Abstract
The complete time dependence of the stress-stress correlation functions in lattice gas cellular automata is calculated from the ring kinetic theory using numerical and analytical methods. This provides corrections, typically of 10–20%, to the usual molecular chaos calculations, where correlation functions decay exponentially. The resulting correlation function crosses over from an initial exponential decay to the long-time behavior calculated from mode coupling theory. The present theory, applied to the viscosity, accounts for a substantial part of the observed difference between the Boltzmann theory and simulations.
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References
U. Frisch, D. d'Humières, B. Hasslacher, P. Lallemand, Y. Pomeau, and J. P. Rivet,Complex Systems 1:649 (1987); see also G. D. Doolen, ed.,Lattice Gas Methods for Partial Differential Equations, reprint volume (Addison-Wesley, 1990), p. 75.
D. d'Humières and P. Lallemand, inLattice Gas Methods for Partial Differential Equations, G. D. Doolen, ed., reprint volume (Addison-Wesley, 1990), p. 299.
B. Boghosian and C. D. Levermore, inDiscrete Kinetic Theory, Lattice Gas Dynamics and Foundations of Hydrodynamics, R. Monaco, ed. (World Scientific, Singapore, 1989), p. 44.
M. Gerits and M. A. van der Hoef, unpublished (1991).
M. A. van der Hoef and D. Frenkel,Phys. Rev. A 41:4277 (1990).
J. R. Dorfman and H. van Beijeren,Statistical Mechanics, Part B: Time-Dependent Processes, B. J. Berne, ed. (Plenum Press, New York, 1977).
T. R. Kirkpatrick and M. H. Ernst,Phys. Rev. A 44:8051 (1991).
D. Frenkel and M. H. Ernst,Phys. Rev. Lett. 63:2165 (1989).
T. Naitoh, M. H. Ernst, M. A. van der Hoef, and D. Frenkel,Phys. Rev. A 44:2484 (1991); and preprint (1991).
M. A. van der Hoef and D. Frenkel,Phys. Rev. Lett. 66:1591 (1991).
T. Naitoh, M. H. Ernst, and J. W. Dufty,Phys. Rev. A 42:7187 (1990).
J. A. Leegwater and G. Szamel,Phys. Rev. Lett. 67:408 (1991).
R. Brito and M. H. Ernst, submitted.
M. H. Ernst and J. W. Dufty,J. Stat. Phys. 58:57 (1990).
R. Brito, M. H. Ernst, and T. R. Kirkpatrick,J. Stat. Phys. 62:283 (1991).
R. Brito and M. H. Ernst,Phys. Rev. A 44:8384 (1991).
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van Velzen, G.A., Brito, R. & Ernst, M.H. Stress-stress correlation functions in lattice gases beyond Boltzmann's approximation. J Stat Phys 70, 811–832 (1993). https://doi.org/10.1007/BF01053596
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DOI: https://doi.org/10.1007/BF01053596