IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v367y2006icp129-135.html
   My bibliography  Save this article

Anomalous motion generated by the Coulomb friction in the Langevin equation

Author

Listed:
  • Mauger, A.

Abstract

We study the stability of the Maxwell–Boltzmann (i.e., Gaussian) distribution for the density of states at equilibrium, against an arbitrary choice of the friction in the Langevin equation. We find that this distribution is Gaussian, if and only if the friction is Lipschitz continuous. In particular, we argue that the origin of the exponential (instead of Gaussian) velocity distribution (PDF) of particles when the viscous friction is replaced by the Coulomb friction in the Langevin equation with white noise is due to the non-Lipschitz continuity of the Coulomb friction, a feature of solid friction. The use of the Fokker–Planck equation to determine the exponential PDF is justified, since the subset on which the friction is not continuous is of zero probability (v=0). The application to the motion of granular gases is discussed.

Suggested Citation

  • Mauger, A., 2006. "Anomalous motion generated by the Coulomb friction in the Langevin equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 129-135.
    • Handle: RePEc:eee:phsmap:v:367:y:2006:i:c:p:129-135
    DOI: 10.1016/j.physa.2005.12.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437105012458
    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/j.physa.2005.12.001?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.

    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:367:y:2006:i:c:p:129-135. 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.