Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spheroidal harmonic expansions for the solution of Laplace's equation
  for a point source near a sphere   We propose a powerful approach to solve Laplace's equation for point sources
near a spherical object. The central new idea is to use prolate spheroidal
solid harmonics, which are separable solutions of Laplace's equation in
spheroidal coordinates, instead of the more natural spherical solid harmonics.
We motivate this choice and show that the resulting series expansions converge
much faster. This improvement is discussed in terms of the singularity of the
solution and its analytic continuation. The benefits of this approach are
illustrated for a specific example: the calculation of modified decay rates of
light emitters close to nanostructures in the long-wavelength approximation. We
expect the general approach to be applicable with similar benefits to a variety
of other contexts, from other geometries to other equations of mathematical
physics.

20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ