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Dipolar response of an ellipsoidal particle with an anisotropic coating

Ambjörnsson, T LU and Mukhopadhyay, G (2003) In Journal of Physics A: Mathematical and General 36(42). p.10651-10665
Abstract
In this paper we study the response of an ellipsoidal particle with a dielectrically anisotropic coating (the coating dielectric function being different parallel and perpendicular to the coating normal) placed in a constant external electric field. For the coating region we find that potential can be written in terms of solutions to a one-dimensional Heun's equation which is derived from the three-dimensional Gauss equation for the potential in ellipsoidal coordinates. We give solutions to Heun's equation in three forms: for the general case we obtain solutions in terms of a series expansion. For the case of spheroidal particles we write the solutions using hypergeometric functions. For large coating anisotropy we derive a simple form of... (More)
In this paper we study the response of an ellipsoidal particle with a dielectrically anisotropic coating (the coating dielectric function being different parallel and perpendicular to the coating normal) placed in a constant external electric field. For the coating region we find that potential can be written in terms of solutions to a one-dimensional Heun's equation which is derived from the three-dimensional Gauss equation for the potential in ellipsoidal coordinates. We give solutions to Heun's equation in three forms: for the general case we obtain solutions in terms of a series expansion. For the case of spheroidal particles we write the solutions using hypergeometric functions. For large coating anisotropy we derive a simple form of the solution for the potential. The inside of the ellipsoid and the surroundings are assumed dielectrically isotropic and the potential is therefore given by standard results. By matching the solutions across the boundaries we obtain the ellipsoidal particle polarizability, which is written in terms of the standard depolarization factors and logarithmic derivatives of the Heun's equation solutions. The results above also allow us to obtain the magnetic polarizability of a coated ellipsoid in a constant external magnetic field. (Less)
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author
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Physics A: Mathematical and General
volume
36
issue
42
pages
10651 - 10665
publisher
IOP Publishing
external identifiers
  • scopus:0242287842
ISSN
0305-4470
DOI
10.1088/0305-4470/36/42/016
language
English
LU publication?
no
id
aa598e90-7e73-45c1-af79-d77282c1e3c1
date added to LUP
2019-05-03 11:47:45
date last changed
2019-08-06 15:51:08
@article{aa598e90-7e73-45c1-af79-d77282c1e3c1,
  abstract     = {In this paper we study the response of an ellipsoidal particle with a dielectrically anisotropic coating (the coating dielectric function being different parallel and perpendicular to the coating normal) placed in a constant external electric field. For the coating region we find that potential can be written in terms of solutions to a one-dimensional Heun's equation which is derived from the three-dimensional Gauss equation for the potential in ellipsoidal coordinates. We give solutions to Heun's equation in three forms: for the general case we obtain solutions in terms of a series expansion. For the case of spheroidal particles we write the solutions using hypergeometric functions. For large coating anisotropy we derive a simple form of the solution for the potential. The inside of the ellipsoid and the surroundings are assumed dielectrically isotropic and the potential is therefore given by standard results. By matching the solutions across the boundaries we obtain the ellipsoidal particle polarizability, which is written in terms of the standard depolarization factors and logarithmic derivatives of the Heun's equation solutions. The results above also allow us to obtain the magnetic polarizability of a coated ellipsoid in a constant external magnetic field.},
  author       = {Ambjörnsson, T and Mukhopadhyay, G},
  issn         = {0305-4470},
  language     = {eng},
  month        = {10},
  number       = {42},
  pages        = {10651--10665},
  publisher    = {IOP Publishing},
  series       = {Journal of Physics A: Mathematical and General},
  title        = {Dipolar response of an ellipsoidal particle with an anisotropic coating},
  url          = {http://dx.doi.org/10.1088/0305-4470/36/42/016},
  doi          = {10.1088/0305-4470/36/42/016},
  volume       = {36},
  year         = {2003},
}