Effective properties of periodic tubular structures

TL;DR

This paper presents an exact method using Weierstrass' quasiperiodic functions to calculate the effective dielectric tensor of periodic tubular structures, with good agreement to experimental data for weakly interacting tubes.

Contribution

It introduces a novel analytical approach for determining the effective properties of periodic tubular dielectric structures using quasiperiodic functions.

Findings

Exact expression for the effective tensor derived.

Maxwell-like approximation validated against experiments.

Method applicable to weakly interacting tubes.

Abstract

A method is described to calculate effective tensor properties of a periodic array of two-phase dielectric tubes embedded in a host matrix. The method uses Weierstrass' quasiperodic functions for representation of the potential that considerably facilitates the problem and allows us to find an exact expression for the effective tensor. For weakly interacting tubes we obtain Maxwell-like approximation of the effective parameter which is in very good agreement with experimental results in considered examples.