Modeling dust growth in protoplanetary disks: The breakthrough case
  Simple toy models are often not sufficient to cover the complexity of the dust coagulation process, and a number of numerical approaches are therefore used, among which integration of the Smoluchowski equation and various versions of Monte Carlo algorithm are the most popular. In this paper, we directly compare the Smoluchowski and Monte Carlo approaches and we find a general agreement for most of the coagulation problems. However, for the sweep-up growth driven by the "lucky" breakthrough mechanism, the methods exhibit very different resolution dependencies. With too few mass bins, the Smoluchowski algorithm tends to overestimate the growth rate and the probability of breakthrough. The Monte Carlo method is less resolution dependent in the growth timescale aspect but it tends to underestimate the breakthrough chance due to its limited dynamic mass range. We discuss the features and drawbacks of both the approaches, which may limit their astrophysical applications. 
Joanna Drazkowska, Fredrik Windmark, and Cornelis P. Dullemond
astro-ph.EP