English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We propose a powerful approach to solve Laplace's equation for point sourcesnear a spherical object. The central new idea is to use prolate spheroidalsolid harmonics, which are separable solutions of Laplace's equation inspheroidal coordinates, instead of the more natural spherical solid harmonics.We motivate this choice and show that the resulting series expansions convergemuch faster. This improvement is discussed in terms of the singularity of thesolution and its analytic continuation. The benefits of this approach areillustrated for a specific example: the calculation of modified decay rates oflight emitters close to nanostructures in the long-wavelength approximation. Weexpect the general approach to be applicable with similar benefits to a varietyof other contexts, from other geometries to other equations of mathematicalphysics.

Spheroidal harmonic expansions for the solution of Laplace's equation for a point source near a sphere