\(S\)-continued fraction method for the investigation of a complex dielectric constant of two-components composite
type: Item
instance of: scholarly article
title: \(S\)-continued fraction method for the investigation of a complex dielectric constant of two-components composite
zbMATH Open document ID: 0888.41010
DOI: 10.1023/A:1005861519473
author: S. Tokarzewski
author: J. J. Telega
published in: Acta Applicandae Mathematicae
publication date: 1998-05-25T00:00:00Z
review text: As it was proved by Bergman (see the references cited in the bibliography), the effective dielectric constant \(\varepsilon_e\) of a two-phase medium can be expressed by means of a Stieltjes function of the ratio of the dielectric constants of both components. Starting from this representation, the authors derive its \(S\)-continued fraction and establish bounds suitable for theoretical and numerical investigation of \(\varepsilon_e\) in the complex domain. Explicit inequalities are given in the real case. As an example, these results are applied to the computation of the bulk dielectric constants for regular arrays of spheres. Moreover, bounds for the square and hexagonal arrays of cylinders are obtained numerically.
Mathematics Subject Classification ID: 41A21
Mathematics Subject Classification ID: 74E05
zbMATH DE Number: 1097678
zbMATH Keywords: composite medium
zbMATH Keywords: continued fractions
zbMATH Keywords: Stieltjes functions
zbMATH Keywords: dielectric constants
zbMATH Keywords: bounds
reviewed by: Andrei Martínez Finkelshtein
MaRDI profile type: Publication
full work available at URL: a:1005861519473
OpenAlex ID: W215154589
description: scientific article; zbMATH DE number 1097678