Jove
Visualize
Contact Us

Related Experiment Videos

Large clusters in supercritical percolation.

P S Grinchuk1

  • 1A. V. Luikov Heat and Mass Transfer Institute, National Academy of Sciences of Belarus, 15 P. Brovka Street, Minsk 220072, Belarus.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
PubMed
Summary

Large clusters in supercritical percolation become compact above the threshold. Cluster surface area significantly influences their statistical behavior, impacting decay laws.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Effect of random internal structure on combustion of binary powder mixtures.

Physical review. E, Statistical, nonlinear, and soft matter physics·2005
Same author

Surfaces of percolation systems in lattice problems.

Physical review. E, Statistical, nonlinear, and soft matter physics·2003
See all related articles
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Area of Science:

  • Statistical physics
  • Percolation theory

Background:

  • Investigating large finite clusters in supercritical percolation on finite lattices below the critical dimension (d(c)=6).
  • Understanding cluster size statistics and decay laws is crucial in various physical systems.

Purpose of the Study:

  • To investigate the statistical behavior of large finite clusters in supercritical percolation.
  • To establish the correlation between critical exponents (zeta) and cluster surface properties.
  • To find corrections to the cluster decay law for compact clusters.

Main Methods:

  • Derivation of an approximate system of ordinary differential equations for finite clusters.
  • Analysis of the relationship between cluster size, surface area, and decay exponents.
  • Numerical testing using Monte Carlo simulations on 2D and 3D lattices.

Main Results:

  • A correlation is found between critical exponents (zeta) and cluster surface area.
  • For clusters without self-intersections, zeta=1; for those with few, zeta=1-eta.
  • The first correction to the cluster decay law for compact clusters was determined.

Conclusions:

  • Above the percolation threshold, most large clusters are compact.
  • Cluster surface area is a primary factor governing behavior in supercritical percolation.
  • The findings are supported by numerical simulations on 2D and 3D lattices.

Related Experiment Videos