Journal Article

Method of pairwise separations and its astronomical applications

A. A. Raikov and V. V. Orlov

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 418, issue 4, pages 2558-2564
Published in print December 2011 | ISSN: 0035-8711
Published online December 2011 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2011.19645.x
Method of pairwise separations and its astronomical applications

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The distribution f(l) of pairwise separations is used for studying geometric and energy-related characteristics of interacting particle systems. We present some formulae for calculating the distribution f(l) for finite regular spherical sets. We also study local properties of fractal systems and show that for small (compared to the system size) separations l one can use the asymptotic approximation f(l) ∝lD− 1 (where D is the fractal dimension). The distribution f(l) can also be used for calculating binding energies of systems having arbitrary shapes and arbitrary interaction potentials.

Keywords: gravitation; methods: statistical; large-scale structure of Universe

Journal Article.  4245 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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