N-vortex equilibrium theory

Discrete and Continuous Dynamical Systems

Volumn 19, Issue 2, 2007, Pages 411-418

  Newton, P K ^a  

^a University of Southern California   (United States)

Author keywords

Hamiltonian systems; Kelvin's variational principle; Optimal approximate equilibria; Point vortex equilibria; Relative equilibria; Singular value decomposition

Indexed keywords

EID: 36248989679     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2007.19.411     Document Type: Conference Paper

References (23)

1. H. Aref, Motion of three vortices, Phys. Fluids, 22 (1979), 393-400.
2. H. Aref, Integrable, chaotic, and turbulent motion in two-dimensional flows, Ann. Rev. Fluid Mech., 15 (1983), 345-389.
3. H. Aref, P.K. Newton, M.A. Stremler, T. Tokieda, D.L. Vainchtein, Vortex crystals, Adv. in Appl. Mech., 39 (2003), 1-79.
4. L.J. Campbell, R. Ziff, A catelog of two-dimensional vortex patterns, LA-7384-MS, Rev., Informal Report, Los Alamos Scientific Laboratory, 1978, pp 1-40.
5. W. Gröbli, Specielle probleme über die bewegung geradliniger paralleler wirbelfäden, Zürcher and Furrer, Zürich, in "Vierteljahrschrift der naturforschenden Gesellschaft in Zürich," 22 (1877), 37-81, 129-167.
6. B.A. Grzybowski, H.A. Stone, C.M. Whitesides, Dynamic self-assembly of magnetized, millimeter-sized objects rotating at a liquid-air interface, Nature, 405 (2000), 1033-1036.
7. R.A. Horn, C.R. Johnson, "Topics in Matrix Analysis," Cambridge University Press, Cambridge England, 1991.
8. M.I. Jamaloodeen, P.K. Newton. The N-vortex problem on a rotating sphere. II. Heterogeneous Platonic solid equilibria, Proc. Roy. Soc. A, 462 (2006), 3277-3299.
9. M. Kirby, "Geometrical Data Analysis: An Empirical Approach to Dimensionality Reduction and the Study of Patterns," John Wiley & Sons (2001).
10. D. Lewis, T. Ratiu, Rotating n-gon/kn-gon vortex configurations, J. Nonlinear Sci., 6 (1996), 385-414.
11. A.M. Mayer, Floating magnets, Nature, 17 (1878), 487-488.
12. V.V. Meleshko, H. Aref, A Bibliography of Vortex Dynamics 1858-1956, preprint (2006).
13. G.J. Mertz, Stability of body-centered polygonal configurations of ideal vortices, Phys. Fluids, 21 (1978), 1092-1095.
14. P.K. Newton, "The N-Vortex Problem: Analytical Techniques," Appl. Math. Sci., 145, Springer-Verlag, New York, 2001.
15. P.K. Newton, B. Khushalani Integrable decomposition methods and ensemble averaging for non-integrable N-vortex problems, J. of Turbulence, (2002) 1-9.
16. P.K. Newton, H. Shokraneh The N-vortex problem on a rotating sphere. I. Multi-frequency states, Proc. Roy. Soc. A, 462 (2006), 149-169.
17. P.K. Newton, G. Chamoun On regular triangular vortex lattices, USC preprint (2006).
18. P.K. Newton, G. Chamoun Construction of point vortex equilibria via Brownian ratchets, Proc. Roy. Soc. A, 463 (2007), 1525-1540.
19. H. A.M. Snelders, A.M. Meyer's experiments with floating magnets and their use in the atomic theories of matter, Ann. Sci., 33 (1976), 67-80.
20. G.W. Stewart, On the early history of the singular value decomposition, SIAM Review, 35 (1993), 551-566.
21. W. Thomson, Floating magnets [illustrating vortex systems], Nature XVIII (1878), 13-14.
22. R.B. Warder, W.P. Shipley, Floating magnets, Am. J. Sci., 20 (1888), 285-288.
23. R.W. Wood, Equilibrium figures formed by floating magnets, Philos. Mag., 46 (1898), 162-164.