Skip to main content

Part of the book series: NATO ASI Series ((ASIC,volume 379))

Abstract

Nonequilibrium systems in thermodynamic steady states can be studied by computer simulation, and the calculated transport coefficients are in agreement with results obtained by equilibrium methods. The basic algorithms are discussed. Although they require the incorporation of a thermostatting procedure, the resulting equations of motion are time-reversible. The observed macroscopic irreversibility is a consequence of the Lyapunov instability of the system measured by the spectrum of Lyapunov exponents. The phase-space distribution does not remain smooth and well-behaved but collapses onto a multifractal strange attractor in phase space with an information dimension smaller than the phase-space dimension. The attractor even remains fractal if it is projected onto a subspace spanned only by phase-space variables which are not directly affected by the computer thermostat. This is demonstrated for boundary-driven planar Couette flow, for which the number of variables associated with the thermostatted boundary can be made small.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. W. G. Hoover, Computational Statistical Mechanics, Studies in Modern Thermodynamics 11 (Elsevier, Amsterdam, 1991).

    Google Scholar 

  2. G. Ciccotti and W. G. Hoover (eds.), Molecular-Dynamics Simulation of Statistical - Mechanical Systems, Course XCVII of Proc. Int. School of Physics Enrico Fermi, Varenna, (North-Holland, Amsterdam, 1986).

    Google Scholar 

  3. M. P. Allen and D. J. Tildesley,Computer Simulations of Liquids(Clarendon Press, Oxford, 1987).

    Google Scholar 

  4. M. S. Green, J. Chem. Phys.20, 1281 (1952);22, 398 (1954).

    Article  CAS  Google Scholar 

  5. R. Kubo, J. Phys. Soc. (Jpn.) 12, 570 (1957).

    Article  Google Scholar 

  6. R. Zwanzig, Ann. Rev. Phys. Chem. 16, 67 (1965).

    Article  CAS  Google Scholar 

  7. B. J. Alder and T. E. Wainwright, Phys. Rev. A 1, 18 (1970).

    Article  Google Scholar 

  8. B. J. Alder and E. E. Alley, in Perspectives in Statistical Physics, edited by H. J. Raveche (Noth-Holland, Amsterdam, 1981), p. 3.

    Google Scholar 

  9. W. G. Hoover and W. T. Ashurst, Adv. Theor. Chemistry 1, 1, 1975.

    CAS  Google Scholar 

  10. D. J. Evans and G. P. Morriss,Statistical Mechanics of Nonequilibrium Liquids(Academic Press, London, 1990).

    Google Scholar 

  11. S. Y. Liem, D. Brown and J. H. R. Clarke, Phys. Rev. A 45, 3706 (1992).

    Article  CAS  Google Scholar 

  12. B. Holian and D. J. Evans, J. Chem. Phys. 83, 3560 (1985).

    Article  CAS  Google Scholar 

  13. D. J. Evans and G. P. Morriss, Molec. Phys. 64, 521 (1988).

    Article  CAS  Google Scholar 

  14. W. T. Ashurst, Ph. D. Thesis, University of California at Davis, 1974.

    Google Scholar 

  15. B. L. Holian and D. J. Evans, J. Chem Phys., 78, 5147 (1983).

    Article  CAS  Google Scholar 

  16. G. Ciccotti, G. Jacucci and I. R. McDonald, Phys. Rev A 13, 426 (1976)

    Article  CAS  Google Scholar 

  17. J. Stat. Phys. 21, 1 (1979).

    Article  Google Scholar 

  18. W. Loose and G. Ciccotti, Phys. Rev. A 45, 3859 (1992).

    Article  CAS  Google Scholar 

  19. W. Loose and S. Hess, Physica A 174, 47 (1991).

    Article  Google Scholar 

  20. A. Baranyai and D. J. Evans, Molec. Phys. 74, 353 (1991).

    Article  CAS  Google Scholar 

  21. S. Nosé, Molec. Phys. 52, 255 (1984).

    Article  Google Scholar 

  22. D. J. Evans, J. Chem. Phys. 78, 3297 (1983).

    Article  CAS  Google Scholar 

  23. D. J. Evans, W. G. Hoover, B. H. Failor, B. Moran A. J. C. Ladd, Phys. Rev. A 28, 1016 (1983).

    Article  CAS  Google Scholar 

  24. A. Sommerfeld, Vorlesungen über Theoretische Physik, Band 1: Mechanik, Akademische Verlagsgesellschaft, Leipzig, 1962.

    Google Scholar 

  25. S. Nosé, J. Chem. Phys. 81, 511 (1984).

    Article  Google Scholar 

  26. W. G. Hoover, Phys. Rev. A 31, 1695 (1985).

    Article  Google Scholar 

  27. H. A. Posch, W. G. Hoover and F. J. Vesely, Phys. Rev. A 33, 4253 (1986).

    Article  Google Scholar 

  28. D. Kusnezov, A. Bulgac and W. Bauer, Annals of Physics 204, 155 (1990)

    Article  CAS  Google Scholar 

  29. R. G. Winkler, Phys. Rev. A 45, 2250 (1992).

    Article  CAS  Google Scholar 

  30. G. J. Martyna, M. L. Klein and M. Tuckerman, “Nosé-Hoover Chains: the Canonical Ensemble via Continuous Dynamics” (Preprint, 1992).

    Google Scholar 

  31. A. Bulgac and D. Kusnezov, Phys. Rev B 45, 1988 (1992).

    Article  CAS  Google Scholar 

  32. H. A. Posch and W. G. Hoover, Phys. Rev. A 38, 473 (1988).

    Article  Google Scholar 

  33. W. G. Hoover, Lecture Notes in Physics 132, Systems far from equilibrium, edited by: J. Ehlers et alii (Springer-Verlag, Berlin, 1980) p. 373.

    Chapter  Google Scholar 

  34. W. G. Hoover, D. J. Evans, R. B. Hickman, A. J. C. Ladd, W. T. Ashurst and B. Moran, Phys. Rev. A 22, 1690 (1980).

    Article  CAS  Google Scholar 

  35. A. W. Lees and S. F. Edwards, J. Phys. C 5, 1921 (1972).

    Article  Google Scholar 

  36. D. J. Evans, Phys. Lett. A 91, 457 (1982)

    Article  Google Scholar 

  37. Phys. Rev. A 34, 1449 (1986).

    Article  CAS  Google Scholar 

  38. M. J. Gillan and M. Dixon, J. Phys. C 16, 869 (1983).

    Article  CAS  Google Scholar 

  39. D. MacGowan D. J. Evans, Phys. Lett. A 117, 414 (1986).

    Article  CAS  Google Scholar 

  40. W. Loose and S. Hess, Rheologica Acta 28, 91 (1989).

    Article  CAS  Google Scholar 

  41. B. J. Ackerson, Physica A 174 15 (1991).

    Article  CAS  Google Scholar 

  42. H. A. Posch and W. G. Hoover, Phys. Rev. A 39, 2175 (1989).

    Article  Google Scholar 

  43. W. G. Hoover, H. A. Posch and C. G. Hoover, Chaos 2, 2 (1992).

    Google Scholar 

  44. H. A. Posch and W. G. Hoover, in preparation.

    Google Scholar 

  45. B. L. Holian, Phys. Rev. A 34, 4238 (1986).

    Article  Google Scholar 

  46. W. G. Hoover, H. A. Posch, B. L. Holian, M. J. Gillan, M. Mareschal and C. Massobrio, Molec. Simulation 1, 79 (1997).

    Article  Google Scholar 

  47. H. A. Posch, W. G. Hoover and B. L. Holian, Ber. Bunsenges. Phys. Chem. 94, 250 (1990).

    Article  CAS  Google Scholar 

  48. W. G. Hoover and B. Moran, Phys. Rev. A 40, 5319 (1989).

    Article  Google Scholar 

  49. G. P. Morriss, Phys. Lett A 143, 307 (1989)

    Article  Google Scholar 

  50. Phys. Rev. A 39 4811 (1989).

    Article  Google Scholar 

  51. J. D. Farmer, E. Ott and J. A. Yorke, Physica 7D, 153 (1983).

    Google Scholar 

  52. J. Mandelbrot, Fluid Mech., 62, 331 (1974).

    Article  Google Scholar 

  53. U. Frisch and G. Parisi, in Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Research, edited by M. Ghil, R. Benzi and G. Parisi (North-Holland, Amsterdam, 1985) p.84.

    Google Scholar 

  54. T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia and B. I. Shraiman, Phys. Rev. A 33, 1141 (1986).

    Article  Google Scholar 

  55. A. B. Chhabra and R. V. Jensen, Phys. Rev. Lett. 62, 1327 (1989).

    Article  Google Scholar 

  56. J. Kaplan and J. Yorke, in Functional Differential Equations and the Approximation of Fixed Points, Vol. 730 of Lecture Notes in Mathematics, eds.: H. 0. Peitgen and H. 0. Walther (Springer-Verlag, Berlin, 1980).

    Google Scholar 

  57. R. Preston, The Mountains of Pi, The New Yorker, Mar. 2,1992, p. 36.

    Google Scholar 

  58. V. I. Arnold, Mathematical methods of classical mechanics(Springer, Berlin, 1989).

    Book  Google Scholar 

  59. D. J. Evans, E. G. D. Cohen and G. P. Morriss, Phys. Rev. A 42, 5990 (1990).

    Article  CAS  Google Scholar 

  60. B. L. Holian, W. G. Hoover and H. A. Posch, Phys. Rev. Lett.59, 10 (1987).

    Article  Google Scholar 

  61. J. L. Lebowitz, first round-table remarks inSimulation of Complex Hydrodynamic Phenomena, edited by M. Mareschal, NATO-ASI in Alghero, Sardinia (Plenum, New York, 1992).

    Google Scholar 

  62. S. Goldstein, C. Kipnis and N. Ianiro, J. Stat. Phys.41, 915 (1985).

    Article  Google Scholar 

  63. S. Goldstein, J. L. Lebowitz and E. Presutti, Colloquia Math. Soc. Janos Bolyai27, Random fields (Esztergom, Hungary, 1981).

    Google Scholar 

  64. E. T. Jaynes, Papers on Probability, Statistics and Statistical Physics, edited by R. D. Rosenkrantz (Kluwer, Dordrecht, 1989).

    Google Scholar 

  65. D. N. Zubarev, Nonequilibrium Statistical Thermodynamics, (Consultants bureau, New York, 1974).

    Google Scholar 

  66. W. G. Hoover, J. Stat. Phys. 42, 587 (1986).

    Article  Google Scholar 

  67. H. A. Posch, H. Narnhofer and W. Thirring, J. Stat. Phys.65, 555 (1991).

    Article  Google Scholar 

  68. W. Pusz and S. L. Woronowicz, Commun. Math. Phys.58, 273 (1978).

    Article  Google Scholar 

  69. A. Lenard, J. Stat. Phys.19, 575 (1978).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Posch, H.A., Hoover, W.G. (1992). Nonequilibrium Molecular Dynamics of Classical Fluids. In: Teixeira-Dias, J.J.C. (eds) Molecular Liquids: New Perspectives in Physics and Chemistry. NATO ASI Series, vol 379. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2832-2_30

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-2832-2_30

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5258-0

  • Online ISBN: 978-94-011-2832-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics