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Lyapunov spectrum of the driven Lorentz gas
Phys. Rev. E 52, 4817 – Published 1 November, 1995
DOI: https://doi.org/10.1103/PhysRevE.52.4817
Abstract
A method for the evaluation of the full Lyapunov spectrum of an externally driven system with a hard-core interaction is presented. It is applied to the periodic Lorentz gas subjected to a homogeneous field and coupled to a Gaussian thermostat. The algorithm treats both the intercollisional streaming and the hard-core collisions exactly and can be easily generalized to many-body systems in nonequilibrium steady states interacting with hard-core potentials. From the Lyapunov spectrum of the Lorentz gas, the information dimension and the associated dimensionality reduction of the underlying fractal attractor were determined and compared to independent box-counting estimates for the same quantities.
References (36)
- J. Machta and R. Zwanzig, Phys. Rev. Lett. 50, 1959 (1983).
- W. G. Hoover, J. Stat. Phys. 42, 587 (1986).
- W. G. Hoover, B. Moran, C. G. Hoover and W. J. Evans, Phys. Lett. A 133, 114 (1988).
- H. van Beijeren and J. R. Dorfman, Phys. Rev. Lett. 74, 4412 (1995).
- B. Moran and W. G. Hoover, J. Stat. Phys. 48, 709 (1987).
- N. J. Chernov, G. L. Eyink, J. L. Lebovitz and Ya. G. Sinai, Commun. Math. Phys. 154, 569 (1993).
- A. Baranyai, D. J. Evans, and E. G. D. Cohen, J. Stat. Phys. 70, 1085 (1993).
- W. G. Hoover, C. G. Hoover, W. J. Evans, B. Moran, J. A. Levatin, and E. A. Craig, in Microscopic Simulations of Complex Flows, Vol. 236 of NATO Advanced Study Institute, Series B: Physics, edited by M. Mareshal (Plenum, New York, 1990), p. 199.
- G. P. Morriss, Phys. Rev. A 39, 4811 (1989).
- J. Petravic, D. J. Isbister and G. P. Morriss, J. Stat. Phys. 76, 1045 (1994).
- D. J. Evans and G. P. Morriss, Statistical Mechanics of Nonequilibrium Liquids (Academic, London, 1990).
- W. G. Hoover, (unpublished).
- W. N. Vance, Phys. Rev. Lett. 69, 1356 (1992).
- W. G. Hoover and B. Moran, Phys. Rev. A 40, 5319 (1989).
- L. A. Bunimovich and Ya. G. Sinai, Commun. Math. Phys. 73, 247 (1980).
- L. A. Bunimovich and Ya. G. Sinai, Commun. Math. Phys. 78, 471 (1981).
- P. Gaspard and G. Nicolis, Phys. Rev. Lett. 65, 1693 (1990).
- P. Gaspard and F. Baras, in Microscopic Simulations of Complex Hydrodynamic Phenomena, Vol. 292 of NATO Advanced Study Institute, Series B: Physics, edited by M. Mareshal and B. Holian (Plenum, New York, 1992), p. 301.
- G. Benettin, L. Galgani, A. Giorgilli and J. M. Strelcyn, Meccanica 15, 9 (1980).
- A. Wolf, J. B. Swift, H. L. Swinney and J. A. Vastano, Physica D 16, 285 (1985).
- P. Cvitanović, P. Gaspard and T. Schreiber, Chaos 2, 85 (1992).
- G. P. Morriss and L. Rondoni, J. Stat. Phys. 76, 553 (1994).
- J. Lloyd, M. Niemeyer, L. Rondoni, and G. P. Morriss, Chaos (to be published).
- Ch. Dellago and H. A. Posch, Phys. Rev. E 52, 2401 (1995).
- Ch. Dellago, H. A. Posch, and W. G. Hoover (unpublished).
- V. I. Oseledec, Trans. Moscow Math. Soc. 19, 197 (1968).
- H. A. Posch and W. G. Hoover, Phys. Rev. A 38, 473 (1988).
- H. A. Posch and W. G. Hoover, Phys. Rev. A 39, 2175 (1989).
- D. J. Evans, E. G. D. Cohen and G. P. Morriss, Phys. Rev. A 42, 5990 (1990).
- H. A. Posch and W. G. Hoover, in Molecular Liquids, New Perspectives in Physics and Chemistry, Vol. 379 of NATO Advanced Study Institute, Series C: Mathematical and Physical Sciences, edited by José J. C. Teixeira Dias (Kluwer, Dordrecht, 1992), p. 527.
- P. Grassberger, Phys. Lett. 97A, 227 (1983).
- H. G. E. Hentschel and I. Procaccia, Physica D 8, 435 (1983).
- M. H. Jensen, L. P. Kadanoff and I. Procaccia, Phys. Rev. A 36, 1409 (1987).
- A. Chabra and R. V. Jensen, Phys. Rev. Lett. 62, 1327 (1989).
- F. J. Vesely, Computational Physics, An Introduction (Plenum, New York, 1994).
- E. G. D. Cohen, Physica A 213, 293 (1995).