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3D morphology of a random field from its 2D cross-section

Lookup NU author(s): Dr Irina Makarenko, Dr Andrew Fletcher, Professor Anvar ShukurovORCiD


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The two aspect ratios of randomly oriented triaxial ellipsoids (representing isosurfaces of an isotropic 3D random field) can be determined from a single 2D cross-section of their sample using the probability density function (PDF) of the filamentarity F of individual structures seen in cross-section (F = 0 for a circle and F = 1 for a line). The PDF of F has a robust form with a sharp maximum and truncation at larger F, and the most probable and maximum values of F are uniquely and simply related to the two aspect ratios of the triaxial ellipsoids. The parameters of triaxial ellipsoids of randomly distributed sizes can still be recovered from the PDF of F. This method is applicable to many shape-recognition problems, here illustrated by the neutral hydrogen density in the turbulent interstellar medium of the Milky Way. The gas distribution is shown to be filamentary with axis ratios of about 1:2:20.

Publication metadata

Author(s): Makarenko I, Fletcher A, Shukurov A

Publication type: Article

Publication status: Published

Journal: Monthly Notices of the Royal Astonomical Society

Year: 2015

Volume: 447

Issue: 1

Pages: L55-L59

Print publication date: 11/02/2015

Online publication date: 10/12/2014

Acceptance date: 22/10/2014

ISSN (print): 0035-8711

ISSN (electronic): 1365-2966

Publisher: Oxford University Press


DOI: 10.1093/mnrasl/slu169


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Funder referenceFunder name
RPG-097Leverhulme Trust