Revealing the building blocks of spatiotemporal chaos: Deviations from extensivity

Physical Review Letters

Volumn 96, Issue 5, 2006, Pages

  Fishman, Matthew P ^a,b   Egolf, David A ^a  

^a GEORGETOWN UNIVERSITY   (United States)

^b MEDICAL COLLEGE OF WISCONSIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; DEGREES OF FREEDOM (MECHANICS); LARGE SCALE SYSTEMS;

CHAOTIC LENGTH SCALE; EXTENSIVITY; SPATIOTEMPORAL SYSTEMS;

CHAOS THEORY;

EID: 33144477407     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.96.054103     Document Type: Article

References (30)

1. M.C. Cross and P.C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993). RMPHAT 0034-6861 10.1103/RevModPhys.65.851
2. M.C. Cross and P.C. Hohenberg, Science 263, 1569 (1994). SCIEAS 0036-8075
3. J.P. Gollub and J.S. Langer, Rev. Mod. Phys. 71, S396 (1999). RMPHAT 0034-6861 10.1103/RevModPhys.71.S396
4. See, for example, A. Garfinkel, M.L. Spano, W.L. Ditto, and J.N. Weiss, Science 257, 1230 (1992). SCIEAS 0036-8075
5. See, for example, Q. Ouyang and J.-M. Flesselles, Nature (London) NATUAS 0028-0836 379, 143 (1996). 10.1038/379143a0
6. See, for example, S.W. Morris, E. Bodenschatz, D.S. Cannell, and G. Ahlers, Phys. Rev. Lett. 71, 2026 (1993). PRLTAO 0031-9007 10.1103/PhysRevLett. 71.2026
7. See, for example, K.J. Lee, E.C. Cox, and R.E. Goldstein, Phys. Rev. Lett. 76, 1174 (1996). PRLTAO 0031-9007 10.1103/PhysRevLett.76.1174
8. B.I. Shraiman, A. Pumir, W.V. Saarloos, P.C. Hohenberg, H. Chaté, and M. Holen, Physica (Amsterdam) 57D, 241 (1992). PDNPDT 0167-2789 10.1016/0167-2789(92)90001-4
9. J. Miller and D.A. Huse, Phys. Rev. E 48, 2528 (1993). PLEEE8 1063-651X 10.1103/PhysRevE.48.2528
10. D.A. Egolf and H.S. Greenside, Phys. Rev. Lett. 74, 1751 (1995). PRLTAO 0031-9007 10.1103/PhysRevLett.74.1751
11. P. Marcq, H. Chaté, and P. Manneville, Phys. Rev. Lett. 77, 4003 (1996). PRLTAO 0031-9007 10.1103/PhysRevLett.77.4003
12. E. Bodenschatz, W. Pesch, and G. Ahlers, Annu. Rev. Fluid Mech. 32, 709 (2000). ARVFA3 0066-4189 10.1146/annurev.fluid.32.1.709
13. D.A. Egolf, Science 287, 101 (2000). SCIEAS 0036-8075 10.1126/science.287.5450.101
14. J.-P. Eckmann and D. Ruelle, Rev. Mod. Phys. 57, 617 (1985). RMPHAT 0034-6861 10.1103/RevModPhys.57.617
15. P. Manneville, Liapounov Exponents for the Kuramoto-Sivashinksy Model, Lecture Notes in Physics Vol. 230 (Springer-Verlag, Berlin, 1985), pp. 319-326.
16. D.A. Egolf and H.S. Greenside, Nature (London) NATUAS 0028-0836 369, 129 (1994). 10.1038/369129a0
17. C.S. O'Hern, D.A. Egolf, and H.S. Greenside, Phys. Rev. E 53, 3374 (1996). PLEEE8 1063-651X 10.1103/PhysRevE.53.3374
18. D.A. Egolf, I.V. Melnikov, W. Pesch, and R.E. Ecke, Nature (London) NATUAS 0028-0836 404, 733 (2000). 10.1038/35008013
19. D. Ruelle, Commun. Math. Phys. 87, 287 (1982). CMPHAY 0010-3616 10.1007/BF01218566
20. J.P. Gollub and M.C. Cross, Nature (London) NATUAS 0028-0836 404, 710 (2000). 10.1038/35008168
21. T. Bohr, E. Bosch, and W. van der Water, Nature (London) NATUAS 0028-0836 372, 48 (1994). 10.1038/372048a0
22. D.A. Egolf, Phys. Rev. Lett. 81, 4120 (1998). PRLTAO 0031-9007 10.1103/PhysRevLett.81.4120
23. H.W. Xi, R. Toral, J.D. Gunton, and M.I. Tribelsky, Phys. Rev. E 62, R17 (2000). PLEEE8 1063-651X 10.1103/PhysRevE.62.R17
24. S. Tajima and H.S. Greenside, Phys. Rev. E 66, 017205 (2002). PLEEE8 1063-651X 10.1103/PhysRevE.66.017205
25. J.A. Glazier, P. Kolodner, and H. Williams, J. Stat. Phys. 64, 945 (1991). JSTPSB 0022-4715 10.1007/BF01048806
26. L. Ning and R.E. Ecke, Phys. Rev. E 47, 3326 (1993). PLEEE8 1063-651X 10.1103/PhysRevE.47.3326
27. I. Aranson and L. Kramer, Rev. Mod. Phys. 74, 99 (2002). RMPHAT 0034-6861 10.1103/RevModPhys.74.99
28. Spectral Methods in Fluid Dynamics, edited by, C. Canuto, M. Hussaini, A. Quarteroni, and, T. Zang, (Springer, Cambridge, England, 1988).
29. E. Ott, Chaos in Dynamical Systems (Cambridge University Press, Cambridge, England, 1993).
30. P. Manneville, in Propagation in Systems Far from Equilibrium, Springer Series in Synergetics Vol. 41 (Springer-Verlag, Berlin, 1988), pp. 265-280.