Efficient topological chaos embedded in the blinking vortex system

Chaos

Volumn 15, Issue 2, 2005, Pages

  Kin, Eiko ^a   Sakajo, Takashi ^b  

^a KYOTO UNIVERSITY   (Japan)

^b HOKKAIDO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 31144457269     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1923207     Document Type: Article

References (22)

1. P. Boyland, H. Aref, and M. Stremler, " Topological fluid mechanics of stirring., " J. Fluid Mech. 403, 277-304 (2000).
2. H. Aref, " Stirring by chaotic advection., " J. Fluid Mech. 143, 1-21 (1984).
3. S. Wiggins and J. M. Ottino, " Foundations of chaotic mixing., " Philos. Trans. R. Soc. London, Ser. A 362, 937-970 (2004).
4. V. Rom-Kedar, A. Leonard, and S. Wiggins, " An analytical study of transport, mixing and chaos in an unsteady vortical flow., " J. Fluid Mech. 214, 347-394 (1990).
5. C. Robinson, Dynamical Systems, Stability, Symbolic Dynamics, and Chaos, 2nd ed. (CRC Press, Ann Arbor, MI, 1995).
6. A. Casson and S. Bleiler, Automorphisms of Surfaces after Nielsen and Thurston, London Math. Soc. Stud. Texts 9 (Cambridge University Press, Cambridge, 1988).
7. W. Thurston, " On the geometry and dynamics of diffeomorphims of surfaces., " Bull., New Ser., Am. Math. Soc. 19, 417-431 (1988).
8. P. Boyland, " Topological methods in surface dynamics., " Topol. Appl. 58, 223-298 (1994).
9. M. Handel, " Global shadowing of pseudo-Anosov homeomorphisms., " Ergod. Theory Dyn. Syst. 5, 373-377 (1985).
10. J. M. Gambaudo, S. Van Strien, and C. Tresser, " The periodic orbit structure of orientation preserving diffeomorphisms on D2 with topological entropy zero., " Ann. I.H.P. Phys. Theor. 50, 335-356 (1989).
11. A. Katok, " Lyapunov exponents, entropy and periodic orbits for diffeomorphisms., " Publ. Math., Inst. Hautes Etud. Sci. 51, 137-174 (1980).
12. J. M. Ottino, The Kinematics of Mixing: Stretching, Chaos, and Transport (Cambridge University Press, Cambridge, 1989).
13. J.-L. Thifferault, " Measuring topological chaos., " Phys. Rev. Lett. 94 (8), 084502 (2005).
14. R. Krasny, " Desingularization of periodic vortex sheet roll-up., " J. Comput. Phys. 69, 292-313 (1986).
15. R. E. Caflisch and J. Lowengrub, " Convergence of the vortex method for vortex sheets., " SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 26, 1060-1080 (1989).
16. M. Nitsche and R. Krasny, " A numerical study of vortex ring formation at the edge of a circular tube., " J. Fluid Mech. 276, 139-161 (1994).
17. M. D. Finn, S. M. Cox, and H. M. Byrne, " Topological chaos in inviscid and viscous mixers., " J. Fluid Mech. 493, 345-361 (2003).
18. A. Vikhansky, " Simulation of topological chaos in laminar flows., " Chaos 14, 14-22 (2004).
19. M. Bestvina and M. Handel, " Train-Tracks for surface homeomorphisms., " Topology 34, 109-140 (1994).
20. T. Hall; the software available at 〈 http://www.liv.ac.uk/maths/PURE/MIN_SET/CONTENT/members/T_Hall.html 〉
21. H. Aref, " The development of chaotic advection., " Phys. Fluids 14, 1315-1325 (2002).
22. P. Walters, An Introduction to Ergodic Theory (Springer, New York, 1982).