Homogenization of spherical inclusions
(2003) In Progress in Electromagnetics ResearchPier PIER 42. p.125 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 HashinShtrikman limits. (Less)
Please use this url to cite or link to this publication:
http://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 ResearchPier
 volume
 PIER 42
 pages
 1  25
 publisher
 EMW Publishing
 external identifiers

 scopus:12844254899
 ISSN
 10704698
 DOI
 10.2528/PIER03012702
 language
 English
 LU publication?
 yes
 id
 b55e305c425745df8f5dbdffc9a8828a (old id 531308)
 date added to LUP
 20080226 14:30:07
 date last changed
 20180107 05:28:24
@article{b55e305c425745df8f5dbdffc9a8828a, 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 HashinShtrikman limits.}, author = {Kristensson, Gerhard}, issn = {10704698}, language = {eng}, pages = {125}, publisher = {EMW Publishing}, series = {Progress in Electromagnetics ResearchPier}, title = {Homogenization of spherical inclusions}, url = {http://dx.doi.org/10.2528/PIER03012702}, volume = {PIER 42}, year = {2003}, }