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tokens: We are grateful to Daisuke Nagai and Fang Peng for giving us a copy of their Fortran code that we used to reproduce the data in their sedimentation model. We are grateful to the anonymous referee for a thoughtful and detailed report. The suggestion to make a more comprehensive comparison between a homogeneous and a heterogeneous ICM inspired us to produce several new figures and helped us to significantly improve the final version of this manuscript. We acknowledge useful discussions with Daisuke Nagai, Matthew Kunz, Prateek Sharma, Ellen Zweibel, and Ian Parrish during the 3rd ICM Theory and Computation Workshopheld at the Niels Bohr Institute in 2014. We also thank Sagar Chakraborty and Henrik Latter for valuable comments. The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013) under ERC grant agreement 306614. T.B. also acknowledges support provided by a Lørup Scholar Stipend and M.E.P. also acknowledges support from the Young Investigator Programme of the Villum Foundation.