Dipolar response of an ellipsoidal particle with an anisotropic coating
(2003) In Journal of Physics A: Mathematical and General 36(42). p.1065110665 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 onedimensional Heun's equation which is derived from the threedimensional 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 onedimensional Heun's equation which is derived from the threedimensional 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)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/aa598e907e7345c1af79d77282c1e3c1
 author
 Ambjörnsson, T ^{LU} and Mukhopadhyay, G
 publishing date
 20031024
 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
 03054470
 DOI
 10.1088/03054470/36/42/016
 language
 English
 LU publication?
 no
 id
 aa598e907e7345c1af79d77282c1e3c1
 date added to LUP
 20190503 11:47:45
 date last changed
 20190806 15:51:08
@article{aa598e907e7345c1af79d77282c1e3c1, 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 onedimensional Heun's equation which is derived from the threedimensional 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 = {03054470}, language = {eng}, month = {10}, number = {42}, pages = {1065110665}, 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/10.1088/03054470/36/42/016}, doi = {10.1088/03054470/36/42/016}, volume = {36}, year = {2003}, }