Abstract
The role of computer studies in the kinetic theory of fluids is briefly reviewed, with emphasis upon the results for hard-core systems. After a short discussion of the advantages and limitations of computer methods, we first consider computer studies directly related to the Boltzmann equation, e.g., calculations of the one-particle distribution function f(r,v,t), by the methods of molecular dynamics and by numerical solution of the Boltzmann equation itself. There then follows a review of the molecular dynamics studies of time-correlation functions and the associated transport coefficients.
Work performed under the auspices of the U.S. Atomic Energy Commission.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
AHARONY, A., 1971, Physics Letters 37A, 45 (1971).
ALDER, B.J., GASS, D.M., and WAINWRIGHT, T.E., 1970, J. Chem. Phys. 53, 3813.
ALDERALDER, B.J., and WAINWRIGHT, T.E., 1958, International Symposium on Statistical Mechanical Theory of Transport Processes, Brussels, 1956, I. Prigogine, editor (Interscience, 1958), p. 97.
ALDER, B.J., and WAINWRIGHT, T.E., 1959, J. Chem. Phys. 31, 459.
ALDER, B.J., and WAINWRIGHT, T.E., 1967, Phys. Rev. Letters 18, 968.
ALDER, B.J., and WAINWRIGHT, T.E., 1969, J. Phys. Soc. Japan 26, Supplement, p. 267 ( Proceedings of the International Conference on Statistical Mechanics, Kyoto, 1968 ).
ALDER, B.J., and WAINWRIGHT, T.E., 1970, Phys. Rev. Al, 18.
BALESCU, R., 1967, Physica 36, 433 (1967).
BERNE, B.J., 1971, in Physical Chemistry, An Advanced Treatise (H. Eyring, D. Henderson, and W. Jost, editors; Academic Press) Vol VIII B, Liquid State, page 539.
BERNE, B.J., and FORSTER, D., 1971, Ann. Rev. Phys. Chem. 22, 563.
BIRD, G.A., 1970, Phys. of Fluids 13, 2676; see also earlier work mentioned therein.
CARLIER, C., and FRISCH, H.L., 1972, Phys. Rev. A6, 1153 (1972).
DORFMAN, J.R., and COHEN, E.G.D., 1970, Phys. Rev. Letters 25, 1257.
DORFMAN, J.R., and COHEN, E.G.D., 1972, Phys. Rev. A6, 776.
DUFTY, J.W., 1972, Phys. Rev. A5, 2247.
ERNST, M.H., 1967, “Transport Coefficients from Time Correlation Functions” in “Lectures in Theoretical Physics”, Vol. IX C, “Kinetic Theory”, W.E. Brittin,editor ( Gordon and Breach, Inc. N.Y. 1967 ), p. 441.
ERNST, M.H., HAUGE, E.H., and van LEEUWEN, J.M.J., 1970Phys. Rev. Letters, 25, 1254.
ERNST, M.H., HAUGE, E.H., and van LEEUWEN, J.M.J., 1971a, Physics Letters 34A, 419.
ERNST, M.H., HAUGE, E.H., and van LEEUWEN, J.M.J., 1971b, Phys. Rev. A4, 2055.
ERPENBECK, J.J., and WOOD, W.W., 1972, preliminary unpublished results.
GRAD, H., 1958, in Encyclopedia of Physics (S. Flügge, ed., Springer, Berlin ), Vol. XII, page 205.
HAUGE, E.H., and COHEN, E.G.D., 1967, Phys. Letters 25A, 78.
HAUGE, E.H., and COHEN, E.G.D., 1969, J. Math. Phys. 10, 397.
HERMAN, P.T., and ALDER, B.J., 1972, J. Chem. Phys. 56, 987.
HICKS, B.L., YEN, S.M., and REILLY, B.J., 1972, J. Fluid Mech. 53, 85.
KAWASAKI, K., 1970, Physics Letters, 32A, 379.
KAWASAKI, K., 1971, Prog. Theoretical Physics (Kyoto) 45, 1691.
LEVESQUE, D., and VERLET, L., 1970, Phys. Rev. A 2, 2514.
ORBAN, J., and BELLEMANS, A., 1967, Physics Letters 24A, 620.
ORBAN, J., and BELLEMANS, A., 1969, J. of Statistical Physics, 1, 467.
RAHMAN, A., 1964, Phys. Rev. 136, A405.
SEGAL, B.H., and FERZIGER, J.H., 1972, Phys. of Fluids 15, 1233.
van EEYEREN, H., and HAUGE, E.H., 1972, Physics Letters 39A, 397.
van LEEUWEN, J.M.J., and BRUIN, C., 1972, Private communication.
van LEEUWEN, J.M.J., and WEIJLAND, A., 1967, Physica 36, 457.
VERLET, L., 1967, Phys. Rev. 159, 98.
WAINWRIGHT, T.E., ALDER, B.J., and GASS, D.M., 1971, Phys. Rev. A4, 233.
WOOD, W.W., and LADO, F., 1971, Journal of Computational Physics 7, 528.
ZWANZIG, R., 1965, Ann. Rev. Phys. Chem. 16, 67.
ZWANZIG, R. and BIXON, M., 1970, Phys. Rev. A2, 2005.
Added in proof
ALDER, B.J., and WAINWRIGHT, T.E., 1972, private communication.
METROPOLIS, N.A., ROSENBLUTH, A.W., ROSENBLUTH, M.N., TELLER, A.H., and TELLER, E., 1953, J. Chem. Phys. 21, 1087.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1973 Springer-Verlag
About this paper
Cite this paper
Wood, W.W. (1973). A Review of Computer Studies in the Kinetic Theory of Fluids. In: Cohen, E.G.D., Thirring, W. (eds) The Boltzmann Equation. Acta Physica Austriaca, vol 10/1973. Springer, Vienna. https://doi.org/10.1007/978-3-7091-8336-6_19
Download citation
DOI: https://doi.org/10.1007/978-3-7091-8336-6_19
Publisher Name: Springer, Vienna
Print ISBN: 978-3-7091-8338-0
Online ISBN: 978-3-7091-8336-6
eBook Packages: Springer Book Archive