{"title":"A Fractional-Differential Approach to Numerical Simulation of\nElectron-Induced Charging of Ferroelectrics","authors":"L. I. Moroz, A. G. Maslovskaya","doi":"10.1134/S1990478924010125","DOIUrl":null,"url":null,"abstract":"<p> The paper proposes a fractional-differential modification of the mathematical model of the\nprocess of nonstationary charging of polar dielectric materials under conditions of irradiation with\nmedium-energy electron beams. The mathematical formalization is based on a spherically\nsymmetric diffusion–drift equation with a fractional time derivative. An implicit finite-difference\nscheme is constructed using the Caputo derivative approximation. An application program has\nbeen developed in <span>Matlab</span> software\nthat implements the designed computational algorithm. Verification of an approximate solution of\nthe problem is demonstrated using a test example. The results of computational experiments to\nevaluate the characteristics of field effects of injected charges in ferroelectrics when varying the\norder of fractional differentiation in subdiffusion regimes are presented.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 1","pages":"137 - 149"},"PeriodicalIF":0.5800,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478924010125","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
The paper proposes a fractional-differential modification of the mathematical model of the
process of nonstationary charging of polar dielectric materials under conditions of irradiation with
medium-energy electron beams. The mathematical formalization is based on a spherically
symmetric diffusion–drift equation with a fractional time derivative. An implicit finite-difference
scheme is constructed using the Caputo derivative approximation. An application program has
been developed in Matlab software
that implements the designed computational algorithm. Verification of an approximate solution of
the problem is demonstrated using a test example. The results of computational experiments to
evaluate the characteristics of field effects of injected charges in ferroelectrics when varying the
order of fractional differentiation in subdiffusion regimes are presented.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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