IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v173y1991i1p141-154.html
   My bibliography  Save this article

Diffusion in classical periodic systems: The Smoluchowski equation approach

Author

Listed:
  • Ferrando, R.
  • Spadacini, R.
  • Tommei, G.E.
  • Levi, A.C.

Abstract

The classical diffusion of a particle in a periodic system is studied employing the Smoluchowski equation with an external periodic field of force. Assuming a two-dimensional rectangular symmetry and an external potential of a simple cosine shape, the resulting eigenvalue problem leads to a Hill equation, which is solved numerically. The dynamic structure factor and its full width at half maximum (fwhm) are calculated up to large values of the momentum transfer extending in several Brillouin zones. It is shown that, decreasing the amplitude of the potential, the Smoluchowski equation describes a diffusive process which changes continuously from a jump to a liquid-like regime, with an intermediate behaviour which has some characteristics of both. In this context, recent scattering experiments on systems (premelting surfaces and absorbed monolayers) which seem to show such a behaviour, are briefly discussed.

Suggested Citation

  • Ferrando, R. & Spadacini, R. & Tommei, G.E. & Levi, A.C., 1991. "Diffusion in classical periodic systems: The Smoluchowski equation approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 173(1), pages 141-154.
    • Handle: RePEc:eee:phsmap:v:173:y:1991:i:1:p:141-154
    DOI: 10.1016/0378-4371(91)90255-B
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/037843719190255B
    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(91)90255-B?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.

    References listed on IDEAS

    as
    1. Festa, R. & d'Agliano, E.Galleani, 1978. "Diffusion coefficient for a Brownian particle in a periodic field of force," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 90(2), pages 229-244.
    2. Matthöfer, Hans & Stoltenberg, Gerhard & Nölling, Wilhelm, 1980. "Finanzpolitik im Dilemma," Wirtschaftsdienst – Zeitschrift für Wirtschaftspolitik (1949 - 2007), ZBW - Leibniz Information Centre for Economics, vol. 60(5), pages 215-225.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Caratti, G. & Ferrando, R. & Spadacini, R. & Tommei, G.E., 1997. "An analytical approximation to the diffusion coefficient in overdamped multidimensional systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(1), pages 115-131.
    2. Mazroui, M. & Boughaleb, Y., 1996. "Interacting Brownian particles in a two dimensional periodic potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 227(1), pages 93-107.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Weaver, D.L., 1979. "Effective diffusion coefficient of a Brownian particle in a periodic potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 98(1), pages 359-362.
    2. Caratti, G. & Ferrando, R. & Spadacini, R. & Tommei, G.E., 1997. "An analytical approximation to the diffusion coefficient in overdamped multidimensional systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(1), pages 115-131.
    3. Mazroui, M. & Boughaleb, Y., 1996. "Interacting Brownian particles in a two dimensional periodic potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 227(1), pages 93-107.
    4. Venditti, Claudia & Adrover, Alessandra & Giona, Massimiliano, 2022. "Inertial effects and long-term transport properties of particle motion in washboard potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).

    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:173:y:1991:i:1:p:141-154. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.