Percolation properties of the classic Sierpinski carpet and sponge
Statistical Mechanics
2023-02-21 v2 Materials Science
Applied Physics
Geophysics
Abstract
Iterative construction of a Sierpinski carpet or sponge is shown to be a critical phenomenon analogous to uncorrelated percolation. Critical exponents are derived or calculated (by random walks over the carpet or sponge at infinite iteration) that are related by equations identical to those obtained from percolation theory. Finite-size scaling then gives accurate values for the scalar transport properties (e.g., effective conductivity) of the carpet or sponge at any stage of iteration.
Keywords
Cite
@article{arxiv.1706.03410,
title = {Percolation properties of the classic Sierpinski carpet and sponge},
author = {Clinton DeW. Van Siclen},
journal= {arXiv preprint arXiv:1706.03410},
year = {2023}
}
Comments
6 pages, 4 figures