Suppose \(f\) is a probability density function in \(d\) dimensions. \(d \geqslant 2\). A single linkage \(a\)-cluster on a sample of size \(n\) from the density \(f\) is a connected component of the union of balls of volume \(a\). centred at the sample points. Let \(\lambda_{i}\) be the percolation
On grey scaling and continuum percolation
โ Scribed by E. Ahmed
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 264 KB
- Volume
- 193
- Category
- Article
- ISSN
- 0921-4526
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โฆ Synopsis
A theorem is given to establish the equality of the critical exponents p, v, y in continuum and lattice percolation. A model is given to simulate electrical transport properties of continuum percolation systems in two and three dimensions where the holes have identical or random radii. The results for constant radii agree with those obtained by other methods. The results for random radii are new. The conductivity exponent is found and is shown to satisfy the rigorous bounds derived using variational methods by Halperin et al.
๐ SIMILAR VOLUMES
## ลฝ . Graph theory through the minimal spanning tree is used to study the so-called long-range percolation LRP . The percolation thresholds are determined for the ten nearest-neighbour connections related to the eleven mosaics permitted in the plane. It is shown that LRP makes it possible to retr