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DY: Dynamik und Statistische Physik

DY 46: Poster

DY 46.87: Poster

Donnerstag, 11. März 2004, 16:00–18:00, Poster D

A Topological Rule-of-Thumb for Percolation Thresholds — •Richard Neher and Herbert Wagner — Sektion Physik, Universität München

Randomly assembled structures exhibit a density driven percolation transition, beyond which an unbounded component is formed. Since properties of those structures change dramatically at the percolation threshold, its accurate knowlegde is important and various empirical formulas, predicting percolation thresholds, have been suggested. The mean Euler characteristic is a topological measure for such random sets and it has been suggested to use its zero crossing to estimate the threshold. In contrast to other formulas, this estimation does not rely on a fit to known thresholds.

We further investigated this matter and found, that for a great variety of two-dimensional lattices the site percolation threshold is bound from above and below by the zero and the inflection point of the Euler characteristic, respectively. In the case of site percolation on three-dimensional lattices, bond-site percolation and continuum percolation, the thresholds are bound from above by the zero of the Euler characteristic.