IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v184y2024ics0960077924005964.html
   My bibliography  Save this article

A survey of fractal features of Bernoulli percolation

Author

Listed:
  • Balankin, Alexander S.

Abstract

This work is devoted to the fractal features of Bernoulli percolation in different space dimensions. The focus is made on the fractal attributes associated with the connectivity, ramification, and loopiness of percolation clusters and their substructures. In this way we ascertain a connection between the connectivity dimension and topological invariants. Consequently we elucidate the difference between the fractal dimensions of the minimum path and the geodesic on the percolation cluster. We also derive a relation between the topological Hausdorff dimension of percolation cluster and the correlation length exponent. Further we establish that the percolation cluster and its hull have the same topological Hausdorff dimension. These findings allow us to found the ranges for admissible values of dimension numbers characterizing the percolation cluster and their substructures in different space dimensions. Thus we scrutinize the data of numerical simulations.

Suggested Citation

  • Balankin, Alexander S., 2024. "A survey of fractal features of Bernoulli percolation," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:chsofr:v:184:y:2024:i:c:s0960077924005964
    DOI: 10.1016/j.chaos.2024.115044
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924005964
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.115044?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:chsofr:v:184:y:2024:i:c:s0960077924005964. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.