Thresholds For 2D Continuum Models
| System | Φc | ηc | nc |
|---|---|---|---|
| Disks of radius r | 0.67634831(2), 0.6763475(6), 0.676339(4) | 1.12808737(6), 1.128085(2), 1.128059(12) | 1.436322(2), 1.436289(16) |
| Aligned squares of side | 0.66674349(3), 0.66653(1), 0.6666(4) | 1.09884280(9), 1.0982(3), 1.098(1) | |
| Randomly oriented squares | 0.62554075(4), 0.6254(2) | 0.9822723(1), 0.9819(6) | |
| Ellipses of aspect ratio 2 | 0.63 | 0.76 | 1.94 |
| Ellipses of aspect ratio 5 | 0.455 | 0.607 | 3.864 |
| Ellipses of aspect ratio 10 | 0.301 | 0.358 | 4.56 |
| Ellipses of aspect ratio 20 | 0.178 | 0.196 | 4.99 |
| Ellipses of aspect ratio 50 | 0.081 | 0.084 | 5.38 |
| Ellipses of aspect ratio 100 | 0.0417 | 0.0426 | 5.42 |
| Ellipses of aspect ratio 1000 | 0.0043 | 0.00431 | 5.5 |
| Sticks of length | 5.6372858(6), 5.63726(2) | ||
| Disks with x=2.05* | 0.993(1) | 4.90(1) | 0.0380(6) |
| Disks with x=2.25 | 0.8591(5) | 1.959(5) | 0.06930(12) |
| Disks with x=2.50 | 0.7836(4) | 1.5307(17) | 0.09745(11) |
| Disks with x=4.00 | 0.69543(6) | 1.18853(19) | 0.18916(3) |
| Disks with x=5.00 | 0.68643(13) | 1.1597(3) | 0.22149(8) |
| Disks with x=6.00 | 0.68241(8) | 1.1470(1) | 0.24340(5) |
| Disks with x=7.00 | 0.6803(8) | 1.140(6) | 0.25933(16) |
| Disks with x=8.00 | 0.67917(9) | 1.1368(5) | 0.27140(7) |
| Disks with x=9.00 | 0.67856(12) | 1.1349(4) | 0.28098(9) |
| Voids around disks of radius r | 0.159(2) |
equals critical total area for disks, where N is the number of objects and L is the system size.
for ellipses of semi-major and semi-minor axes of a and b, respectively. Aspect ratio
for squares.
* for disks with power in, .
equals critical area fraction.
equals number of objects of length per unit area.
For ellipses,
For void percolation, is the critical void fraction.
For more ellipse values, see
Read more about this topic: Percolation Threshold
Famous quotes containing the words continuum and/or models:
“The further jazz moves away from the stark blue continuum and the collective realities of Afro-American and American life, the more it moves into academic concert-hall lifelessness, which can be replicated by any middle class showing off its music lessons.”
—Imamu Amiri Baraka (b. 1934)
“Friends broaden our horizons. They serve as new models with whom we can identify. They allow us to be ourselves—and accept us that way. They enhance our self-esteem because they think we’re okay, because we matter to them. And because they matter to us—for various reasons, at various levels of intensity—they enrich the quality of our emotional life.”
—Judith Viorst (20th century)