... viscosity

$\nu_{\rm m} = c_{\rm g} \mu m_{\rm H}/2\rho_{\rm g} \sigma_{\rm mol}$ with $\mu$ and $\sigma_{\rm mol}$, respectively, the mean molecular weight and mean molecular cross-section of the gas molecules.

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... is

The Epstein limit holds for particles with sizes smaller than the mean-free-path of the gas, $a < \frac{9}{4}\lambda_{\rm mfp}$. If this limit is exceeded, friction times increase by a factor $\frac{4}{9}a/\lambda_{\rm mfp}$ and quadratically scale with radius (Schräpler & Henning 2004; Whipple 1972; Weidenschilling 1977).

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... read

Dullemond & Dominik (2005) note that the second expression in Eq. (5) may not exceed v₀.

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... particles

The reader should note that the words "particle'', "agglomerate'' and "aggregate'' are frequently interchanged throughout this and other paragraphs.

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... present

Note that we start compaction already at $E=E_{\rm roll}$ instead of $E=5E_{\rm roll}$. We have found, however, that the simulations are insensitive to the precise energy at which compaction starts.

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...$N_2 =1; \psi_2=1$)

Here we take $\psi_2 =1$ as the enlargement factor of single monomers.

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... equation

Which reads:

$$\frac{\partial f(m)}{\partial t} - f(m) \int {\rm d}m'\ K(m,m') f(m')$$ =

$$+\frac{1}{2} \int {\rm d}m'\ K(m',m-m') f(m') f(m-m'),$$ (21)

describing losses of m due to all collisions with m (first term on right hand side) and gains in the distribution of m due to collisions between m' and m-m' (second term), where the factor $\frac{1}{2}$ ensures collisions are not twice accounted for. Ossenkopf (1993) provides a general extension of the Smoluchowski equation including source and sink terms.

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... needed

Due to the duplication, the mean mass of the system increases with a factor (N+1)/N. The growth factor after $\kappa$-steps then becomes

$${\rm GF} = \left( \frac{N+1}{N} \right)^\kappa\cdot$$ (24)

Thus, $\ln {\rm GF} = \kappa \ln (1+N^{-1}) \approx \kappa/N$ if $N \gg 1$ and $\kappa \approx N \ln {\rm GF}$.

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... is

The mean mass of the population is inversely proportional to the number of particles per unit volume.

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... unity

The Schmidt number measures the ratio of the gas to particle diffusivity; it is supposed to be close to unity if $\tau_{\rm f} < t_0$. (Schräpler & Henning 2004).

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... line

References to colours only apply to the electronic version of this paper.

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