Abstract
The Fokker-Planck equation for a heavy particle in a dilute gas of light particles is derived from a Boltzmann equation. Inelastic collisions between the heavy and light particles are considered, and explicit quadratures for the frictional coefficients are given in terms of the scattering kernels. It is shown that the general formulation reduces properly to known results in the cases of pure elastic and pure diffuse scattering, respectively.
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W. G. N. Slinn, S. F. Shen, and R. M. Mazo,J. Stat. Phys. 2:251 (1970).
W. G. N. Slinn, and S. F. Shen,J. Stat. Phys. 3:291 (1971).
R. M. Mazo,J. Chem. Phys. 60:2634 (1974).
C. S. Wang Chang and G. E. Uhlenbeck, inStudies in Statistical Mechanics, Vol. 5, J. de Boer and G. E. Uhlenbeck, eds., North-Holland, Amsterdam (1970) [reprinted from a University of Michigan unpublished report (1956)].
R. M. Mazo,J. Chem. Phys. 35:831 (1961).
D. Montgomery,Phys. Fluids 14:2088 (1971).
S. Harris,An Introduction to the Theory of the Boltzmann Equation, Holt, Rinehart and Winston, New York (1971).
M. M. R. Williams,Z. Naturforsch. 27a:1798, 1804 (1972);J. Phys. D 6:744, 759 (1973).
L. Waldmann, inHandbuch der Physik, Vol. XII, S. Flugge, ed., Springer-Verlag, Berlin (1958), p. 348ff.
J. H. Ferziger and H. G. Kaper,Mathematical Theory of Transport Processes in Gases, North-Holland, Amsterdam (1972).
M. Epstein,AIAA J 5:1797 (1967).
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Supported by NSF Grant GP-27455.
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Mazo, R.M. On the theory of brownian motion. VIII. A Brownian particle in a dilute gas with inelastic collisions. J Stat Phys 12, 427–436 (1975). https://doi.org/10.1007/BF01012886
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DOI: https://doi.org/10.1007/BF01012886