Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T17:24:24.040Z Has data issue: false hasContentIssue false
  • English
  • Français

MHD Kamchatnov-Hopf soliton in the model of primordial solar nebula

Published online by Cambridge University Press:  01 September 2008

Vladimir V. Salmin
Vladimir V. Salmin*
Affiliation:
Siberian Federal University, Svobodny ave., 79, Krasnoyarsk, 660041, Russia email: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Stereographic projection of Hopf field on the 3-sphere into Euclidean 3-space is used as a model of 3D steady flow of ideal compressible fluid in MHD. In such case, flow lines are Villarceau circles lying on tori corresponding to the levels of Bernoulli function. Existence of an optimal torus with minimal relative surface free energy is shown. Beat of oscillations with wave numbers corresponding to structural radii of optimal torus leads to scaling of optimal tori. Spatial intersection of homothetic tori within one torus result in formation of cluster with the size depending on scaling factor. Optimal tori are considered as precursors of planetary orbits.

Keywords

MHDsolar system: formation
Type
Contributed Papers
Information
Proceedings of the International Astronomical Union , Volume 4 , Symposium S257: Universal Heliophysical Processes , September 2008 , pp. 523 - 525
Copyright
Copyright © International Astronomical Union 2009

References

Kamchatnov, A. M. 1982, Sov. JETP, 82, No 1, 117Google Scholar
Semenov, V. S., Korovinski, D. B., & Biernat, H. K. 2001, preprint (arXiv: physics/0111212v1)Google Scholar
Arnold, V. I. & Khesin, B. A. 1998, in Topological Methods in Hydrodynamics, (Springer-Verlag, New York)CrossRefGoogle Scholar
Gil-Merdano, O. & Llinares-Fuster, E. 2001, Math. Ann., 320, 531Google Scholar
Yampolsky, A. 2003, Acta Math. Hungar., 101, 73Google Scholar
Gibbons, G. W. 2006, Applications of Differential Geometry to Physics Part III (Cambridge University, Great Britain)Google Scholar