{"title":"Inverse Problem for a Distributed System from Pulse Technology","authors":"R. V. Khachaturov","doi":"10.1134/s1064230723060060","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>An inverse problem with distributed parameters for the process of the self-focusing of cylindrical X-ray pulses in a plasma is considered, and a mathematical model of the studied process in a cylindrical coordinate system is described, taking into account the symmetry of the pulse relative to the direction of its propagation. A similar process in the case of plane pulses is compared, a computational method for solving the direct problem of interaction between the plasma and pulse for the given parameter values is presented, the second order of approximation and the asymptotic stability of the constructed difference scheme are proved. It is proposed to use the equivalence set method to solve the inverse problem of determining the initial parameters of the plasma and pulse from the shape of a cylindrical X-ray pulse passing through it and the dynamics of its maximum intensity. Using this problem as an example, an algorithm for using the equivalence set method to solve inverse problems is described.</p>","PeriodicalId":50223,"journal":{"name":"Journal of Computer and Systems Sciences International","volume":"151 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computer and Systems Sciences International","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1134/s1064230723060060","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
Abstract
An inverse problem with distributed parameters for the process of the self-focusing of cylindrical X-ray pulses in a plasma is considered, and a mathematical model of the studied process in a cylindrical coordinate system is described, taking into account the symmetry of the pulse relative to the direction of its propagation. A similar process in the case of plane pulses is compared, a computational method for solving the direct problem of interaction between the plasma and pulse for the given parameter values is presented, the second order of approximation and the asymptotic stability of the constructed difference scheme are proved. It is proposed to use the equivalence set method to solve the inverse problem of determining the initial parameters of the plasma and pulse from the shape of a cylindrical X-ray pulse passing through it and the dynamics of its maximum intensity. Using this problem as an example, an algorithm for using the equivalence set method to solve inverse problems is described.
摘要 考虑到脉冲相对于其传播方向的对称性，研究了等离子体中圆柱形 X 射线脉冲自聚焦过程的分布参数逆问题，并描述了在圆柱坐标系中研究过程的数学模型。比较了平面脉冲情况下的类似过程，提出了在给定参数值下直接解决等离子体和脉冲之间相互作用问题的计算方法，证明了所构建差分方案的二阶近似性和渐进稳定性。建议使用等价集方法来解决逆问题，即根据穿过等离子体的圆柱形 X 射线脉冲的形状及其最大强度的动态来确定等离子体和脉冲的初始参数。以这个问题为例，描述了使用等价集方法解决逆问题的算法。
期刊介绍：
Journal of Computer and System Sciences International is a journal published in collaboration with the Russian Academy of Sciences. It covers all areas of control theory and systems. The journal features papers on the theory and methods of control, as well as papers devoted to the study, design, modeling, development, and application of new control systems. The journal publishes papers that reflect contemporary research and development in the field of control. Particular attention is given to applications of computer methods and technologies to control theory and control engineering. The journal publishes proceedings of international scientific conferences in the form of collections of regular journal articles and reviews by top experts on topical problems of modern studies in control theory.
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