Abstract
The Enskog repeated ring equations (ERRE) for tagged molecule motion are derived from the BBGKY hierarchy. The hierarchical deviation demonstrates the problem associated with using naive truncations for complex fluid systems. A moment-variational solution is suggested for the ERRE. The moment-variational method is applied to the ERRE for the two- and three-dimensional overlapping Lorentz gas (LG). Both self-consistent and non-self-consistent equations for the diffusion constant are solved. The results compare favorably with previous calculations and molecular dynamics (MD).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Special issue, “Fluids out of equilibrium,”Physics Today 37(1):25 (1984).
P. Resibois and M. DeLeener,Classical Kinetic Theory of Fluids (Wiley, New York, 1977).
J. R. Dorfman, inFundamental Problems in Statistical Mechanics, Vol. 3, E. G. Cohen, ed. (North-Holland, Amsterdam, 1975).
M. H. Ernst and J. R. Dorfman,Physics 61:157 (1972).
J. R. Dorfman, H. van Beijeren, and C. F. McClure,Arch. Mech. 28:333 (1976); H. van Beijeren and J. R. Dorfman,J. Stat. Phys. 23:335 (1980); H. van Beijeren and J. R. Dorfman,J. Stat. Phys. 23:443 (1980).
R. I. Cukier, R. Kapral, J. R. Lebenhaft, and J. R. Mehaffey,J. Chem. Phys. 73:5244 (1980).
J. Mercer, Ph.D. thesis, Yale Yniversity (1981), unpublished.
B. Alder and T. Wainwright,Phys. Rev. A 1:18 (1970).
J. Dorfman and E. Cohen,Phys. Rev. A 6:776 (1972).
A. Masters and T. Keyes,Phys. Rev. 26:2129 (1982).
A. J. Masters, Ph.D. thesis, University of Cambridge (1980), unpublished.
W. Gotze, E. Leutheusser, and S. Yip,Phys. Rev. A 23:2634 (1981);25:533 (1982).
W. Sung and J. S. Dahler,J. Chem. Phys. 78:6267 (1983).
A. Masters and T. Keyes,J. Slat. Phys. 33:149 (1983).
A. J. Masters and T. Keyes,Phys. Rev. A 25:1010 (1982).
A. J. Masters and T. Keyes,Phys. Rev. A 27:2603 (1983).
C. Cercignani,Theory and Application of the Boltzmann Equation (Elsevier, New York, 1975).
C. Cercignani,J. Stat. Phys. 1:297 (1969).
C. Bruin,Physica 72:261 (1974).
B. J. Alder and W. E. Alley,J. Stat. Phys. 19:341 (1978).
M. J. Ernst, J. R. Dorfman, W. R. Hoegy, and J. M. J. van Leeuwen,Physica 45:127 (1968).
R. G. Cole, D. R. Evans, and D. K. Hoffman,J. Chem. Phys. 82:2061 (1985).
J. Karkheck and G. Stell,Phys. Rev. A 25:3302 (1982).
T. Keyes and J. Mercer,Physica 95A:473 (1979).
J. A. McLennen,Phys. Fluids 8:1580 (1965).
P. F. Bhatnagar, E. P. Gross, and M. Krook,Phys. Rev. 94:511 (1954).
C. Cercignani and G. Tironi,J. Plasma Phys. 2:293 (1968).
J. T. Hynes, R. Kapral, and M. Weinberg,J. Chem. Phys. 70:1456 (1979).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cole, R.G., Keyes, T. The Enskog repeated ring equations for tagged molecule motion and variational solutions. J Stat Phys 51, 249–273 (1988). https://doi.org/10.1007/BF01015330
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01015330