Braids of entangled particle trajectories

Chaos

Volumn 20, Issue 1, 2010, Pages

  Thiffeault, Jean Luc ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; HYDRODYNAMICS; METHODOLOGY; MOTION; NONLINEAR SYSTEM; OSCILLOMETRY; PARTICLE SIZE; PHYSICS; STATISTICAL MODEL;

ALGORITHMS; HYDRODYNAMICS; MODELS, STATISTICAL; MOTION; NONLINEAR DYNAMICS; OSCILLOMETRY; PARTICLE SIZE; PHYSICS;

EID: 77953507389     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3262494     Document Type: Article

References (42)

1. 2004, WOCE subsurface float data assembly center,
2. LaCasce J.H. Transport and Mixing in Geophysical Flows 2008, 744:165-218. J. B. Weiss, A. Provenzale, 10.1007/978-3-540-75215-8_8, in, Lecture Notes in Physics Vol., edited by and (Springer, Berlin).
3. Wolf A. Swift J.B. Swinney H.L. Vastano J.A. Physica D 1985, 16:285. PDNPDT, 0167-2789, 10.1016/0167-2789(85)90011-9
4. Aref H. J. Fluid Mech. 1984, 143:1. JFLSA7, 0022-1120, 10.1017/S0022112084001233
5. Boyland P.L. Aref H. Stremler M.A. J. Fluid Mech. 2000, 403:277. JFLSA7, 0022-1120, 10.1017/S0022112099007107.
6. Boyland P.L. Stremler M.A. Aref H. Physica D 2003, 175:69. PDNPDT, 0167-2789, 10.1016/S0167-2789(02)00692-9.
7. Thiffeault J.-.L. Phys. Rev. Lett. 2005, 94:084502. PRLTAO, 0031-9007, 10.1103/PhysRevLett.94.084502
8. Kin E. Sakajo T. Chaos 2005, 15:023111. CHAOEH, 1054-1500, 10.1063/1.1923207.
9. Gouillart E. Finn M.D. Thiffeault J.-.L. Phys. Rev. E 2006, 73:036311. PLEEE8, 1063-651X, 10.1103/PhysRevE.73.036311.
10. Thiffeault J.-.L. Finn M.D. Gouillart E. Hall T. Chaos 2008, 18:033123. CHAOEH, 1054-1500, 10.1063/1.2973815
11. Finn M.D. Cox S.M. Byrne H.M. J. Fluid Mech. 2003, 493:345. JFLSA7, 0022-1120, 10.1017/S0022112003005858.
12. Binder B.J. Cox S.M. Fluid Dyn. Res. 2008, 40:34. FDRSEH, 0169-5983, 10.1016/j.fluiddyn.2006.09.001.
13. Vikhansky A. Chaos 2004, 14:14. CHAOEH, 1054-1500, 10.1063/1.1621092
14. Finn M.D. Thiffeault J.-.L. SIAM J. Appl. Dyn. Syst. 2007, 6:79. SJADAY, 1536-0040.
15. Finn M.D. Thiffeault J.-.L. Gouillart E. Physica D 2006, 221:92. PDNPDT, 0167-2789, 10.1016/j.physd.2006.07.018.
16. Thiffeault J.-.L. Finn M.D. Philos. Trans. R. Soc. London, Ser. A 2006, 364:3251. PTRMAD, 0962-8428, 10.1098/rsta.2006.1899.
17. Stremler M.A. Chen J. Phys. Fluids 2007, 19:103602. PHFLE6, 1070-6631, 10.1063/1.2772881.
18. Vikhansky A. Phys. Fluids 2003, 15:1830. PHFLE6, 1070-6631, 10.1063/1.1577344
19. Berger M.A. Topological Fluid Mechanics 1990, 440-448. H. K. Moffatt, A. Tsinober, in, edited by and (Cambridge University Press, Cambridge).
20. Nechaev S.K. Statistics of Knots and Entangled Random Walks 1996, (World Scientific, Singapore).
21. Artin E. Ann. Math. 1947, 48:101. ANMAAH, 0003-486X, 10.2307/1969218
22. Birman J.S. Ko K.H. Lee S.J. Adv. Math. 1998, 139:322. ADMTA4, 0001-8708, 10.1006/aima.1998.1761.
23. Birman J.S. Brendle T.E. Handbook of Knot Theory 2005, W. Menasco, M. Thistlethwaite. in, edited by and (Elsevier, Amsterdam).
24. Dynnikov I. Wiest B. J. Eur. Math. Soc. 2007, 9:801. and,
25. Gambaudo J.-.M. Pécou E.E. Ergod. Theory Dyn. Syst. 1999, 19:627. ZZZZZZ, 0143-3857, 10.1017/S0143385799130207.
26. Lefranc M. Phys. Rev. E 2006, 74:035202. PLEEE8, 1063-651X, 10.1103/PhysRevE.74.035202, (R) .
27. Fathi A. Laundenbach F. Poénaru V. Asterisque 1979, 66-67:1. ZZZZZZ, 0303-1179.
28. Thurston W.P. Bull., New Ser., Am. Math. Soc. 1988, 19:417. ZZZZZZ, 0273-0979, 10.1090/S0273-0979-1988-15685-6
29. Casson A.J. Bleiler S.A. Automorphisms of Surfaces After Nielsen and Thurston, London Mathematical Society Student Texts 1988, 9. and, (Cambridge University Press, Cambridge), Vol.
30. Boyland P.L. Topol. Appl. 1994, 58:223. TIAPD9, 0166-8641, 10.1016/0166-8641(94)00147-2
31. Birman J.S. Braids, Links, and Mapping Class Groups, Annals of Mathematics Studies 1975, (Princeton University Press, Princeton, NJ).
32. Newhouse S.E. Pignataro T. J. Stat. Phys. 1993, 72:1331. JSTPBS, 0022-4715, 10.1007/BF01048189.
33. Moussafir J.-.O. Func. Anal. Other Math. 2006, 1:37. .
34. Dynnikov I.A. Russ. Math. Surveys 2002, 57:592. RMSUAF, 0036-0279, 10.1070/RM2002v057n03ABEH000519
35. Hall T. Yurttaş S. Topol. Appl. 2009, 156:1554. TIAPD9, 0166-8641, 10.1016/j.topol.2009.01.005.
36. i as clockwise interchanges rather than counterclockwise.
37. Bestvina M. Handel M. Topology 1995, 34:109. TPLGAF, 0040-9383, 10.1016/0040-9383(94)E0009-9.
38. Amon A. Lefranc M. Phys. Rev. Lett. 2004, 92:094101. PRLTAO, 0031-9007, 10.1103/PhysRevLett.92.094101.
39. Gilmore R. Rev. Mod. Phys. 1998, 70:1455. RMPHAT, 0034-6861, 10.1103/RevModPhys.70.1455
40. Kamada S. Braid and Knot Theory in Dimension Four, Mathematical Surveys & Monographs 2002, (American Mathematical Society, Providence).
41. Berger M.A. Lett. Math. Phys. 2001, 55:181. LMPHDY, 0377-9017, 10.1023/A:1010979823190
42. See supplementary material at for the source code of the MATLAB files in this appendix.