An asymptotic homogenization formula for complex permittivity and its application

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Advances in the Theory of Nonlinear Analysis and its Application
Volume:7 Issue:1
An asymptotic homogenization formula for complex permittivity and its application

An asymptotic homogenization formula for complex permittivity and its application

Authors : Vladimir MİTYUSHEV, Tatjana GRİC, Zh Kh ZHUNUSSOVA, Karlygash DOSMAGULOVA

Pages : 243-252

Doi:10.31197/atnaa.1223064

View : 92 | Download : 107

Publication Date : 2023-03-31

Article Type : Research Paper

Abstract :The $\\mathbb R$-linear boundary value problem in a multiply connected domain on a flat torus is considered. This problem is closely related to the Riemann-Hilbert problem on analytic functions. The considered problem arises in the homogenization procedure of random media with complex constants which express the permittivity of components. A new asymptotic formula for the effective permittivity tensor is derived. The formula contains location of inclusions in symbolic form. The application of the derived formula to investigation of the morphology of the tumor cells in disordered biological media is discussed.
Keywords : Composites, Asymptotic formulas, homogenization

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