NOTICE: Due to a lapse in annual appropriations, most of this website is not being updated. Learn more.

Form submissions will still be accepted but will not receive responses at this time. Sections of this site for programs using non-appropriated funds (such as NVLAP) or those that are excepted from the shutdown (such as CHIPS and NVD) will continue to be updated.

U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

PUBLICATIONS

Separation of variables in an asymmetric cyclidic coordinate system

Published

Author(s)

Howard S. Cohl, Hans Volkmer

Abstract

A global analysis is presented of solutions for Laplace's equation on three-dimensional Euclidean space in one of the most general orthogonal asymmetric confocal cyclidic coordinate system which admits solutions through separation of variables. We refer to this coordinate system as five- cyclide coordinates since the coordinate surfaces are given by two confocal cyclides of genus zero, a cyclide of genus one, and two disconnected cyclides of genus zero. This coordinate system is obtained by stereographic projection of sphero-conal coordinates on four-dimensional Euclidean space. The harmonics in this coordinate system are given by products of solutions of second-order Fuchsian ordinary differential equations with five elementary singularities. The Dirichlet problem for the global harmonics in this coordinate system is solved using multiparameter spectral theory in the regions bounded by the asymmetric confocal cyclidic coordinate surfaces.
Citation
Journal of Mathematical Physics
Volume
54
Pub Type
Journals

Download Paper

https://doi.org/10.1063/1.4812321

Keywords

Separation of variables, Laplace's equation, Orthogonal curvilinear coordinate systems, Multiparameter spectral theory Orthogonal curvilinear coordinate systems, Multiparameter spectral theory
Modeling and simulation research

Citation

Cohl, H. and Volkmer, H. (2013), Separation of variables in an asymmetric cyclidic coordinate system, Journal of Mathematical Physics, [online], https://doi.org/10.1063/1.4812321 (Accessed October 22, 2025)

Issues

If you have any questions about this publication or are having problems accessing it, please contact [email protected].

Created June 27, 2013, Updated June 2, 2021
Was this page helpful?