Thresholds For 3D Continuum Models
All overlapping except for jammed spheres.
| System | Φc | ηc |
|---|---|---|
| Spheres of radius r | 0.289573(2) | 0.341889(3) |
| Aligned cylinders | 0.2819(2) | 0.3312(1) |
| Aligned cubes of side | 0.2773(2) | 0.3247(3), 0.3248(3) |
| Randomly oriented icosahedra | 0.3030(5) | |
| Randomly oriented dodecahedra | 0.2949(5) | |
| Randomly oriented octahedra | 0.2514(6) | |
| Randomly oriented cubes of side | 0.2168(2) | 0.2444(3), 0.2443(5) |
| Randomly oriented tetrahedra | 0.1701(7) | |
| Randomly oriented disks of radius r (in 3D) | 0.9614(5) | |
| Randomly oriented square plates of side | 0.8647(6) | |
| Randomly oriented triangular plates of side | 0.7295(6) | |
| Voids around disks of radius r | 22.86(2) | |
| Voids around oblate ellipsoids of major radius r and aspect ratio 10 | 15.42(1) | |
| Voids around oblate ellipsoids of major radius r and aspect ratio 2 | 6.478(8) | |
| Voids around spheres of radius r | 0.030(2), 0.0301(3), 0.0294, 0.0300(3) | 3.506(8), 3.515(6) |
| Jammed spheres (average z = 6) | 0.183(3) |
is the total volume, where N is the number of objects and L is the system size.
is the critical volume fraction.
For disks and plates, these are effective volumes and volume fractions.
For void ("Swiss-Cheese" model), is the critical void fraction.
For more results on void percolation around ellipsoids and elliptical plates, see.
Read more about this topic: Percolation Threshold
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