Open Access
Table D.1
List of commonly used symbols.
| Symbol | Description | Reference |
|---|---|---|
| βjk | boost factor | Sect. 4.4 |
| Λ(q, q′) | raw grain–boulder collision rate | Sect. 5 |
| Λj | mutual collision rate between boulder j and a grain | Eq. (63); Eq. (B.3) |
| λ(q, q′) | raw collision rate | Sect. 3.1 |
| λjk | true collision rate (with self-collision suppressed) | Eq. (4) |
| λj | cumulative collision rate of particle j | Eq. (5) |
| λ | total rate of collisions | Eq. (6) |
 |
RP–swarm collision rate | Eq. (19) |
 |
cumulative collision rate of RP j | Eq. (20) |
 |
total rate of collisions of representative particles | Eq. (9) |
 |
simplified RP–swarm collision rate | Eq. (23) |
 |
simplified cumulative collision rate of RP j | Eq. (24) |
 |
simplified total rate of collisions of representative particles | Eq. (24) |
 |
boosted collision rate | Eq. (41) |
| λg | grain–boulder collision rate | Eq. (B.1) |
 |
RP–swarm collision rate for a grain-mass RP with boulder j | Eq. (64) |
 |
cumulative grain-mass RP collision rate | Eq. (65) |
 |
variance of boulder masses | Eq. (B.12) |
| 𝔗g, 𝔗B | index sets of grains and boulders | Eqs. (61) |
| M | total mass in the system | Sect. 3.1 |
| Mk | total mass of particles in swarm k | Eq. (13) |
| mg | grain mass | Sect. 5 |
 |
initial boulder mass | Sect. 5 |
| N | number of physical particles | Sect. 3.1 |
| Nk | number of physical particles in swarm k | Sect. 3.1 |
| Njk | swarm multiplicity factor | Eq. (37) |
 |
boosted swarm multiplicity factor | Eq. (42) |
| Nth | particle number threshold | Sect. 4.3 |
 |
number of grains after duration ∆t | Eq. (68) |
 |
number of boulders remaining in boulder-mass swarms after duration ∆t | Eq. (70) |
 |
number of boulders emerging from grain-mass swarms after duration ∆t | Eq. (76) |
| Ng | number of grains | Eq. (62) |
 |
initial number of grains | Sect. 5 |
| NB | number of boulders | Eq. (62) |
| n | number of representative particles | Sect. 3.2 |
| qm | mass accumulation threshold | Sect. 4.4.2 |
| qk | properties of particle k | Sect. 3.1 |
| qcoll | properties of particle sampled from collision outcome | Sect. 3.5 |
| Wk | sampling weight of RP k | Eq. (34) |
| 〈·〉B | boulder average | Eq. (66); Eq. (B.2) |
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