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
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