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Table 4
Definition of the variables used in this paper.
| Variable | Definition | Unit | |
| Input variables | |||
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| α t | Turbulence strength parameter | – | |
| u f | Fragmentation threshold velocity | cm s-1 | |
| Σg | Gas surface density | g cm-2 | |
| Σd | Dust surface density | g cm-2 | |
| ξ | Power-law index of the mass distribution of fragments, see Eq. (10) | – | |
| T | Mid-plane temperature | K | |
| ρ s | Volume density of a dust particle | g cm-3 | |
|
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| a | Grain size, a = (3 m/(4π ρs))1/3 | cm | |
| Other variables | α | Slope of the number density distribution n(m) ∝ m − α, see Eq. (4) | – |
| a BT | Eq. (37) | cm | |
| a 12 | Eq. (40) | cm | |
| a max | Eq. (43) | cm | |
| a L | Left boundary of the bump function b(a), see Sect. 5, paragraph 3 | cm | |
| a P | Peak size of the bump function b(a), see Sect. 5, paragraph 3 | cm | |
| a R | Right boundary of the bump function b(a), see Sect. 5, paragraph 3 | cm | |
| a sett | Eq. (27) | cm | |
| a inc | Eq. (52) | cm | |
| b(a) | Bump function, see Eq. (53) | – | |
| C m1,m2 | Collision kernel, see Eq. (3) | cm3 s-1 | |
|
Collision kernel including settling effects, see Eq. (3) | cm2 s-1 | |
| c s | Sound speed, see Eq. (41) | cm s-1 | |
| δ i | Slopes of the fit-function, see Table 3 | – | |
| δu | Width of the transition between sticking and fragmentation, taken to be 0.2 uf | cm s-1 | |
| ϵ | Interpolation parameter, see Eq. (47) | – | |
| γ | Power-law index of the function h(m2/m1) for large ratios of m2/m1, as defined in Eq. (21) | – | |
| J | Empirical parametrization of the discontinuity, see Eq. (50) | – | |
| K | Integral defined in Eq. (7) | – | |
| k b | Boltzmann constant | erg K-1 | |
| m | Mass of the particle, m = 4π/3 ρs a3 | g | |
| m 0 | Monomer mass | g | |
| m 1 | Mass above which particles fragment | g | |
| μ | Mean molecular weight in proton masses, taken to be 2.3 | – | |
| m p | Proton mass | g | |
| n(m) | Number density distribution | g cm-3 | |
| N(m) | Vertically integrated number density distribution | g cm-2 | |
| ν | Degree of homogeneity of the kernel as defined in Eq. (3) | – | |
| Re | Reynolds number, see Eq. (38) | – | |
| ρ s | Density of a dust grain | g cm-3 | |
| St | Mid-plane Stokes number in the Epstein regime, see Eq. (26) | – | |
| σ H2 | Cross-section of molecular hydrogen | cm2 | |
| u gas | Mean square turbulent gas velocity, see Eq. (46) | cm s-1 | |
|
Relative velocities between monomers and grains of size ai, see Eq. (45) | cm s-1 | |
|
Relative velocities between grains of size ai, see Eq. (48) | cm s-1 | |
| V | Parameter used in the calculation of J, see Eq. (49) | cm s-1 | |
| y a | Equals 1.6, parameter from Ormel & Cuzzi (2007) | – | |
Notes. The variables grouped as “input variables” are the parameters of the fitting recipe in Sect. 5. “Other variables” summarizes the definitions of all other variables used in this recipe.
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