RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, Issue 4, Pages 60–79 (Mi vuu296)  

This article is cited in 2 scientific papers (total in 2 papers)

MECHANICS

Hodge's idea in percolation: percolation threshold estimation by the unit cell

S. R. Gallyamov, S. A. Mel'chukov

Udmurt State University, Izhevsk, Russia

Abstract: We consider a percolation problem of knots. The percolation threshold of triangular lattice $x_c=1/2$ was confirmed by the two lattices method and percolation threshold of quadratic 1,2 lattice $x_c=0.40725616$ was obtained.
We propose the method based on Hodge's idea from algebraic geometry to estimate the percolation threshold $x_c$ of the infinite lattice by percolation properties of its unit sell. The model of unit cell of Bete lattice was studied and in the following it was applied for estimation of percolation thresholds of body-centered and face-centered cubic lattices in the three-dimensional case and of hexagonal lattice in the planar case. As a result of estimation the values of $x_c(bcc)=0.24595716$ for BCC, $x_c(fcc)=0.19925370$ for FCC and $x_c=0.69700003$ for hexagonal lattices were obtained.

Keywords: percolation, percolation threshold, unit cell, Hodge's idea, site problem.

Full text: PDF file (420 kB)
References: PDF file   HTML file
UDC: 531.19+519.24
MSC: 60K35, 82B43
Received: 17.09.2011

Citation: S. R. Gallyamov, S. A. Mel'chukov, “Hodge's idea in percolation: percolation threshold estimation by the unit cell”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, no. 4, 60–79

Citation in format AMSBIB
\Bibitem{GalMel11}
\by S.~R.~Gallyamov, S.~A.~Mel'chukov
\paper Hodge's idea in percolation: percolation threshold estimation by the unit cell
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2011
\issue 4
\pages 60--79
\mathnet{http://mi.mathnet.ru/vuu296}


Linking options:
  • http://mi.mathnet.ru/eng/vuu296
  • http://mi.mathnet.ru/eng/vuu/y2011/i4/p60

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Stuchinsky V.A., “Size Effects in Percolation of Small Regions on Planar and Cylindrical Surfaces”, Tech. Phys. Lett., 39:4 (2013), 380–383  crossref  isi  elib
    2. Volkova N.V. Kourov N.I. Marchenkov V.V., “Kinetic Properties of Ternary Alloys Ni3Mn (X) Al1-X”, Phys. Metals Metallogr., 115:12 (2014), 1200–1207  crossref  isi
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
    Number of views:
    This page:670
    Full text:105
    References:38
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020