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Fractal planetary rings: energy inequalities and random field model
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (Mathematics/Applied Mathematics)ORCID iD: 0000-0002-0139-0747
University of Illinois at Urbana-Champaign, USA.ORCID iD: 0000-0002-3493-363X
(English)In: International Journal of Modern Physics B, ISSN 0217-9792Article in journal (Refereed) Epub ahead of print
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.

Keyword [en]
Planetary rings; fractal; dynamics
National Category
Astronomy, Astrophysics and Cosmology Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-36232DOI: 10.1142/S0217979217502368OAI: oai:DiVA.org:mdh-36232DiVA: diva2:1131468
Available from: 2017-08-14 Created: 2017-08-14 Last updated: 2017-08-24Bibliographically approved

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Publisher's full texthttp://www.worldscientific.com/doi/abs/10.1142/S0217979217502368

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Malyarenko, AnatoliyOstoja-Starzewski, Martin
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Astronomy, Astrophysics and CosmologyProbability Theory and Statistics

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
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