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Fractal planetary rings: energy inequalities and random field model
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. (MAM)ORCID-id: 0000-0002-0139-0747
University of Illinois at Urbana-Champaign, USA.ORCID-id: 0000-0002-3493-363X
2017 (engelsk)Inngår i: International Journal of Modern Physics B, ISSN 0217-9792, Vol. 31, nr 30, artikkel-id 1750236Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

This study is motivated by a recent observation, based on photographs from the Cassini mission, that Saturn’s rings have a fractal structure in radial direction. Accordingly, two questions are considered: (1) What Newtonian mechanics argument in support of such a fractal structure of planetary rings is possible? (2) What kinematics model of such fractal rings can be formulated? Both challenges are based on taking planetary rings’ spatial structure as being statistically stationary in time and statistically isotropic in space, but statistically nonstationary in space. An answer to the first challenge is given through an energy analysis of circular rings having a self-generated, noninteger-dimensional mass distribution [V. E. Tarasov, Int. J. Mod Phys. B 19, 4103 (2005)]. The second issue is approached by taking the random field of angular velocity vector of a rotating particle of the ring as a random section of a special vector bundle. Using the theory of group representations, we prove that such a field is completely determined by a sequence of continuous positive-definite matrix-valued functions defined on the Cartesian square F^2 of the radial cross-section F, where F is a fat fractal.

sted, utgiver, år, opplag, sider
2017. Vol. 31, nr 30, artikkel-id 1750236
Emneord [en]
Planetary rings; fractal; dynamics
HSV kategori
Forskningsprogram
matematik/tillämpad matematik
Identifikatorer
URN: urn:nbn:se:mdh:diva-36232DOI: 10.1142/S0217979217502368ISI: 000417105300012Scopus ID: 2-s2.0-85022178407OAI: oai:DiVA.org:mdh-36232DiVA, id: diva2:1131468
Tilgjengelig fra: 2017-08-14 Laget: 2017-08-14 Sist oppdatert: 2018-01-23bibliografisk kontrollert

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Malyarenko, Anatoliy

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