IDEAS home Printed from https://ideas.repec.org/a/spr/eurphb/v44y2005i1p79-92.html
   My bibliography  Save this article

A deterministic model of competitive cluster growth: glassy dynamics, metastability and pattern formation

Author

Listed:
  • J. M. Luck
  • A. Mehta

Abstract

We investigate a model of interacting clusters which compete for growth. For a finite assembly of coupled clusters, the largest one always wins, so that all but this one die out in a finite time. This scenario of ‘survival of the biggest’ still holds in the mean-field limit, where the model exhibits glassy dynamics, with two well separated time scales, corresponding to individual and collective behaviour. The survival probability of a cluster eventually falls off according to the universal law (ln t)-1/2. Beyond mean field, the dynamics exhibits both aging and metastability, with a finite fraction of the clusters surviving forever and forming a non-trivial spatial pattern. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005

Suggested Citation

  • J. M. Luck & A. Mehta, 2005. "A deterministic model of competitive cluster growth: glassy dynamics, metastability and pattern formation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 44(1), pages 79-92, March.
    • Handle: RePEc:spr:eurphb:v:44:y:2005:i:1:p:79-92
    DOI: 10.1140/epjb/e2005-00102-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1140/epjb/e2005-00102-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1140/epjb/e2005-00102-y?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. Jean-Marc Luck & Anita Mehta, 2023. "Evolution of grammatical forms: some quantitative approaches," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(2), pages 1-15, February.
    2. Anita Mehta, 2012. "Predatory trading and risk minimisation: how to (b)eat the competition," Papers 1202.1374, arXiv.org.

    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:spr:eurphb:v:44:y:2005:i:1:p:79-92. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.