{"title":"Duality and effective conductivity of random two-phase flat systems","authors":"S.A. Bulgadaev","doi":"10.1016/S0375-9601(03)00648-0","DOIUrl":null,"url":null,"abstract":"<div><div>The possible functional forms of the effective conductivity <em>σ</em><sub><em>e</em></sub> of the randomly inhomogeneous two-phase systems at arbitrary values of concentrations are discussed. Two explicit approximate expressions for effective conductivity are found using a duality relation, a series expansion of <em>σ</em><sub><em>e</em></sub> in the inhomogeneity parameter <em>z</em> and some additional conjectures about functional form of <em>σ</em><sub><em>e</em></sub>. They differ from the effective medium approximation, satisfy all necessary requirements and reproduce the known formulas for <em>σ</em><sub><em>e</em></sub> in weakly inhomogeneous case. This can signify also that <em>σ</em><sub><em>e</em></sub> of the two-phase randomly inhomogeneous systems may be a nonuniversal function, depending on some details of the structure of the random inhomogeneities.</div></div>","PeriodicalId":20172,"journal":{"name":"Physics Letters A","volume":"313 1","pages":"Pages 106-111"},"PeriodicalIF":2.6000,"publicationDate":"2003-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physics Letters A","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0375960103006480","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The possible functional forms of the effective conductivity σe of the randomly inhomogeneous two-phase systems at arbitrary values of concentrations are discussed. Two explicit approximate expressions for effective conductivity are found using a duality relation, a series expansion of σe in the inhomogeneity parameter z and some additional conjectures about functional form of σe. They differ from the effective medium approximation, satisfy all necessary requirements and reproduce the known formulas for σe in weakly inhomogeneous case. This can signify also that σe of the two-phase randomly inhomogeneous systems may be a nonuniversal function, depending on some details of the structure of the random inhomogeneities.
期刊介绍：
Physics Letters A offers an exciting publication outlet for novel and frontier physics. It encourages the submission of new research on: condensed matter physics, theoretical physics, nonlinear science, statistical physics, mathematical and computational physics, general and cross-disciplinary physics (including foundations), atomic, molecular and cluster physics, plasma and fluid physics, optical physics, biological physics and nanoscience. No articles on High Energy and Nuclear Physics are published in Physics Letters A. The journal''s high standard and wide dissemination ensures a broad readership amongst the physics community. Rapid publication times and flexible length restrictions give Physics Letters A the edge over other journals in the field.
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