IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v129y1984i1p81-94.html
   My bibliography  Save this article

The covariant form of the Klein-Kramers equation and the associated moment equations

Author

Listed:
  • Kneller, Gerald R.
  • Titulaer, U.M.

Abstract

We provide a covariant, coordinate-free formulation of the many-dimensional Klein-Kramers equation for the phase space distribution of a Brownian particle. We construct a complete set of eigenfunctions of the collision operator adapted to the coordinate system, which involve covariant tensorial Hermite polynomials. The Klein-Kramers equation can then be reformulated as a system of coupled equations for the expansion coefficients with respect to this system. Truncation of this system of moment equations and application of a subsidiary condition yields a covariant generalization of Grad's thirteen-moment equations. As an application we give the explicit form of these equations for spherically symmetric, stationary solutions in spherical coordinates. We briefly comment on possible extensions of our treatment to slightly more complicated cases.

Suggested Citation

  • Kneller, Gerald R. & Titulaer, U.M., 1984. "The covariant form of the Klein-Kramers equation and the associated moment equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 129(1), pages 81-94.
    • Handle: RePEc:eee:phsmap:v:129:y:1984:i:1:p:81-94
    DOI: 10.1016/0378-4371(84)90022-0
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437184900220
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/0378-4371(84)90022-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Theiss, W. & Titulaer, U.M., 1985. "The systematic adiabatic elimination of fast variables from a many-dimensional Fokker-Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 130(1), pages 123-142.
    2. Menon, S.V.G. & Kumar, Vinod & Sahni, D.C., 1986. "Green's function approach to the solution of the time dependent Fokker-Planck equation with an absorbing boundary," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 135(1), pages 63-79.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:129:y:1984:i:1:p:81-94. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.