Homogenization of spherical inclusions
(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:
https://lup.lub.lu.se/record/531308
- author
- Kristensson, Gerhard LU
- organization
- publishing date
- 2003
- 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
- 10.2528/PIER03012702
- language
- English
- LU publication?
- yes
- id
- b55e305c-4257-45df-8f5d-bdffc9a8828a (old id 531308)
- date added to LUP
- 2016-04-01 11:51:31
- date last changed
- 2022-01-26 19:14:53
@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/10.2528/PIER03012702}},
doi = {{10.2528/PIER03012702}},
volume = {{PIER 42}},
year = {{2003}},
}