Topology of chaotic mixing patterns

Chaos

Volumn 18, Issue 3, 2008, Pages

  Thiffeault, Jean Luc ^a   Finn, Matthew D ^b   Gouillart, Emmanuelle ^c   Hall, Toby ^d  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b UNIVERSITY OF ADELAIDE   (Australia)

^c SAINT GOBAIN RECHERCHE   (France)

^d UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 54749139692     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2973815     Document Type: Article

References (33)

1. E. Gouillart, N. Kuncio, O. Dauchot, B. Dubrulle, S. Roux, and J.-L. Thiffeault, Phys. Rev. Lett. 99, 114501 (2007).
2. H. Aref, J. Fluid Mech. 143, 1 (1984).
3. H. Aref, Phys. Fluids 14, 1315 (2002).
4. A. Fathi, F. Laundenbach, and V. Pónaru, Asterisque 66-67, 1 (1979).
5. W. P. Thurston, Bull., New Ser., Am. Math. Soc. 19, 417 (1988).
6. P. L. Boyland, H. Aref, and M. A. Stremler, J. Fluid Mech. 403, 277 (2000).
7. E. Gouillart, M. D. Finn, and J.-L. Thiffeault, Phys. Rev. E 73, 036311 (2006).
8. P. L. Boyland, M. A. Stremler, and H. Aref, Physica D 175, 69 (2003).
9. A. Vikhansky, Phys. Fluids 15, 1830 (2003).
10. M. D. Finn, S. M. Cox, and H. M. Byrne, J. Fluid Mech. 493, 345 (2003).
11. M. D. Finn, S. M. Cox, and H. M. Byrne, Phys. Fluids 15, L77 (2003).
12. J.-L. Thiffeault, Phys. Rev. Lett. 94, 084502 (2005).
13. J.-L. Thiffeault and M. D. Finn, Philos. Trans. R. Soc. London, Ser. A 364, 3251 (2006).
14. T. Kobayashi and S. Umeda, in Proceedings of the International Workshop on Knot Theory for Scientific Objects, Osaka, Japan, (Osaka Municipal Universities Press, Osaka, 2007), p. 97.
15. B. J. Binder and S. M. Cox, Fluid Dyn. Res. 49, 34 (2008).
16. M. D. Finn, J.-L. Thiffeault, and E. Gouillart, Physica D 221, 92 (2006).
17. M. D. Finn and J.-L. Thiffeault, SIAM J. Appl. Dyn. Syst. 6, 79 (2007).
18. S. C. Jana, G. Metcalfe, and J. M. Ottino, J. Fluid Mech. 269, 199 (1994).
19. J. S. Birman, Braids, Links, and Mapping Class Groups, in Annals of Mathematics Studies (Princeton University Press, Princeton, 1975).
20. M. Handel, Ergod. Theory Dyn. Syst. 8, 373 (1985).
21. P. L. Boyland, Contemp. Math. 246, 17 (1999).
22. V. I. Arnold and A. Avez, Ergodic Problems of Classical Mechanics (W. A. Benjamin, New York, 1968).
23. R. C. Penner and J. L. Harer, Combinatorics of Train Tracks, in Annals of Mathematics Studies Vol. 125 (Princeton University Press, Princeton, 1991).
24. More generally, the Euler characteristic of a surface of genus g with b boundaries is 2-2g-b, where the genus is the number of "handles" attached to a sphere. In particular, sphere =2, disk =2-1=1, and torus =2-21=0.
25. J. W. Milnor, Topology from the Differentiable Viewpoint, revised edition (Princeton University Press, Princeton, 1997).
26. W. P. Thurston, Three-dimensional Geometry and Topology, edited by, S. Levy, (Princeton University Press, Princeton, 1997), Vol. 1.
27. G. Band and P. L. Boyland, Algebraic Geom. Topol. 7, 1345 (2007).
28. G. E. Andrews, The Theory of Partitions (Addison-Wesley, Reading, 1976).
29. M. A. Stremler and J. Chen, Phys. Fluids 19, 103602 (2007).
30. T. Hall, " Train: A C++ program for computing train tracks of surface homeomorphisms.," http://www.liv.ac.uk/maths/PURE/MIN_SET/CONTENT/ members/T_Hall.html.
31. E. Gouillart, Ph.D. thesis, Universit́ Pierre et Marie Curie Paris 6, 2007, http://tel.archives-ouvertes.fr/tel-00204109/en.
32. M. Bestvina and M. Handel, Topology 34, 109 (1995).
33. J.-L. Thiffeault, E. Gouillart, and M. D. Finn, " The size of ghost rods.," arXiv:nlin/0507076.