Hydrodynamic Lyapunov modes in coupled map lattices

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 73, Issue 1, 2006, Pages

  Yang, Hong Liu ^a   Radons, Günter ^a  

^a CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CRYSTAL LATTICES; DAMPING; HAMILTONIANS; HYDRODYNAMICS;

COUPLED MAP LATTICES; HYDRODYNAMIC LYAPUNOV MODES; TANGENT SPACE DYNAMICS;

LYAPUNOV METHODS;

EID: 32844474161     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.73.016202     Document Type: Article

References (57)

1. N. S. Krylov, Works on the Foundations of Statistical Mechanics (Princeton University Press, Princeton, 1979).
2. P. Gaspard, Chaos, Scattering, and Statistical Mechanics (Cambridge University Press, Cambridge, 1998).
3. J. P. Dorfman, An Introduction to Chaos in Nonequilibrium Statistical Mechanics (Cambridge University Press, Cambridge, 1999).
4. D. J. Evans and G. P. Morriss, Statistical Mechanics of Nonequilibrium Liquids (Academic, New York, 1990).
5. Wm. G. Hoover, Computational Statistical Mechanics (Elsevier, New York, 1991).
6. Wm. G. Hoover, Time Reversibility, Computer Simulation, and Chaos (World Scientific, Singapore, 1999).
7. H. A. Posch and R. Hirschl, " Simulation of Billiards and of Hard-Body Fluids, " in Hard Ball Systems and the Lorentz Gas, edited by, D. Szasz, Encyclopedia of the Mathematical Sciences, Vol. 101, p. 269 (Springer Verlag, Berlin, 2000).
8. H. A. Posch and Ch. Forster, in Collective Dynamics of Nonlinear and Disordered Systems, edited by, G. Radons, W. Just, and, P. Häussler, (Springer, Berlin, 2005), p. 309.
9. C. Forster, R. Hirschl, H. A. Posch, and Wm. G. Hoover, Physica D PDNPDT 0167-2789 10.1016/j.physd.2003.09.013 187, 294 (2004).
10. J.-P. Eckmann and O. Gat, J. Stat. Phys. JSTPBS 0022-4715 10.1023/A:1018679609870 98, 775 (2000).
11. S. McNamara and M. Mareschal, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.051103 64, 051103 (2001);
12. M. Mareschal and S. McNamara, Physica D PDNPDT 0167-2789 10.1016/j.physd.2003.09.018 187, 311 (2004).
13. A. S. de Wijn and H. van Beijeren, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.016207 70, 016207 (2004).
14. T. Taniguchi and G. P. Morriss, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.056202 65, 056202 (2002);
15. T. Taniguchi and G. P. Morriss, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.026218 68, 026218 (2003);
16. T. Taniguchi and G. P. Morriss, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.046203 68, 046203 (2003).
17. J.-P. Eckmann, C. Forster, H. A. Posch, and E. Zabey, J. Stat. Phys. JSTPBS 0022-4715 118, 813 (2005);
18. see also arXiv: nlin.CD/0404007.
19. H. L. Yang and G. Radons, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.036211 71, 036211 (2005)
20. see also arXiv: nlin.CD/0404027.
21. G. Radons and H. L. Yang, arXiv: nlin.CD/0404028.
22. C. Forster and H. A. Posch, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/7/1/032 7, 32 (2005)
23. see also arXiv: nlin.CD/0404019.
24. T. Taniguchi and G. P. Morriss, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.016218 71, 016218 (2005);
25. T. Taniguchi and G. P. Morriss, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.154101 94, 154101 (2005).
26. K. Kaneko, Prog. Theor. Phys. PTPKAV 0033-068X 72, 480 (1984);
27. K. Kaneko, " Simulating Physic in Coupled Map Lattices, " in Formation, Dynamics, and Statistics of Patterns, Vol. 1, edited by, K. Kawasaki, A. Onuki, and, M. Suzuki, (World Scientific, Singapore, 1990).
28. See the special issue on Coupled Map Lattices, Chaos CHAOEH 1054-1500 10.1063/1.165869 2, 279-460 (1992).
29. R. Tenny, L. S. Tsimring, L. Larson, and H. D. I. Abarbanel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.047903 90, 047903 (2003);
30. T. Bohr, M. van Hecke, R. Mikkelsen, and M. Ipsen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.5482 86, 5482 (2001);
31. F. Ginelli, R. Livi, A. Politi, and A. Torcini, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.046217 67, 046217 (2003);
32. O. Rudzick and A. Pikovsky, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.54.5107 54, 5107 (1996);
33. H. L. Yang and E. J. Ding, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.50.R3295 50, R3295 (1994).
34. See for example T. Bohr, G. Grinstein, and C. Jayaprakash, Chaos CHAOEH 1054-1500 10.1063/1.166111 5, 412 (1995).
35. Y. Pomeau, A. Pumir, and P. Pelce, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01012904 37, 39 (1984);
36. K. Kaneko, Physica D PDNPDT 0167-2789 10.1016/0167-2789(86)90149-1 23, 436 (1986).
37. G. Giacomelli and A. Politi, Europhys. Lett. EULEEJ 0295-5075 15, 387 (1991).
38. A. Pikovsky and A. Politi, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/11/4/016 11, 1049 (1998);
39. A. Pikovsky and A. Politi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.63.036207 63, 036207 (2001).
40. H. L. Yang and G. Radons (unpublished).
41. J. P. Boon and S. Yip, Molecular Hydrodynamics (McGraw-Hill, New York, 1980).
42. V. I. Oseledec, Trans. Mosc. Math. Soc. TMMSD4 0077-1554 19, 197 (1968).
43. R. A. Johnson, K. J. Palmer, and G. R. Sell, SIAM J. Math. Anal. SJMAAH 0036-1410 10.1137/0518001 18, 1 (1987).
44. I. Goldhirsch, P. L. Sulem, and S. A. Orszag, Physica D PDNPDT 0167-2789 27, 331 (1987).
45. S. V. Ershov and A. B. Potapov, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(98)00013-X 118, 167 (1998).
46. G. Benettin, L. Galgani, and J. M. Strelcyn, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.14.2338 14, 2338 (1976).
47. I. Shimada and T. Nagashima, Prog. Theor. Phys. PTPKAV 0033-068X 61, 1605 (1979).
48. K. Kaneko and T. Konishi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.40.6130 40, R 6130 (1989).
49. M. S. Bourzutschky and M. C. Cross, Chaos CHAOEH 1054-1500 10.1063/1.165905 2, 173 (1992).
50. R. Livi, M. Pettini, S. Ruffo, M. Sparpaglione, and A. Vulpiani, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.31.1039 31, 1039 (1985).
51. U. Dressler, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.38.2103 38, 2103 (1988);
52. G. P. Morriss and C. P. Dettmann, Chaos CHAOEH 1054-1500 10.1063/1.166314 Invariante Varlationsprobleme, " Nachr. d. König. Gesellsch. d. Wiss. zu Göttingen, Math-phys. Klasse (1918), pp. 235-257;
53. English translation M. A. Travel, Transp. Theory Stat. Phys. TTSPB4 0041-1450 1, 183 (1971).
54. C. M. Newman, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01464284 103, 121 (1986);
55. R. Livi, A. Politi, S. Ruffo, and A. Vulpiani, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01010337 46, 147 (1987);
56. J.-P. Eckmann and C. E. Wayne, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01019144 50, 853 (1988);
57. Y. Yamaguchi, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/31/1/020 31, 195 (1998).