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

Abstract EN

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.