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Title:
Topological data analysis and diagnostics of compressible magnetohydrodynamic turbulence
Authors:
Makarenko, I.; Bushby, P.; Fletcher, A.; Henderson, R.; Makarenko, N.; Shukurov, A.
Affiliation:
AA(School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, UK), AB(School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, UK), AC(School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, UK), AD(School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, UK), AE(Central Astronomical Observatory, Russian Academy of Sciences, 65 Pulkovskoye Chaussee, Saint-Petersburg, 196140, Russia), AF(School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, UK)
Publication:
Journal of Plasma Physics, Volume 84, Issue 4, article id. 735840403, 24 pp.
Publication Date:
08/2018
Origin:
CUP
Keywords:
astrophysical plasmas, plasma diagnostics, plasma flows
Abstract Copyright:
(c) 2018: © Cambridge University Press 2018
DOI:
10.1017/S0022377818000752
Bibliographic Code:
2018JPlPh..84d7303M

Abstract

The predictions of mean-field electrodynamics can now be probed using direct numerical simulations of random flows and magnetic fields. When modelling astrophysical magnetohydrodynamics, it is important to verify that such simulations are in agreement with observations. One of the main challenges in this area is to identify robust quantitative measures to compare structures found in simulations with those inferred from astrophysical observations. A similar challenge is to compare quantitatively results from different simulations. Topological data analysis offers a range of techniques, including the Betti numbers and persistence diagrams, that can be used to facilitate such a comparison. After describing these tools, we first apply them to synthetic random fields and demonstrate that, when the data are standardized in a straightforward manner, some topological measures are insensitive to either large-scale trends or the resolution of the data. Focusing upon one particular astrophysical example, we apply topological data analysis to H i observations of the turbulent interstellar medium (ISM) in the Milky Way and to recent magnetohydrodynamic simulations of the random, strongly compressible ISM. We stress that these topological techniques are generic and could be applied to any complex, multi-dimensional random field.
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