Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semi-analytical computation of Laplacian Green functions in
  three-dimensional domains with disconnected spherical boundaries   We apply the generalized method of separation of variables (GMSV) to solve
boundary value problems for the Laplace operator in three-dimensional domains
with disconnected spherical boundaries (i.e., an arbitrary configuration of
non-overlapping partially reactive spherical sinks or obstacles). We consider
both exterior and interior problems and all most common boundary conditions:
Dirichlet, Neumann, Robin, and conjugate one. Using the translational addition
theorems for solid harmonics to switch between the local spherical coordinates,
we obtain a semi-analytical expression of the Green function as a linear
combination of partial solutions whose coefficients are fixed by boundary
conditions. Although the numerical computation of the coefficients involves
series truncation and matrix inversion, the use of the solid harmonics as basis
functions naturally adapted to the intrinsic symmetries of the problem makes
the GMSV particularly efficient, especially for exterior problems. The obtained
Green function is the key ingredient to solve boundary value problems and to
determine various characteristics of stationary diffusion such as reaction
rate, escape probability, harmonic measure, residence time, and mean first
passage time, to name but a few. The relevant aspects of the numerical
implementation and potential applications in chemical physics, heat transfer,
electrostatics, and hydrodynamics are discussed.

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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: math