Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Developments toward a series solution of the Maxwell-Boltzmann equation

This is a preview of subscription content, log in to check access.

References

  1. [1]

    Bayet, M., J. L. Delcroix et J. F. Denisse: Sur la résolution de l'équation de Boltzmann dans le cas d'un gaz de Lorentz; application aux gaz faiblement ionisés. Académie des Sciences, Comptes Rendus 238, 2146–2148 (1954).

  2. [2]

    Bohm, D.: Quantum Theory. New York: Prentice-Hall Inc. 1951.

  3. [3]

    Boĺtzmann, L.: Gastheorie, vol. I. Leipzig: Johann Ambrosius Barth (Arthur Meiner), 1896.

  4. [4]

    Burnett, D.: The Distribution of Molecular Velocities and the Mean Motion in a Non-uniform Gas. Proceedings of the London Mathematical Society 40, 382–435 (1934).

  5. [5]

    Chapman, S., & T. G. Cowling: The Mathematical Theory of Non-uniform Gases. Cambridge: Cambridge University Press 1939.

  6. [6]

    Enskog, D.: Kinetische Theorie der Vorgänge in mäßig verdünnten Gasen. Inaugural-Dissertation. Upsala 1917.

  7. [7]

    Enskog, D.: Zur Elektronentheorie der Dispersion und Absorption der Metalle. Annalen der Physik 38, 731–763 (1912).

  8. [8]

    Grad, H.: On the Kinetic Theory of Rarified Gases. Communications on Pure and Applied Mathematics 2, 331–407 (1949).

  9. [9]

    Hobson, E. W.: The Theory of Spherical and Ellipsoidal Harmonics. Cambridge: Cambridge University Press 1931.

  10. [10]

    Ikenberry, E.: On the Distribution Function in Phase Space, with Application to the Statistical Theory of Liquids. The Journal of Chemical Physics 19, 467–470 (1951).

  11. [11]

    Ikenberry, E., & C. Truesdell: On the Pressures and the Flux of Energy in a Gas according to Maxwell's Kinetic Theory, I. Journal of Rational Mechanics and Analysis 5, 1–54 (1956).

  12. [12]

    Jaffé, G.: Zur Methodik der kinetischen Gastheorie. Annalen der Physik, 5. Folge 6, 195–252 (1930).

  13. [13]

    Margenau, H., & G. M. Murphy: The Mathematics of Physics and Chemistry. Second edition. Princeton: D. Van Nostrand Company, Inc. 1956.

  14. [14]

    Maxwell, J. C.: On the Dynamical Theory of Gases. The Scientific Papers of James Clerk Maxwell. Vol. 2, pp. 26–78. New York: Dover Publications, Inc. 1890.

  15. [15]

    Maxwell, J. C.: On Stresses in Rarified Gases Arising from Inequalities of Temperature. The Scientific Papers of James Clerk Maxwell. Vol. 2, pp. 681–712. New York: Dover Publications, Inc. 1890.

  16. [16]

    Morse, P. M., & H. Feshbach: Methods of Theoretical Physics, Part II. New York: McGraw-Hill Book Company, Inc. 1953.

  17. [17]

    Mott-Smith, H. M.: A New Approach in the Kinetic Theory of Gases. Lincoln Laboratory Group Report v-2 (Massachusetts Institute of Technology, Cambridge, Massachusetts, December, 1954).

  18. [18]

    Schaefer, C.: Einführung in die theoretische Physik. Dritter Band, II. Teil. Berlin: W. de Gruyter and Company 1937.

  19. [19]

    Schmeidler, W.: Integralgleichungen mit Anwendungen in Physik und Technik. Leipzig: Akademische Verlagsgesellschaft Geest & Portig, K.G. 1950.

  20. [20]

    Truesdell, C.: On the Pressures and the Flux of Energy in a Gas according to Maxwell's Kinetic Theory, II. Journal of Rational Mechanics and Analysis 5, 55–128 (1956).

  21. [21]

    Wang Chang, C. S., & G. E. Uhlenbeck: On the Propagation of Sound in Monatomic Gases. University of Michigan Engineering Research Institute Report (October, 1952), O.N.R. Contract N60nr-23222, Project M 999.

  22. [22]

    Watson, G. N.: A Treatise on the Theory of Bessel Functions. Second edition. Cambridge: Cambridge University Press 1948.

  23. [23]

    Whittaker, E. T., & G. N. Watson: A Course of Modern Analysis. Cambridge: Cambridge University Press 1950.

Download references

Author information

Additional information

Communicated by C. Truesdell

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Johnson, D.E., Ikenberry, E. Developments toward a series solution of the Maxwell-Boltzmann equation. Arch. Rational Mech. Anal. 2, 41–65 (1958). https://doi.org/10.1007/BF00277918

Download citation

Keywords

  • Neural Network
  • Complex System
  • Nonlinear Dynamics
  • Electromagnetism
  • Series Solution