Microextensive chaos of a spatially extended system

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 66, Issue 1, 2002, Pages

  Tajima, Shigeyuki ^a   Greenside, Henry S ^a  

^a DUKE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANNIHILATION; MICRODOMAINS; PHYSICAL SYSTEM; SMECTIC SYSTEM;

ATOMIC FORCE MICROSCOPY; COMPOSITION; FILM GROWTH; LIQUID CRYSTALS; SCANNING ELECTRON MICROSCOPY; SURFACE PHENOMENA; THICKNESS MEASUREMENT; THIN FILMS;

COPOLYMERS;

EID: 41349088356     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.017205     Document Type: Article

References (34)

1. M.C. Cross and P.C. Hohenberg, Science 263, 1569 (1994).
2. M.C. Cross and P.C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
3. Philippe Marcq, Hugues Chaté, and Paul Manneville, Phys. Rev. E 55, 2606 (1997).
4. D.A. Egolf and H.S. Greenside, Phys. Lett. A 185, 395 (1994).
5. B.J. Gluckman, C.B. Arnold, and J.P. Gollub, Phys. Rev. E 51, 1128 (1995).
6. Henry S. Greenside, in Semi-Analytic Methods for the Navier Stokes Equations, edited by K. Coughlin, CRM Proceedings and Lecture Notes, Vol. 20. (American Mathematical Society, Providence, RI, 1999), URL: http://arXiv.org/abs/chao-dyn/9612004.
7. Corey O’Hern, David Egolf, and Henry Greenside, Phys. Rev. E 53, 3374 (1996).
8. T. Bohr, Nature (London) 372, 48 (1994);
9. Scott M. Zoldi, Phys. Rev. E 58, R6903 (1998);
10. Ralf W. Wittenberg and Philip Holmes, Chaos 9, 452 (1999).
11. David Ruelle, Commun. Math. Phys. 87, 287 (1982).
12. Paul Manneville, Macroscopic Modeling of Turbulent Flows, edited by O. Pironneau, Lecture Notes in Physics, Vol. 230 (Springer, New York, 1985), pp. 319–326.
13. Haowen Xi, Raúl Toral, J.D. Gunton, and Michael I. Tribelsky, Phys. Rev. E 62, R17 (2000).
14. J.-P. Eckmann and C.E. Wayne, J. Stat. Phys. 50, 853 (1988);
15. K. Kaneko, Prog. Theor. Phys. Suppl. 99, 263 (1989);
16. P. Grassberger, Phys. Scr. 40, 346 (1989);
17. L. Keefe, Phys. Lett. A 140, 317 (1989);
18. M.C. Strain and H.S. Greenside, Phys. Rev. Lett. 80, 2306 (1998);
19. D.A. Egolf, Nature (London) 404, 733 (2000).
20. L. Landau and E. Lifshitz. Statistical Physics, 3rd ed. (Pergamon, New York, 1980), Vol. 5, Pt. 1.
21. Y. Pomeau, A. Pumir, and P. Pelce, J. Stat. Phys. 37, 39 (1984).
22. P. Manneville, in Propagation in Systems Far from Equilibrium, edited by J.E. Wesfried Springer Series in Synergetics, Vol. 41 (Springer-Verlag, New York, 1988), pp. 265–280.
23. P. Grassberger, Phys. Scr. 40, 346 (1989);
24. A. Torcini, Physica D 53, 85 (1991);
25. I. Aranson and L. Kramer, Rev. Mod. Phys. 74, 99 (2002).
26. Paul Manneville, Dissipative Structures and Weak Turbulence. Perspectives In Physics (Academic Press, New York, 1990).
27. Edward Ott, Chaos in Dynamical Systems (Cambridge University Press, New York, 1993).
28. T.S. Parker and L.O. Chua, Practical Numerical Algorithms for Chaotic Systems (Springer, New York, 1989);
29. see, also, the earlier references, I. Shimada and T. Nagashima, Prog. Theor. Phys. 61, 1605 (1979);
30. G. Benettin, Meccanica 9, 21 (1980).
31. Isaac Goldhirsch, Pierre-Louis Sulem, and Steven A. Orszag, Physica D 27, 311 (1994).
32. Pierre Bergé, Yves Pomeau, and Christian Vidal, Order Within Chaos (Wiley, New York, 1984).
33. It is interesting to note that the number of positive Lyapunov exponents increases more slowly than the dimension D as (Formula presented), while the number of unstable modes increases more rapidly as (Formula presented) 14.
34. As summarized in Manneville’s review article 15, others have studied states and their bifurcations for the 1d KS equation with periodic boundary conditions over about the same range in length. A different sequence of different dynamical behaviors is observed compared to what we find in Fig. 22.