Approximations to the gelation phase of an aerosol

We investigate a time discretized version of the Smoluchowski coagulation equation. By means of a numerical example we prove its suitability as a basis for the efficient simulation of the transition to gelation

Self-Consistent Theory of Halo Mergers

The rate of merging of dark-matter halos is an absolutely essential ingredient for studies of both structure and galaxy formation. Remarkably, however, our quantitative understanding of the halo merger rate is still quite limited, and current analytic descriptions based upon the extended Press-Schechter formalism are fundamentally flawed. We show that a mathematically self-consistent merger rate must be consistent with the evolution of the halo abundance in the following sense: The merger rate must, when inserted into the Smoluchowski coagulation equation, yield the correct evolution of the halo abundance. We then describe a numerical technique to find merger rates that are consistent with this evolution. We present results from a preliminary study in which we find merger rates that reproduce the evolution of the halo abundance according to Press-Schechter for power-law power spectra. We discuss the limitations of the current approach and outline the questions that must still be answered before we have a fully consistent and correct theory of halo merger rates.Comment: 13 pages, 8 figures, submitted to MNRAS. Version with full resolution figures available at http://www-astro.physics.ox.ac.uk/~abenson/Papers/smoluchow.pd

Numerical Modeling of the Coagulation and Porosity Evolution of Dust Aggregates

Porosity evolution of dust aggregates is crucial in understanding dust evolution in protoplanetary disks. In this study, we present useful tools to study the coagulation and porosity evolution of dust aggregates. First, we present a new numerical method for simulating dust coagulation and porosity evolution as an extension of the conventional Smoluchowski equation. This method follows the evolution of the mean porosity for each aggregate mass simultaneously with the evolution of the mass distribution function. This method reproduces the results of previous Monte Carlo simulations with much less computational expense. Second, we propose a new collision model for porous dust aggregates on the basis of our N-body experiments on aggregate collisions. We first obtain empirical data on porosity changes between the classical limits of ballistic cluster-cluster and particle-cluster aggregation. Using the data, we construct a recipe for the porosity change due to general hit-and-stick collisions as well as formulae for the aerodynamical and collisional cross sections. Simple coagulation simulations using the extended Smoluchowski method show that our collision model explains the fractal dimensions of porous aggregates observed in a full N-body simulation and a laboratory experiment. Besides, we discover that aggregates at the high-mass end of the distribution can have a considerably small aerodynamical cross section per unit mass compared with aggregates of lower masses. We point out an important implication of this discovery for dust growth in protoplanetary disks.Comment: 17 pages, 15 figures; v2: version to appear in ApJ (typos corrected

Self-Consistent Theory of Halo Mergers - II: CDM Power Spectra

We place additional constraints on the three parameters of the dark matter halo merger rate function recently proposed by Parkinson, Cole & Helly by utilizing Smoluchowski's coagulation equation, which must be obeyed by any binary merging process which conserves mass. We find that the constraints from Smoluchowski's equation are degenerate, limiting to a thin plane in the three dimensional parameter space. This constraint is consistent with those obtained from fitting to N-body measures of progenitor mass functions, and provides a better match to the evolution of the overall dark matter halo mass function, particularly for the most massive halos. We demonstrate that the proposed merger rate function does not permit an exact solution of Smoluchowski's equation and, therefore, the choice of parameters must reflect a compromise between fitting various parts of the mass function. The techniques described herein are applicable to more general merger rate functions, which may permit a more accurate solution of Smoluchowski's equation. The current merger rate solutions are most probably sufficiently accurate for the vast majority of applications.Comment: 11 pages, submitted to MNRA