{"title":"A generalized differential scheme for the effective conductivity of percolating microinhomogeneous materials with the Hall effect","authors":"Anatoly Markov , Mikhail Markov , Valery Levin","doi":"10.1016/j.ijengsci.2024.104175","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we propose a self-consistent scheme for the calculation of the components of the effective electrical conductivity tensor. The calculations were fulfilled for a microinhomogeneous material, the components of which have the Hall effect. The presence of the Hall effect leads to appearance of asymmetry of the components of the conductivity tensor and to dependence of these components on the magnitude of the magnetic field applied to the material. Our approach is based on the Generalized Differential Effective Medium (GDEM) method. This method generalizes the classical differential scheme (DEM) for the case of several inclusion types instead of one. In this case, the GDEM scheme leads to a system of matrix differential equations that were solved numerically. This solution was obtained for materials containing spherical or cylindrical inclusions (3D and 2D-problems). In the case of cylindrical inclusions, the results were obtained for inclusions with the symmetry axes orthogonal to the magnetic field. The application of the GDEM method allows us to consider the percolation effect for 2D and 3D-microheterogeneous materials. The results obtained are compared to the experimental data and the calculation results obtained by other self-consistent schemes.</div></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"206 ","pages":"Article 104175"},"PeriodicalIF":5.7000,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Engineering Science","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0020722524001599","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we propose a self-consistent scheme for the calculation of the components of the effective electrical conductivity tensor. The calculations were fulfilled for a microinhomogeneous material, the components of which have the Hall effect. The presence of the Hall effect leads to appearance of asymmetry of the components of the conductivity tensor and to dependence of these components on the magnitude of the magnetic field applied to the material. Our approach is based on the Generalized Differential Effective Medium (GDEM) method. This method generalizes the classical differential scheme (DEM) for the case of several inclusion types instead of one. In this case, the GDEM scheme leads to a system of matrix differential equations that were solved numerically. This solution was obtained for materials containing spherical or cylindrical inclusions (3D and 2D-problems). In the case of cylindrical inclusions, the results were obtained for inclusions with the symmetry axes orthogonal to the magnetic field. The application of the GDEM method allows us to consider the percolation effect for 2D and 3D-microheterogeneous materials. The results obtained are compared to the experimental data and the calculation results obtained by other self-consistent schemes.
期刊介绍:
The International Journal of Engineering Science is not limited to a specific aspect of science and engineering but is instead devoted to a wide range of subfields in the engineering sciences. While it encourages a broad spectrum of contribution in the engineering sciences, its core interest lies in issues concerning material modeling and response. Articles of interdisciplinary nature are particularly welcome.
The primary goal of the new editors is to maintain high quality of publications. There will be a commitment to expediting the time taken for the publication of the papers. The articles that are sent for reviews will have names of the authors deleted with a view towards enhancing the objectivity and fairness of the review process.
Articles that are devoted to the purely mathematical aspects without a discussion of the physical implications of the results or the consideration of specific examples are discouraged. Articles concerning material science should not be limited merely to a description and recording of observations but should contain theoretical or quantitative discussion of the results.