Abstract
The purpose of this thesis is to analyze some basic spherical structures in electrostatics using separable coordinate systems. The main emphasis is on a dielectric body immersed in a constant electric field. This setting gives rise to the concept of polarizability, which encapsulates the scattering properties of the dielectric body in a single matrix called a polarizability tensor. For simple structures, such as a sphere and ellipsoid, the polarizability tensor can be found in a closed-form. For more complicated geometries, where there is no separable coordinate system available, one usually must resort to numerical methods.
This thesis focuses on intersecting dielectric double spheres (both two- and three-dimensional). The coordinate system considered in three dimensions is a toroidal coordinate system (R-separable), which leads to an elegant numerical solution scheme (Neumann series) that can be implemented efficiently, for example, in a Java Applet. A special case of the toroidal coordinate system is the tangent sphere frame, representing spheres that intersect each other at a single point, in which the solution of the scattering problem is reduced to a second order linear ordinary differential equation with elementary coefficients. The two-dimensional double hemisphere (or double half-disk) is considered in the bipolar coordinate system, which leads to a closed form solution for the polarizability.
Translated title of the contribution | Exact solutions for some spherical electrostatic scattering problems |
---|---|
Original language | English |
Qualification | Doctor's degree |
Awarding Institution |
|
Supervisors/Advisors |
|
Publisher | |
Print ISBNs | 978-952-60-3056-2 |
Electronic ISBNs | 978-952-60-3057-9 |
Publication status | Published - 2010 |
MoE publication type | G5 Doctoral dissertation (article) |
Keywords
- toroidal coordinate system
- double sphere
- polarizability
- electrostatics
- half-cylinder