ssi30 {SPSL}

Site cluster on Square Isotropic 3D lattice with (1,0)-neighborhood

Description

ssi30() function provides sites labeling of the isotropic cluster on 3D square lattice with von Neumann (1,0)-neighborhood.

Usage

ssi30(x=33, p=0.311608, 
      set=(x^3+1)/2, all=TRUE, shape=c(1,1))

Arguments

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.

Details

The percolation is simulated on 3D square lattice with uniformly weighted sites acc and the constant parameter p.

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

To form the cluster the condition acc[set+e]<p is iteratively tested for sites of the von Neumann (1,0)-neighborhood e for the current cluster perimeter 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).

Forming cluster ends with the exhaustion of accessible sites in von Neumann (1,0)-neighborhood of the current cluster perimeter.

Value

acc

an accessiblity matrix for 3D square percolation lattice:
if acc[e]<p then acc[e] is accessible site;
if acc[e]==1 then acc[e] is non-accessible site;
if acc[e]==2 then acc[e] belongs to a sites cluster.

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. (2013) The structure of site percolation models on three-dimensional square lattices. Computer Research and Modeling, Vol.5, No.4, pp.607–622; in Russian.

See Also

fssi30, ssi20, ssa20, ssa30, ssi2d, ssi3d

Examples

# Example No.1. Axonometric projection of 3D cluster
require(lattice)
set.seed(20120507)
x <- y <- z <- seq(33)
cls <- which(ssi30(p=.285)>1, arr.ind=TRUE)
cloud(cls[,3] ~ cls[,1]*cls[,2],
xlim=range(x), ylim=range(y), zlim=range(z), 
col=rgb(1,0,0,0.4), xlab="x", ylab="y", zlab="z", main.cex=1,
main="Isotropic (1,0)-cluster")

# Example No.2. Z=17 slice of 3D cluster
set.seed(20120507)
cls <- ssi30(p=.285)
x <- y <- z <- seq(33)
image(x, y, cls[,,17], zlim=c(0,2), cex.main=1, 
main="Z=17 slice of an isotropic (1,0)-cluster")
abline(h=17, lty=2); abline(v=17, lty=2)