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Abstract Pebble accretion is recognized as a significant accelerator of planet formation. Yet only formulae for single-sized (monodisperse) distribution have been derived in the literature. These can lead to significant underestimates for Bondi accretion, for which the best accreted pebble size may not be the one that dominates the mass distribution. We derive in this paper the polydisperse theory of pebble accretion. We consider a power-law distribution in pebble radius, and we find the resulting surface and volume number density distribution functions. We derive also the exact monodisperse analytical pebble accretion rate for which 3D accretion and 2D accretion are limits. In addition, we find analytical solutions to the polydisperse 2D Hill and 3D Bondi limits. We integrate the polydisperse pebble accretion numerically for the MRN distribution, finding a slight decrease (by an exact factor 3/7) in the Hill regime compared to the monodisperse case. In contrast, in the Bondi regime, we find accretion rates 1–2 orders of magnitude higher compared to monodisperse, also extending the onset of pebble accretion to 1–2 orders of magnitude lower in mass. We find megayear timescales, within the disk lifetime, for Bondi accretion on top of planetary seeds of masses 10−6to 10−4M⊕, over a significant range of the parameter space. This mass range overlaps with the high-mass end of the planetesimal initial mass function, and thus pebble accretion is possible directly following formation by streaming instability. This alleviates the need for mutual planetesimal collisions as a major contribution to planetary growth.
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How Many Monodisperse Fractions are Required to Discretize Polydisperse Polymers?
Abstract The linear viscoelasticity of polydisperse samples and their discretization into a blend ofnfmonodisperse fractions is compared. The molecular weight distribution of the polydisperse sample is described using a lognormal distribution, which has two parameters that are related to the weight‐averaged molecular weight,Zw, and the polydispersity index, ρ. Due to its success on similar systems, a variant of the double reptation model is used to describe the linear rheology. GivenZwand ρ, the optimal number of monodisperse fractions is obtained using the Bayesian information criterion. It quantifies and negotiates the tradeoff between accuracy (discrepancy with the response of the polydisperse sample) and complexity (number of fractions). The optimal number of fractions was found to be somewhat insensitive toZw; however, it increased with ρ from about 6 for ρ = 1.01 to about 20 for ρ = 2.0. Changing the underlying viscoelastic model had only a weak effect on the conclusions. Furthermore, using a blend of monodisperse fractions was found to be preferable to direct sampling even when an ensemble of chains was requested.
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- Award ID(s):
- 1727870
- PAR ID:
- 10456189
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Macromolecular Theory and Simulations
- Volume:
- 29
- Issue:
- 5
- ISSN:
- 1022-1344
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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