling and processing of human daily thermometry data. The first method consists in applying linear discrete stochastic models in the state space with Gaussian noises and known vector of input actions, while the estimation of the state vector is performed by discrete covariance Kalman filter. The second method assumes that the vector of input actions is unknown, and the S. Gillijns and B.D. Moor algorithm is used to process daily thermometry data. An alternative option is to use a model with an extended state vector and a Kalman filtering algorithm. The third method takes into account the presence of anomalous measurements (outliers) in the measurement data, and correntropy filter is proposed for their effective filtering. Numerical experiments for modeling and processing of daily thermometry data in MATLAB were carried out in order to compare the quality of discrete filtering algorithms. Modeling of thermometry data was carried out using a three-dimensional model 3dDRCM (3-dimension Discrete-time Real-valued Canonical Model). The results obtained can be used in the study of human daily thermometry processes, for example, to study the reaction of the athlete’s body to the received load.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121423635","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 simulation of selective laser melting by the SPH method 选择性激光熔化的SPH法数值模拟

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-12-31 DOI: 10.15507/2079-6900.24.202204.419-435

Alexander N. Bykov, Marina N. Vishnyakova, Y. Deryugin, Andrey B. Emelyanov, Alexey A. Lazarev, S. N. Polishchuk, Christina V. Cherenkova

{"title":"Numerical simulation of selective laser melting by the SPH method","authors":"Alexander N. Bykov, Marina N. Vishnyakova, Y. Deryugin, Andrey B. Emelyanov, Alexey A. Lazarev, S. N. Polishchuk, Christina V. Cherenkova","doi":"10.15507/2079-6900.24.202204.419-435","DOIUrl":"https://doi.org/10.15507/2079-6900.24.202204.419-435","url":null,"abstract":"Abstract. Currently, additive manufacturing technologies develop actively. This requires creation of computational methods to describe physical processes occurring at the time of manufacturing. One of the methods used for the production of metal powder parts is the method of selective laser melting. This paper presents an SPH-based numerical technique for modeling the process of powder sintering under the influence of a laser beam. The flow of liquid formed as a result of melting is described by the Navier-Stokes equations. Pressure forces, viscous effects and surface forces at the interface are included in the force balance. The thermal state is determined from the energy conservation law, which takes into account thermal processes, volumetric absorption of laser radiation energy, convective heat exchange with the external environment and radiation. Phase transitions between solid and liquid phases are described in the framework of the generalized formulation of the Stefan problem. The calculation method is verified on tests specific to the class of problems under consideration. A comparison is made with the analytical solution, as well as with solutions obtained by other modifications of the SPH method, and with experimental data.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133129898","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

Peridynamics method for problems solve of solids destruction 固体破坏问题求解的周动力学方法

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-12-31 DOI: 10.15507/2079-6900.24.202204.452-468

Dmitry A. Shishkanov, Maxim V. Vetchinnikov, Y. Deryugin

{"title":"Peridynamics method for problems solve of solids destruction","authors":"Dmitry A. Shishkanov, Maxim V. Vetchinnikov, Y. Deryugin","doi":"10.15507/2079-6900.24.202204.452-468","DOIUrl":"https://doi.org/10.15507/2079-6900.24.202204.452-468","url":null,"abstract":"Abstract. The article investigates the method of peridynamics, which is an alternative approach to solving destruction problems based on integral equations. It is assumed that particles in a continuum interact with each other at a finite distance, as in molecular dynamics. Damage is part of the theory at the level of two-particle interactions, so damage finding and destruction occurs when solving the equation of motion. During this work, bondbased and state-based peridynamics models of destruction used in the Sandia Laboratory were described and implemented within the framework of the MoDyS molecular dynamics software package. In the bond-based model, the defining relationship is the bond stiffness function, which corrects the force of particle-particle interaction and imposes a restriction on the use of the Poisson’s ratio. The state-based model generalizes the bond-based approach and may be applied to materials with any Poisson’s ratio. The relationship of both models is ascertained. Calculation convergence is demonstrated on the example of a one-dimensional elasticity problem. The possibility of using the implemented models for fracture problems is also shown.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125182427","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

PID controllers with delay in a problem of stabilization of robotic manipulators’ desired motions 具有时滞的PID控制器在机器人期望运动镇定问题中的应用

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-09-30 DOI: 10.15507/2079-6900.24.202203.267-279

A. Andreev, Lubov V. Kolegova

引用次数: 1

Theoretical study of stability of nodal completely conservative difference schemes with viscous filling for gas dynamics equations in Euler variables 欧拉变量气体动力学方程粘性填充节点完全保守差分格式稳定性的理论研究

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-09-30 DOI: 10.15507/2079-6900.24.202203.317-330

M. Ladonkina, Yu.A. Poveshenko, Orkhan R. Ragimli, Haochen Zhang

{"title":"Theoretical study of stability of nodal completely conservative difference schemes with viscous filling for gas dynamics equations in Euler variables","authors":"M. Ladonkina, Yu.A. Poveshenko, Orkhan R. Ragimli, Haochen Zhang","doi":"10.15507/2079-6900.24.202203.317-330","DOIUrl":"https://doi.org/10.15507/2079-6900.24.202203.317-330","url":null,"abstract":"For the equations of gas dynamics in Eulerian variables, a family of twolayer time-fully conservative difference schemes (FCDS) with space-profiled time weights is investigated. Nodal schemes and a class of divergent adaptive viscosities for FCDS with spacetime profiled weights connected with variable masses of moving nodal particles of the medium are developed. Considerable attention is paid to the methods of constructing regularized flows of mass, momentum and internal energy that preserve the properties of fully conservative difference schemes of this class, to the analysis of their stability and to the possibility of their use on uneven grids. The effective preservation of the internal energy balance in this class of divergent difference schemes is ensured by the absence of constantly operating sources of difference origin that produce “computational” entropy (including entropy production on the singular features of the solution). Developed schemes may be used in modelling of hightemperature flows in temperature-disequilibrium media, for example, if it is necessary to take into account the electron-ion relaxation of temperature in a short-living plasma under conditions of intense energy input.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"210 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":"132075571","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

Lp -approximations for solutions of parabolic differential equations on manifolds 流形上抛物型微分方程解的Lp逼近

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-09-30 DOI: 10.15507/2079-6900.24.202203.297-303

A. Smirnova

引用次数: 0

Fast converging Chernoff approximations to the solution of heat equation with variable coefficient of thermal conductivity 变导热系数热方程解的快速收敛Chernoff近似

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-09-30 DOI: 10.15507/2079-6900.24.202203.280-288

A. V. Vedenin

{"title":"Fast converging Chernoff approximations to the solution of heat equation with variable coefficient of thermal conductivity","authors":"A. V. Vedenin","doi":"10.15507/2079-6900.24.202203.280-288","DOIUrl":"https://doi.org/10.15507/2079-6900.24.202203.280-288","url":null,"abstract":"This paper is devoted to a new method for constructing approximations to the solution of a parabolic partial differential equation. The Cauchy problem for the heat equation on a straight line with a variable heat conduction coefficient is considered. In this paper, a sequence of functions is constructed that converges to the solution of the Cauchy problem uniformly in the spatial variable and locally uniformly in time. The functions that make up the sequence are explicitly expressed in terms of the initial condition and the thermal conductivity coefficient, i.e. through functions that play the role of parameters. When constructing functions that converge to the solution, ideas and methods of functional analysis are used, namely, Chernoff's theorem on approximation of operator semigroups, which is why the constructed functions are called Chernoff approximations. In most previously published papers, the error (i. e., the norm of the difference between the exact solution and the Chernoff approximation with number n) does not exceed const/n. Therefore, approximations, when using which the error decreases to zero faster than const/n, we call fast convergent. This is exactly what the approximations constructed in this work are, as follows from the recently proved Galkin-Remizov theorem. Key formulas, explicit forms of constructed approximations, and proof schemes are given in the paper. The results obtained in this paper point the way to the construction of fast converging Chernoff approximations for a wider class of equations.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"22 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":"117026925","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