Approximate Formulas For Thresholds of Archimedean Lattices
| Lattice | z | Site Percolation Threshold | Bond Percolation Threshold |
|---|---|---|---|
| (3, 122 ) | 3 | ||
| (4, 6, 12) | 3 | ||
| (4, 82) | 3 | 0.676835..., 4p3 + 3p4 - 6 p5- 2 p6 = 1 | |
| honeycomb (63) | 3 | ||
| kagome (3, 6, 3, 6) | 4 | 0.524430..., 3p2 + 6p3 - 12 p4+ 6 p5 - p6 = 1 | |
| (3, 4, 6, 4) | 4 | ||
| square (44) | 4 | 1/2 (exact) | |
| (34,6 ) | 5 | 0.434371..., 12p3 + 36p4 -21 p5- 327 p6 + 69p7 + 2532p8 - 6533 p9
+ 8256 p10 - 6255p11 + 2951p12 - 837 p13+ 126 p14 - 7p15= 1 |
|
| snub square, puzzle (32, 4, 3, 4 ) | 5 | ||
| (33, 42) | 5 | ||
| triangular (36) | 6 | 1/2 (exact) |
Read more about this topic: Percolation Threshold
Famous quotes containing the words approximate and/or formulas:
“All fashions are charming, or rather relatively charming, each one being a new striving, more or less well conceived, after beauty, an approximate statement of an ideal, the desire for which constantly teases the unsatisfied human mind.”
—Charles Baudelaire (1821–1867)
“It is sentimentalism to assume that the teaching of life can always be fitted to the child’s interests, just as it is empty formalism to force the child to parrot the formulas of adult society. Interests can be created and stimulated.”
—Jerome S. Bruner (20th century)