Lyapunov instability of rough hard-disk fluids

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

Volumn 80, Issue 1, 2009, Pages

  Van Meel, Jacobus A ^a   Posch, Harald A ^b  

^a FOM INSTITUTE AMOLF   (Netherlands)

^b UNIVERSITY OF VIENNA   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICAL INSTABILITIES; HARD-DISK FLUIDS; HIGH-DENSITY; KOLMOGOROV-SINAI ENTROPY; LOWER DENSITY; LYAPUNOV; LYAPUNOV INSTABILITIES; LYAPUNOV SPECTRUM; MAXIMUM LYAPUNOV EXPONENT; MOMENTS OF INERTIA; PERTURBATION VECTORS; PHASE SPACES; ROTATIONAL DEGREES OF FREEDOM; SPATIAL LOCALIZATION; TWO-DIMENSION;

CHAOS THEORY; COMPUTATIONAL COMPLEXITY; DIFFERENTIAL EQUATIONS; DISKS (STRUCTURAL COMPONENTS); MECHANICS; PHASE SPACE METHODS; ROTATION;

DENSITY OF GASES;

EID: 68949113975     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.80.016206     Document Type: Article

References (58)

1. H. A. Posch and W. G. Hoover, Phys. Rev. A 38, 473 (1988). 10.1103/PhysRevA.38.473
2. P. Gaspard, Chaos, Scattering, and Statistical Mechanics (Cambridge University Press, Cambridge, 1998).
3. The Weeks-Chandler-Anderson potential contains only the repulsive part of the Lennard-Jones potential and is a good reference potential for perturbation theories of fluids. See J. D. Weeks, D. Chandler, and H. C. Anderson, J. Chem. Phys. 54, 5237 (1971). 10.1063/1.1674820
4. J. B. Pesin, Sov. Math. Dokl. 17, 196 (1976).
5. Ch. Forster and H. A. Posch, New J. Phys. 7, 32 (2005). 10.1088/1367-2630/7/1/032
6. S. Toxvaerd, Phys. Rev. Lett. 51, 1971 (1983). 10.1103/PhysRevLett.51. 1971
7. H. A. Posch, Wm. G. Hoover, and B. L. Holian, Ber. Bunsenges. Phys. Chem. 94, 250 (1990).
8. D. M. Heyes and H. Okumura, J. Chem. Phys. 124, 164507 (2006). 10.1063/1.2176675
9. Wm. G. Hoover, Time Reversibility, Computer Simulation and Chaos (World Scientific, Singapore, 1999).
10. Wm. G. Hoover and H. A. Posch, Chaos 8, 366 (1998). 10.1063/1.166318
11. Ch. Forster, R. Hirschl, H. A. Posch, and Wm. G. Hoover, Physica D 187, 294 (2004). 10.1016/j.physd.2003.09.013
12. T. Taniguchi and G. P. Morriss, Phys. Rev. E 68, 046203 (2003). 10.1103/PhysRevE.68.046203
13. A. Pikovsky and A. Politi, Nonlinearity 11, 1049 (1998) 10.1088/0951-7715/11/4/016
14. A. Pikovsky and A. Politi, Phys. Rev. E 63, 036207 (2001). 10.1103/PhysRevE.63.036207
15. Lj. Milanović, H. A. Posch, and Wm. G. Hoover, Mol. Phys. 95, 281 (1998). 10.1080/002689798167205
16. L. J. Milanović and H. A. Posch, J. Mol. Liq. 96-97, 221 (2002). 10.1016/S0167-7322(01)00350-6
17. H. A. Posch and R. Hirschl, see pp. 279-314 of Ref..
18. T. Taniguchi and G. P. Morriss, Phys. Rev. E 68, 026218 (2003). 10.1103/PhysRevE.68.026218
19. J. P. Eckmann, Ch. Forster, H. A. Posch, and E. Zabey, J. Stat. Phys. 118, 813 (2005). 10.1007/s10955-004-2687-4
20. H.-L. Yang and G. Radons, Phys. Rev. E 71, 036211 (2005) 10.1103/PhysRevE.71.036211
21. H.-L. Yang and G. Radons, Phys. Rev. Lett. 96, 074101 (2006). 10.1103/PhysRevLett.96.074101
22. I. Borzsák, H. A. Posch, and A. Baranyai, Phys. Rev. E 53, 3694 (1996). 10.1103/PhysRevE.53.3694
23. O. Kum, Y. H. Shin, and E. K. Lee, Phys. Rev. E 58, 7243 (1998). 10.1103/PhysRevE.58.7243
24. G. H. Bryan, "Report on the Present State of our Knowledge of Thermodynamics," Reports of the British Association for the Advancement of Science, Vol. 64, p. 64-101 (p. 83 in particular) (1894).
25. F. B. Pidduck, Proc. R. Soc. London, Ser. A 101, 101 (1922). 10.1098/rspa.1922.0028
26. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-uniform Gases, 3rd ed. (Cambridge University Press, New York, 1990).
27. J. O'Dell and B. J. Berne, J. Chem. Phys. 63, 2376 (1975). 10.1063/1.431666
28. B. J. Berne, J. Chem. Phys. 66, 2821 (1977). 10.1063/1.434355
29. C. S. Pangali and B. J. Berne, J. Chem. Phys. 67, 4571 (1977). 10.1063/1.434617
30. J. A. Montgomery, Jr. and B. J. Berne, J. Chem. Phys. 67, 4580 (1977). 10.1063/1.434618
31. Ch. Dellago, H. A. Posch, and W. G. Hoover, Phys. Rev. E 53, 1485 (1996). 10.1103/PhysRevE.53.1485
32. Ch. Dellago and H. A. Posch, Physica A 240, 68 (1997). 10.1016/S0378-4371(97)00131-3
33. D. C. Rapaport, The Art of Molecular Dynamics Simulation (Cambridge University Press, Cambridge, England, 1995).
34. G. Benettin, L. Galgani, A. Giorgilli, and J. M. Strelcyn, Meccanica 15, 29 (1980).
35. I. Shimada and T. Nagashima, Prog. Theor. Phys. 61, 1605 (1979). 10.1143/PTP.61.1605
36. F. Bonetto, E. G. D. Cohen, and C. Pugh, J. Stat. Phys. 92, 587 (1998). 10.1023/A:1023040621826
37. F. Scheck, Mechanics (Springer Verlag, Berlin, 2005).
38. Ch. Dellago and H. A. Posch, Phys. Rev. E 55, R9 (1997). 10.1103/PhysRevE.55.R9
39. N. S. Krylov, Works on the Foundations of Statistical Mechanics (Princeton University Press, Princeton, NJ, 1979)
40. Ya. G. Sinai, Works on the Foundations of Statistical Mechanics (Princeton University Press, Princeton, NJ, 1979). p. 239.
41. G. M. Zaslavsky, Chaos in Dynamical Systems (Harwood Academic Publishers, Chur, 1985).
42. Ch. Forster, D. Mukamel, and H. A. Posch, Phys. Rev. E 69, 066124 (2004). 10.1103/PhysRevE.69.066124
43. R. van Zon, H. van Beijeren, and J. R. Dorfman, see pp. 231-278 of Ref..
44. R. van Zon and H. van Beijeren, J. Stat. Phys. 109, 641 (2002). 10.1023/A:1020414615453
45. H. van Beijeren, J. R. Dorfman, H. A. Posch, and Ch. Dellago, Phys. Rev. E 56, 5272 (1997). 10.1103/PhysRevE.56.5272
46. A. S. de Wijn, Phys. Rev. E. 71, 046211 (2005). 10.1103/PhysRevE.71. 046211
47. A. S. de Wijn and H. van Beijeren, Phys. Rev. E 70, 016207 (2004). 10.1103/PhysRevE.70.016207
48. H. A. Posch and Ch. Forster, in Lecture Notes on Computational Science-ICCS 2002, edited by, P. M. A. Sloot, C. J. K. Tan, J. J. Dongarra, and, A. G. Hoekstra, (Springer, Berlin, 2002), p. 1170.
49. P. Manneville, in Macroscopic Modelling of Turbulent Flows, Lecture Notes in Physics Vol. 230, edited by, Araki, (Springer, New York, 1985), p. 319.
50. R. Livi and S. Ruffo, in Nonlinear Dynamics, edited by, G. Turchetti, (World Scientific, Singapore, 1989), p. 220.
51. M. Falcioni, U. M. B. Marconi, and A. Vulpiani, Phys. Rev. A 44, 2263 (1991). 10.1103/PhysRevA.44.2263
52. T. Taniguchi and G. P. Morriss, Phys. Rev. E 73, 036208 (2006). 10.1103/PhysRevE.73.036208
53. G. Jumarie, Relative Information (Springer-Verlag, Berlin, 1990).
54. J. van Meel, Master's thesis, University of Vienna, 2005.
55. H. Bosetti and H. A. Posch (unpublished).
56. F. Ginelli, P. Poggi, A. Turchi, H. Chaté, R. Livi, and A. Politi, Phys. Rev. Lett. 99, 130601 (2007). 10.1103/PhysRevLett.99.130601
57. C. Dellago, W. G. Hoover, and H. A. Posch, Phys. Rev. E 65, 056216 (2002). 10.1103/PhysRevE.65.056216
58. Hard Ball Systems and the Lorenz Gas, Encyclopedia of the Mathematical Sciences No. 101, edited by, D. Szasz, (Springer Verlag, Berlin, 2000).