Search results
Results From The WOW.Com Content Network
The percolation threshold is a mathematical concept in percolation theory that describes the formation of long-range connectivity in random systems. Below the threshold a giant connected component does not exist; while above it, there exists a giant component of the order of system size.
Percolation is the study of connectivity in random systems, such as electrical conductivity in random conductor/insulator systems, fluid flow in porous media, gelation in polymer systems, etc. [1] At a critical fraction of connectivity or porosity, long-range connectivity can take place, leading to long-range flow.
For site percolation on the square lattice, the value of p c is not known from analytic derivation but only via simulations of large lattices which provide the estimate p c = 0.59274621 ± 0.00000013. [7] A limit case for lattices in high dimensions is given by the Bethe lattice, whose threshold is at p c = 1 / z − 1 for a ...
Percolation typically exhibits universality. Statistical physics concepts such as scaling theory, renormalization, phase transition, critical phenomena and fractals are used to characterize percolation properties. Combinatorics is commonly employed to study percolation thresholds.
Localized percolation refers to removing a node its neighbors, next nearest neighbors etc. until a fraction of of nodes from the network is removed. It was shown that for random graph with Poisson distribution of degrees p c = 1 k {\displaystyle p_{c}={\tfrac {1}{\langle k\rangle }}} exactly as for random removal.
Percolation threshold; R. Random cluster model; W. Water retention on random surfaces This page was last edited on 20 May 2018, at 05:31 (UTC). Text is available ...
What links here; Related changes; Upload file; Special pages; Permanent link; Page information; Cite this page; Get shortened URL; Download QR code
Percolation clusters become self-similar precisely at the threshold density for sufficiently large length scales, entailing the following asymptotic power laws: . The fractal dimension relates how the mass of the incipient infinite cluster depends on the radius or another length measure, () at = and for large probe sizes, .