IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v266y1999i1p92-95.html
   My bibliography  Save this article

Cluster growth at the percolation threshold with a finite lifetime of growth sites

Author

Listed:
  • Ordemann, Anke
  • Roman, H.Eduardo
  • Bunde, Armin

Abstract

We revisit, by means of Monte Carlo simulations and scaling arguments, the growth model of Bunde et al. (J. Stat. Phys. 47(1987)1) where growth sites have a lifetime τ and are available with a probability p. For finite τ, the clusters are characterized by a crossover mass s×(τ)∝τφ. For masses s⪡s×, the grown clusters are percolation clusters, being compact for p>pc. For s⪢s×, the generated structures belong to the universality class of self-avoiding walk with a fractal dimension df=43 for p=1 and df≅1.28 for p=pc in d=2. We find that the number of clusters of mass s scales as N(s)=N(0)exp[−s/s×(τ)], indicating that in contrary to earlier assumptions, the asymptotic behavior of the structure is determined by rare events which get more unlikely as τ increases.

Suggested Citation

  • Ordemann, Anke & Roman, H.Eduardo & Bunde, Armin, 1999. "Cluster growth at the percolation threshold with a finite lifetime of growth sites," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 266(1), pages 92-95.
    • Handle: RePEc:eee:phsmap:v:266:y:1999:i:1:p:92-95
    DOI: 10.1016/S0378-4371(98)00580-9
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437198005809
    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/S0378-4371(98)00580-9?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. Hector Eduardo Roman & Fabrizio Croccolo, 2021. "Spreading of Infections on Network Models: Percolation Clusters and Random Trees," Mathematics, MDPI, vol. 9(23), pages 1-22, November.

    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:266:y:1999:i:1:p:92-95. 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.