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Bulletin of Abai KazNPU. Series of Physical and mathematical sciences
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Vol. 81 No. 1 (2023)

ON AN ASYMPTOTICAL FORMULA FOR COMPLEX-VALUED PERMITTIVITY OF RANDOM COMPOSITES

Published March 2023

241

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V. Mityushev+−
Cracow University of Technology
T. Gric+−
Center for Physical Sciences and Technology
Zh. Zhunussova+−
Al-Farabi Kazakh National University, Institute of Mathematics and Mathematical Modeling
K. Dosmagulova+−
Al-Farabi Kazakh National University, Institute of Mathematics and Mathematical Modeling
Cracow University of Technology
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V. Mityushev

Faculty of Computer Science and Telecommunications, Professor

Center for Physical Sciences and Technology
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T. Gric

Professor of Department of Electronic Systems

Al-Farabi Kazakh National University, Institute of Mathematics and Mathematical Modeling
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Zh. Zhunussova

Department of Mathematics, Professor

Al-Farabi Kazakh National University, Institute of Mathematics and Mathematical Modeling
DOI: 10.51889/2959-5894.2023.81.1.002
Abstract

The - 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 analytical functions. The considered problem arises in the homogenization procedure of random media with complex constants which express the permittivity of components. A new asymptotical 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. Glioma cells are modeled by elliptic inclusion and neuron cells by disks. In the considered two-phase medium, the dependencies of permittivity of glioma and neuron on the frequency and their different shapes can allow to investigate the impact of the tumor cells morphology on the effective permittivity tensor expressed through the complex gradient.

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Keywords
R - linear boundary value problem, Riemann-Hilbert problem, analytic function, permittivity tensor, flat torus, inclusion.
Language

English

How to Cite

[1]
Mityushev, V., Gric, T., Zhunussova, Z. and Dosmagulova, K. 2023. ON AN ASYMPTOTICAL FORMULA FOR COMPLEX-VALUED PERMITTIVITY OF RANDOM COMPOSITES. Bulletin of Abai KazNPU. Series of Physical and mathematical sciences. 81, 1 (Mar. 2023), 18–27. DOI:https://doi.org/10.51889/2959-5894.2023.81.1.002.