Abstract
We define an integral transform of the energy distribution function for an isotropic and homogeneous diluted gas. It may be interpreted as a linear combination of equilibrium states with variable temperatures. We show that the temporal evolution features of the distribution function are determined by the singularities of this temperature transform. We compare the relaxation to the equilibrium process for Maxwell and very hard-particle interaction models, finding many basic discrepancies. Finally, we formulate an alternative approach, which is given by anN-pole approximation with a clear physical meaning.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. L. Lebowitz and E. W. Montroll, eds.,Non-equilibrium Phenomena I, The Boltzmann Equation (North-Holland, Amsterdam, 1983).
M. H. Ernst,Phys. Rep. 78:1 (1981).
A. V. Bobylev,Sov. Phys. Dokl. 20:820, 822 (1976).
E. H. Hauge and E. Praestgaard,J. Stat. Phys. 24:21 (1981).
M. Alexanian,Phys. Lett. 74A:1 (1979).
M. Krook and T. T. Wu,Phys. Fluids 20:1589 (1977).
M. H. Ernst,Phys. Lett. 69A:390 (1979).
H. Cornille and A. Gervois,Phys. Lett. 79A:291 (1980).
E. M. Hendriks and M. H. Ernst,Physica 120A:545 (1983).
C. Cercignani,Theory and Application of the Boltzmann Equation (Scottish Academic Press, Edinburgh, 1975).
S. Simons,Phys. Lett. 69A:239 (1978).
R. O. Barrachina, D. H. Fujii and C. R. Garibotti,Phys. Lett. 109A:447 (1985).
R. Courant and D. Hilbert,Methods of Mathematical Physics, Vol.1 (Interscience, New York, 1953).
P. Henrici,Applied and Computational Complex Analysis, Vol. 2 (Wiley, New York, 1977).
M. Barnsley and H. Cornille,J. Math. Phys. 25:1176 (1980).
E. M. Hendriks and T. M. Nieuwenhuizen,J. Stat. Phys. 29:591 (1982).
A. V. Bobylev,Sov. Phys. Dokl. 25:257 (1980).
D. H. Fujii, R. O. Barrachina and C. R. Garibotti,J. Stat. Phys. 44:95 (1986).
G. A. Baker, Jr.,Essential of Padé Approximants (Academic Press, New York, 1975).
R. G. Gordon,J. Math. Phys. 9:655 (1968).
H. Rutishauser,Der Quotienten-Differenzen Algorithmus (Birkhauser, Basel/Stuttgart, 1957).
M. Barnsley and G. Turchetti,Lett. Nuovo Cimento 26:188 (1979).
Author information
Authors and Affiliations
Additional information
Fellow of the Conselho Nacional de Desenvolvimento Cientifico e Tecnólogico, Brazil.
Rights and permissions
About this article
Cite this article
Barrachina, R.O., Fujii, D.H. & Garibotti, C.R. Temperature transform of the Boltzmann equation. J Stat Phys 45, 647–668 (1986). https://doi.org/10.1007/BF01021089
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01021089