fssi20 {SPSL}

Frequency of Sites on a Square Isotropic 2D lattice with (1,0)-neighborhood

Description

fssi20() function calculates the relative frequency distribution of isotropic clusters on 2D square lattice with von Neumann (1,0)-neighborhood.

Usage

fssi20(n=1000, x=33, p=0.592746, 
       set=(x^2+1)/2, all=TRUE, shape=c(1,1))

Arguments

n

a sample size.

x

a linear dimension of 2D square percolation lattice.

p

the relative fractions (0<p)&(p<1) of accessible sites (occupation probability) for percolation lattice.

set

a vector of linear indexes of a starting sites subset.

all

logical; if all=TRUE, mark all sites from a starting subset; if all=FALSE, mark only accessible sites from a starting subset.

shape

a vector with two shape parameters of beta-distributed random variables, weighting the percolation lattice sites.

Details

The percolation is simulated on 2D square lattice with uniformly weighted sites and the constant parameter p.

The isotropic cluster is formed from the accessible sites connected with initial sites subset set.

Von Neumann (1,0)-neighborhood on 2D square lattice consists of sites, only one coordinate of which is different from the current site by one: e=c(-1, 1, -x, x).

Each element of the matrix frq is equal to the relative frequency with which the 2D square lattice site belongs to a cluster sample of size n.

Value

rfq

a 2D matrix of relative sampling frequencies for sites of the percolation lattice.

Author(s)

Pavel V. Moskalev

References

[1] Moskalev, P.V. Percolation modeling of porous structures. Moscow: URSS, 2018. 240 pp; in Russian.
[2] Moskalev, P.V. (2014) Estimates of threshold and strength of percolation clusters on square lattices with (1,d)-neighborhood. Computer Research and Modeling, Vol.6, No.3, pp.405–414; in Russian.

See Also

ssi20, fssi30, fssa20, fssa30, fssi2d, fssi3d

Examples

x <- y <- seq(33) 
image(x, y, rfq <- fssi20(n=200), cex.main=1,
main="Frequencies of isotropic (1,0)-clusters")
contour(x, y, rfq, levels=seq(.2,.3,.05), add=TRUE)
abline(h=17, lty=2); abline(v=17, lty=2)