SPSL (version 0.1-9)

fssi30: Frequency of Sites on a Square Isotropic 3D lattice with (1,0)-neighborhood

Description

fssi30() function calculates the relative frequency distribution of isotropic clusters on 3D square lattice with von Neumann (1,0)-neighborhood.

Usage

fssi30(n=1000, x=33, p=0.311608, 
       set=(x^3+1)/2, all=TRUE, shape=c(1,1))

Arguments

n

a sample size.

x

a linear dimension of 3D 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.

Value

rfq

a 3D matrix of relative sampling frequencies for sites of the percolation lattice.

Details

The percolation is simulated on 3D 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 3D square lattice consists of sites, only one coordinate of which is different from the current site by one: e=c(-1, 1, -x, x, -x^2, x^2).

Each element of the matrix frq is equal to the relative frequency with which the 3D square lattice site belongs to a cluster sample of size n.

References

[1] Moskalev, P.V. Percolation modeling of porous structures. Moscow: URSS, 2018. 240 pp; in Russian.

See Also

ssi30, fssi20, fssa20, fssa30, fssi2d, fssi3d

Examples

# NOT RUN {
x <- y <- seq(33)
rfq <- fssi30(n=200, p=0.37)
image(x, y, rfq[,,17], cex.main=1, 
main="Frequencies in the z=17 slice of isotropic (1,0)-clusters")
contour(x, y, rfq[,,17], levels=c(0.2,0.25,0.3), add=TRUE)
abline(h=17, lty=2); abline(v=17, lty=2)
# }