Abstract
The eigenmodes of a classical fluid in thermal equilibrium are discussed. For long wavelengths and times, they can be computed from linear hydrodynamic equations. They are then the hydrodynamic modes, in particular, the heat mode, which describes the diffusion of heat in the fluid and two sound modes. For short wavelengths and times they can be derived from linear kinetic operators. For low densities, the linear Boltzmann operator can be employed and the three most important eigenmodes are direct extensions of the kinetic analogues of the heat and sound modes. For high densities, a generalization of the Boltzmann operator is used. The most important eigenmode is the extended heat mode, while next in importance come two eigenmodes that are extensions of the sound modes. These three extended hydrodynamic modes can be used to obtain the light and neutron spectra of fluids and vice versa.
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References
Boon, J. P. and Yip, S., Molecular Hydrodynamics, (McGraw Hill, New York, 1980).
Résibois, P. and de Leener, M., Classical Kinetic Theory of Fluids, (Wiley-Interscience, New York, 1977).
Hansen, J. P. and McDonald, I. R., The Theory of Simple Liquids, (Academic Press, London, 1976).
Zwanzig, R., Ann. Rev. Phys. Chem. 16 (1965) 67.
Berne, B. J. and Pecora, R., Dynamic Light Scattering, (Wiley-Interscience, New York, 1976).
Wood, W. W., in: Fundamental Problems in Statistical Mechanics, III, Cohen, E. G. D., ed., (North-Holland, Amsterdam, 1975)
Wood, W. W. and Erpenbeck, J. J., Ann. Rev. Phys. Chem. 27 (1976) 319.
Mountain, R. D., Rev. Mod. Phys. 38 (1966) 205.
Foch, J. D. and Ford G. W., in: Studies in Statistical Mechanics, V, de Boer, J. and Uhlenbeck, G. E., eds., (North-Holland, Amsterdam, 1970), Part B, Chap. Ii.
See, for instance, Ernst, M. H. and Dorfman, J. R., J. Stat. Phys. 12 (1975) 311.
DeMasi, A., Ianiro, N., Pellegrinotti, A. and Presutti, in: Studies in Statistical Mechanics, XI, Lebowitz, J. L. and Montroll, E. W., eds. (North-Holland, Amsterdam, 1984).
de Schepper, I. M., van Rijs, J. C. and Cohen, E. G. D., Physica A, 1986.
Ref. [9], Part B, Ch. III.
Greenberg, W., Polewezak, J. and Zweifel, P. F., in: The Boltzmann Equation in Studies in Statistical Mechanics, X, Montroll, E. W. and Lebowitz, J. L., eds., (North-Holland, Amsterdam, 1983).
Wang Chang, C. S. and Uhlenbeck, G. E., in: Studies in Statistical Mechanics, V, de Boer, J. and Uhlenbeck, G. E., eds., (North-Holland, Amsterdam, 1970), Part A, Ch. IV.
Alterman, Z., Frankowski, K. and Pekeris, C. S., Am. Astrophys. J. Suppl. 69, VII, (1962) 291.
Chapman, S. and Cowling, T. G., The Mathematical Theory of Nonuniform Gases, (Cambridge University Press, Cambridge, 1970).
Grad, H., Commun. Pure and Appl. Math. 2 (1949) 331.
Kamgar-Parsi, B. and Cohen, E. G. D., to be published.
Lebowitz, J. L., Percus, J. K. and Sykes, J., Phys. Rev. 188 (1969) 487.
Mazenko, G. F., Phys. Rev. A7 (1973) 209, 222; 9 (1974) 360.
Konijnendijk, H. M. U. and van Leeuwen, J. M. J., Physica 64 (1973) 232.
Beijeren, H. and Ernst, M. H., Physica 68 (1973) 43, J. Stat. Phys. 21 (1979) 125.
Dorfman, J. R. and Cohen, E. G. D., Phys. Rev. A12 (1975) 292.
Mazenko, G. F. and Yip, S., in: Mondern Theoretical Chemistry, Vol. 6, (Plenum Press, New York, 1977).
de Schepper, I. M. and Cohen, E. G. D., J. Stat. Phys. 27 (1982) 223.
Ref. [15], Ch. V.
de Schepper, I. M., Cohen, E. G. D. and Zuilhof, M. J., Phys. Lett. 101A (1984) 399.
Zuilhof, M. J., Cohen, E. G. D. and de Schepper, I. M., Phys. Lett. 103A (1984) 120.
Cohen, E. G. D., de Schepper, I. M. and Zuilhof, M. J., Physica 127B (1984) 282.
Kirkpatrick, T. R., Phys. Rev. A32 (1985).
Cohen, E. G. D., de Schepper, I. M. and Kamgar-Parsi, B., Phys. Letts., (1986).
Alley, W. E. and Alder, B. J., Phys. Rev. A27 (1983) 3158.
Alley, W. E., Alder, B. J. and Yip, S., Phys. Rev. A27 (1983) 3174.
de Schepper, I. M., and Cohen, E. G. D., Phys. Rev. A22 (1980) 287.
de Schepper, I. M., Verkerk, P., van Well, A. A. and de Graaf, L. A., Phys. Rev. Lett. 50 (1983) 974.
van Well, A. A., de Graaf, L. A., Verkerk, P., Suck, J. B. and Copley, J. R., Phys. Rev. A31 (1985) 3391.
Verkerk, P., Ph. D. Thesis, University of Technology, Delft (1985).
van Well, A. A. and de Graaf, L. A., Phys. Rev. A32 (1985).
van Well, A. A. and de Graaf, L. A., Phys. Rev. A32 (1985).
van Well, A. A., Ph. D. Thesis, University of Technology, Delft (1985).
de Schepper, I. M., van Rijs, J. C., van Well, A. A., Verkerk, P., de Graaf, L. A. and Bruin, C., Phys. Rev. 29A (1984) 1602.
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Cohen, E.G.D. (1986). Eigenmodes of classical fluids in thermal equilibrium. In: Kröner, E., Kirchgässner, K. (eds) Trends in Applications of Pure Mathematics to Mechanics. Lecture Notes in Physics, vol 249. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0016379
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DOI: https://doi.org/10.1007/BFb0016379
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