{"title":"Quantitative analysis for rod-shaped inclusion in three-dimensional conductivity problem","authors":"Youjun Deng, Ghadir Shokor","doi":"10.1002/mma.10541","DOIUrl":null,"url":null,"abstract":"<p>We show a quantitative analysis of the perturbed electric field of a 3D anisotropic conductive rod geometry embedded in homogeneous background, which is an extension of the work in 2D case. The solution to the perturbed problem is presented by layer potential techniques, and dedicated asymptotic analysis is employed for characterization of the density function. The asymptotic result shows that near the high curvature boundary of the rod, the electric field is much strong, compared with other parts adjacent to the rod.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"4212-4231"},"PeriodicalIF":1.8000,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.10541","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
We show a quantitative analysis of the perturbed electric field of a 3D anisotropic conductive rod geometry embedded in homogeneous background, which is an extension of the work in 2D case. The solution to the perturbed problem is presented by layer potential techniques, and dedicated asymptotic analysis is employed for characterization of the density function. The asymptotic result shows that near the high curvature boundary of the rod, the electric field is much strong, compared with other parts adjacent to the rod.
期刊介绍：
Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome.
Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted.
Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.
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