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Homogenization of spherical inclusions

Kristensson, Gerhard LU (2003) In Progress in Electromagnetics Research-Pier PIER 42. p.1-25
Abstract
The homogenization of cubically arranged, homogeneous

spherical inclusions in a background material is addressed. This is

accomplished by the solution of a local problem in the unit cell.

An exact series representation of the effective relative permittivity of

the heterogeneous material is derived, and the functional behavior

for small radii of the spheres is given. The solution is utilizing

the translation properties of the solutions to the Laplace equation

in spherical coordinates. A comparison with the classical mixture

formulas, e.g., the Maxwell Garnett formula, the Bruggeman formula,

and the Rayleigh formula, shows that all classical mixture... (More)
The homogenization of cubically arranged, homogeneous

spherical inclusions in a background material is addressed. This is

accomplished by the solution of a local problem in the unit cell.

An exact series representation of the effective relative permittivity of

the heterogeneous material is derived, and the functional behavior

for small radii of the spheres is given. The solution is utilizing

the translation properties of the solutions to the Laplace equation

in spherical coordinates. A comparison with the classical mixture

formulas, e.g., the Maxwell Garnett formula, the Bruggeman formula,

and the Rayleigh formula, shows that all classical mixture formulas

are correct to the first (dipole) order, and, moreover, that the Maxwell

Garnett formula predicts several higher order terms correctly. The

solution is in agreement with the Hashin-Shtrikman limits. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Progress in Electromagnetics Research-Pier
volume
PIER 42
pages
1 - 25
publisher
EMW Publishing
external identifiers
  • scopus:12844254899
ISSN
1070-4698
DOI
language
English
LU publication?
yes
id
b55e305c-4257-45df-8f5d-bdffc9a8828a (old id 531308)
date added to LUP
2008-02-26 14:30:07
date last changed
2018-05-29 10:54:31
@article{b55e305c-4257-45df-8f5d-bdffc9a8828a,
  abstract     = {The homogenization of cubically arranged, homogeneous<br/><br>
spherical inclusions in a background material is addressed. This is<br/><br>
accomplished by the solution of a local problem in the unit cell.<br/><br>
An exact series representation of the effective relative permittivity of<br/><br>
the heterogeneous material is derived, and the functional behavior<br/><br>
for small radii of the spheres is given. The solution is utilizing<br/><br>
the translation properties of the solutions to the Laplace equation<br/><br>
in spherical coordinates. A comparison with the classical mixture<br/><br>
formulas, e.g., the Maxwell Garnett formula, the Bruggeman formula,<br/><br>
and the Rayleigh formula, shows that all classical mixture formulas<br/><br>
are correct to the first (dipole) order, and, moreover, that the Maxwell<br/><br>
Garnett formula predicts several higher order terms correctly. The<br/><br>
solution is in agreement with the Hashin-Shtrikman limits.},
  author       = {Kristensson, Gerhard},
  issn         = {1070-4698},
  language     = {eng},
  pages        = {1--25},
  publisher    = {EMW Publishing},
  series       = {Progress in Electromagnetics Research-Pier},
  title        = {Homogenization of spherical inclusions},
  url          = {http://dx.doi.org/},
  volume       = {PIER 42},
  year         = {2003},
}