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Advances in Condensed Matter Physics
Volume 2017, Article ID 8963839, 4 pages
Research Article

Stability and Dissipation of Many Components’ Systems and Application to Metamaterials

1Theoretical Physics Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam
2Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam

Correspondence should be addressed to Valeriy E. Arkhincheev; nv.ude.tdt@veehcnihkra.yirelav

Received 28 February 2017; Accepted 5 April 2017; Published 30 April 2017

Academic Editor: Xian-Ping Chen

Copyright © 2017 Valeriy E. Arkhincheev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Dykhne’s method, based on rotational symmetry of two-dimensional equations of constant direct current, was applied to study the properties of the medium, consisting of reactances—of inductors and capacitors (nondissipative elements). The exact solution for the 4-component system consisting of the two different types of 2 inductors and 2 capacitors, randomly placed and connected, was obtained. The obtained solution for investigated system has the two features: (1) the finite dissipation in the nondissipative system of inductors and capacitors; (2) appearance of plateau—the constant value of effective conductivity in a wide range of concentrations of components. The obtained results were useful for description of composite metamaterials.