IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v404y2014icp279-284.html
   My bibliography  Save this article

A theoretical characterization of scaling properties in a bouncing ball system

Author

Listed:
  • Leonel, Edson D.
  • Livorati, Andé L.P.
  • Cespedes, André M.

Abstract

Analytical arguments are used to describe the behavior of the average velocity in the problem of an ensemble of particles bouncing a heavy and periodically moving platform. The dynamics of the system is described by using a two-dimensional mapping for the variables’ velocity and discrete time n. In the absence of dissipation and depending on the control parameter and initial conditions, diffusion in energy is observed. Considering the introduction of dissipation via inelastic collisions, we prove that the diffusion is interrupted and a transition from unlimited to limited energy growth is characterized. Our result is general and can be used when the initial condition is a very low velocity leading to a growth of average velocity with n or for large initial velocity where an exponential decay of the average velocity is observed. The results obtained generalize the scaling observed in the bouncer model as well as the stochastic and dissipative Fermi–Ulam model. The formalism can be extended to many other different types of models, including a class of time-dependent billiards.

Suggested Citation

  • Leonel, Edson D. & Livorati, Andé L.P. & Cespedes, André M., 2014. "A theoretical characterization of scaling properties in a bouncing ball system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 404(C), pages 279-284.
    • Handle: RePEc:eee:phsmap:v:404:y:2014:i:c:p:279-284
    DOI: 10.1016/j.physa.2014.02.053
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437114001629
    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.2014.02.053?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. Oliveira, Diego F.M. & Roberto Silva, Mario & Leonel, Edson D., 2015. "A symmetry break in energy distribution and a biased random walk behavior causing unlimited diffusion in a two dimensional mapping," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 909-915.

    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:404:y:2014:i:c:p:279-284. 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.