15 research outputs found
Rigidity percolation on aperiodic lattices
We studied the rigidity percolation (RP) model for aperiodic (quasi-crystal)
lattices. The RP thresholds (for bond dilution) were obtained for several
aperiodic lattices via computer simulation using the "pebble game" algorithm.
It was found that the (two rhombi) Penrose lattice is always floppy in view of
the RP model. The same was found for the Ammann's octagonal tiling and the
Socolar's dodecagonal tiling. In order to impose the percolation transition we
used so c. "ferro" modification of these aperiodic tilings. We studied as well
the "pinwheel" tiling which has "infinitely-fold" orientational symmetry. The
obtained estimates for the modified Penrose, Ammann and Socolar lattices are
respectively: , , . The bond RP threshold of the pinwheel tiling was estimated to
. It was found that these results are very close to the
Maxwell (the mean-field like) approximation for them.Comment: 9 LaTeX pages, 3 PostScript figures included via epsf.st
On Site Percolation on Correlated Simple Cubic Lattice
We consider site percolation on a correlated bi-colored simple cubic lattice.
The correlated medium is constructed from a strongly alternating bi-colored
simple cubic lattice due to anti-site disordering. The percolation threshold is
estimated. The cluster size distribution is obtained. A possible application to
the double 1:1 perovskites is discussed.Comment: 10 pages, 12 figures, Submitted to IJMP
An algorithm to calculate the transport exponent in strip geometries
An algorithm for solving the random resistor problem by means of the
transfer-matrix approach is presented. Preconditioning by spanning clusters
extraction both reduces the size of the conductivity matrix and speed up the
calculations.Comment: 17 pages, RevTeX2.1, HLRZ - 97/9
Cluster counting: The Hoshen-Kopelman algorithm vs. spanning tree approaches
Two basic approaches to the cluster counting task in the percolation and
related models are discussed. The Hoshen-Kopelman multiple labeling technique
for cluster statistics is redescribed. Modifications for random and aperiodic
lattices are sketched as well as some parallelised versions of the algorithm
are mentioned. The graph-theoretical basis for the spanning tree approaches is
given by describing the "breadth-first search" and "depth-first search"
procedures. Examples are given for extracting the elastic and geometric
"backbone" of a percolation cluster. An implementation of the "pebble game"
algorithm using a depth-first search method is also described.Comment: LaTeX, uses ijmpc1.sty(included), 18 pages, 3 figures, submitted to
Intern. J. of Modern Physics