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- 1
- Gary D. Doolen, ed.,
Lattice Gas Methods for Partial Differential Equations
(Addison-Wesley, Redwood City, California, 1990);
Lattice Gas Methods: Theory, Applications, and Hardware
(MIT, Cambridge, 1991).
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- Journal of Statistical Physics,81(1/2), (1995).
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A. K. Gunstensen, D. H. Rothman, S. Zaleski, and G. Zanetti,
Phys. Rev. A 43, 4320 (1991);
A. K. Gunstensen, Ph.D. thesis, M.I.T., (1992);
A. K. Gunstensen and D. H. Rothman,
Europhys. Lett. 18, 157 (1992);
J. Geophys. Res. 98, 6431 (1993).
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- X. Shan and H. Chen,
Phys. Rev. E 47, 1815 (1992);
ibid 49, 2941 (1994).
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- M. R. Swift, W. R. Osborn, and J. M. Yeomans,
Phys. Rev. Lett. 75, 830 (1995);
W. R. Osborn, E. Orlandini, M. R. Swift, J. M. Yeomans, and
J. R. Banavar,
ibid 75, 4031 (1995);
E. Orlandini, M. R. Swift, and J. M. Yeomans,
Europhys. Lett. 32, 463 (1995).
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- N. S. Martys and H. Chen,
Phys. Rev. E 53, 743 (1996).
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- N. S. Martys, X. Shan and H. Chen,
Phys. Rev. E 58, 6855 (1998).
- 8
- B. T. Nadiga,
Euro. J. Mech. B:Fluids 15, 885 (1996).
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- J. H. Irving and J. G. Kirkwood,
J. Chem. Phys. 18, 817 (1950).
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- F. Mohling,
Statistical Mechanics: Methods and Applications
(John Wiley and Sons, Inc., New York, 1982).
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- P. L. Bhatnagar, E. P. Gross, and M. Krook,
Phys. Rev. 94, 511 (1954).
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- X. Shan and X. He,
Phys. Rev. Lett. 90, 65 (1998).
- 13
- Most of the results described in this section can be
found, or are minor extensions of that, in
references number [9] and [10].
- 14
- T. M. Reed and K. E. Gubbins ,
Applied Statistical Mechanics
(Butterworth-Heinemann, Stoneham, MA 1991).
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- S. Chapman and T. G. Cowling,
The Mathematical Theory of Non-Uniform Gases, 3rd ed.,
Cambridge University Press, London, (1970).
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- W. E. Alley, B. J. Alder, and S. Yip,
Phys. Rev. A 27, 3174 (1983).
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- W. E. Alley, and B. J. Alder,
Physical Rev. A 27, 3158 (1983).
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- C. Cercignani,
Theory and Application of the Boltzmann Equation
(Elsevier, New York , 1975).
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- H. Grad,
Commun. Pure Appl. Math. 2, 325 (1949).
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- A. Santos, J. M. Montanero, J. Dufty, and J. J. Brey,
Phys. Rev. E 57, 1644 (1983).
- 21
- As an alternative approach, W, the contribution to the
stress tensor due to non-local interactions may be derived from
a free energy. For instance see: R. Evans, Adv. in Phys., 28, 143, (1979) and L. M. Lust, O. T. Valls, and C.
Dasgupta, Phys. Rev. E 48, 1787 (1993).
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- G. McNamara and B. Alder, Physica A 194, 218 (1993).
- 23
- Y. Chen, H. Ohashi, and M. Akiyama, PRE 50, 2776 (1994).
- 24
- See for instance, M. R. Swift. E. Orlandini, W. R. Osborn, and, J. M.
Yeomans, Phys. Rev. E 54 5041 (1996). X. He., X. Shan, and G. Doolen, Phys. Rev. E
57 R13 (1998).
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- H. Chen, C. Teixera, and K. Molvig, International Journal of Modern Physics
C 8 675 (1997).
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- J.A. Leegwater, Ph.D.Thesis, Utrecht Univ. (1991).
- 27
- J.P. Boon and S. Yip, Molecular Hydrodynamics,
Dover Publications, Inc., New York (1980).
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