IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v416y2014icp273-278.html
   My bibliography  Save this article

A percolation system with extremely long range connections and node dilution

Author

Listed:
  • de Almeida, M.L.
  • Albuquerque, E.L.
  • Fulco, U.L.
  • Serva, M.

Abstract

We study the very long-range bond-percolation problem on a linear chain with both node and bond dilution. Very long-range means that the probability pij for a connection between two nodes i,j at a distance rij decays as a power-law, i.e. pij=ρ/[rijαN1−α] when α∈[0,1), and pij=ρ/[rijln(N)] when α=1. Node dilution means that the probability that a node is present in a site is ps∈(0,1]. The behavior of this model results from the competition between long-range connectivity which enhances the percolation, and node dilution which weakens percolation. The case α=0 with ps=1 is well-known, being the exactly solvable mean-field model. The percolation order parameter P∞ is investigated numerically for different values of α, ps and ρ. We show that in all range α∈[0,1] the percolation order parameter P∞ depends only on the average connectivity γ of the nodes, which can be explicitly computed in terms of the three parameters α, ps and ρ.

Suggested Citation

  • de Almeida, M.L. & Albuquerque, E.L. & Fulco, U.L. & Serva, M., 2014. "A percolation system with extremely long range connections and node dilution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 273-278.
    • Handle: RePEc:eee:phsmap:v:416:y:2014:i:c:p:273-278
    DOI: 10.1016/j.physa.2014.08.041
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437114007262
    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.2014.08.041?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. Zhang, Zhongyang & Zhang, Lixin, 2013. "Scaling limits for one-dimensional long-range percolation: Using the corrector method," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2459-2466.
    2. Serva, Maurizio, 2011. "Exact and approximate solutions for the dilute Ising model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(13), pages 2443-2451.
    3. Serva, Maurizio, 2010. "Magnetization densities as replica parameters: The dilute ferromagnet," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2700-2707.
    4. Rego, Henio H.A & Lucena, Liacir S & da Silva, Luciano R & Tsallis, Constantino, 1999. "Crossover from extensive to nonextensive behavior driven by long-range d=1 bond percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 266(1), pages 42-48.
    Full references (including those not matched with items on IDEAS)

    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. Serva, Maurizio, 2011. "Exact and approximate solutions for the dilute Ising model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(13), pages 2443-2451.
    2. Silveira, Paulo S.P. & Alencar, Adriano M. & Majumdar, Arnab & Lemos, Miriam & Fredberg, Jeffrey J. & Suki, Béla, 2009. "Percolation in a network with long-range connections: Implications for cytoskeletal structure and function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1521-1526.
    3. Moukarzel, Cristian F., 2006. "Percolation in networks with long-range connections," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 372(2), pages 340-345.
    4. Cirto, Leonardo J.L. & Assis, Vladimir R.V. & Tsallis, Constantino, 2014. "Influence of the interaction range on the thermostatistics of a classical many-body system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 286-296.

    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:416:y:2014:i:c:p:273-278. 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.