An asymptotic homogenization formula for complex permittivity and its application

Vladimir Mityushev; Tatjana Gric; Zhanat Zhunussova; Karlygash Dosmagulova

doi:10.31197/ATNAA.1223064

An asymptotic homogenization formula for complex permittivity and its application

Vladimir Mityushev, Tatjana Gric, Zhanat Zhunussova, Karlygash Dosmagulova

Research output: Contribution to journal › Article › peer-review

Abstract

The R-linear boundary value problem in a multiply con-nected 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 compo-nents. 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 morphol-ogy of the tumor cells in disordered biological media is discussed.

Original language	English
Pages (from-to)	243-252
Number of pages	10
Journal	Advances in the Theory of Nonlinear Analysis and its Applications
Volume	7
Issue number	1
DOIs	https://doi.org/10.31197/ATNAA.1223064
Publication status	Published - 31 Mar 2023

Bibliographical note

Funding Information:
This research, V. Mityushev, Zh. Zhunussova and K. Dosmagulova, is funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP08856381). Tatjana Gric was supported by the European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska Curie grant agreement No 713694.

Publisher Copyright:
© 2023, DergiPark. All rights reserved.

Keywords

Asymptotic formulas
Composites
homogenization

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An asymptotic homogenization formulaFinal published version, 196 KB

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N2 - The R-linear boundary value problem in a multiply con-nected 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 compo-nents. 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 morphol-ogy of the tumor cells in disordered biological media is discussed.

AB - The R-linear boundary value problem in a multiply con-nected 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 compo-nents. 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 morphol-ogy of the tumor cells in disordered biological media is discussed.

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KW - Composites

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JF - Advances in the Theory of Nonlinear Analysis and its Applications

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ER -

An asymptotic homogenization formula for complex permittivity and its application

Abstract

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Keywords

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