fssa2d {SPSL}

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

Description

fssa2d() function calculates the relative frequency distribution of anisotropic clusters on 2D square lattice with Moore (1,d)-neighborhood.

Usage

fssa2d(n=1000, x=33, 
       p0=runif(4, max=0.8), 
       p1=colMeans(matrix(p0[c(1,3, 2,3, 1,4, 2,4)], nrow=2))/2,
       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.

p0

a vector of relative fractions (0<p0)&(p0<1) of accessible sites (occupation probability) for lattice directions: (-x,+x,-y,+y).

p1

averaged double combinations of p0-components weighted by Minkowski distance: p1=colMeans(matrix(p0[c(1,3,...)], nrow=2))/rhoMe1.

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 vectors p0 and p1, distributed over the lattice directions, and their combinations.

The anisotropic cluster is formed from the accessible sites connected with the initial subset set, and depends on the direction in 2D square lattice.

Moore (1,d)-neighborhood on 2D square lattice consists of sites, at least one coordinate of which is different from the current site by one: e=c(e0,e1), where
e0=c(-1, 1, -x, x);
e1=colSums(matrix(e0[c(1,3, 2,3, 1,4, 2,4)], nrow=2)).

Minkowski distance between sites a and b depends on the exponent d:
rhoM <- function(a, b, d=1)
if (is.infinite(d)) return(apply(abs(b-a), 2, max))
else return(apply(abs(b-a)^d, 2, sum)^(1/d)).

Minkowski distance for sites from e1 subset with the exponent d=1 is equal to rhoMe1=2.

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 <[e-mail]>

References

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

See Also

ssa2d, fssa3d, fssa20, fssa30, fssi2d, fssi3d

Examples

x <- y <- seq(33) 
image(x, y, rfq <- fssa2d(n=200, p0=c(.3,.4,.75,.5)), cex.main=1,
main="Frequencies of anisotropic (1,1)-clusters")
contour(x, y, rfq, levels=seq(.2,.3,.05), add=TRUE)
abline(h=17, lty=2); abline(v=17, lty=2)