Theory of growth of ballistic aggregates

An analytical treatment of the ballistic-driven-aggregation model with a one-sided rain of particles onto the aggregate is presented. The probability distributions for the width and the height of the resulting fanlike structure are obtained. Though the distribution for the width is exactly derived, that for the height is found to depend on the nature of the top surface and approximate expressions for the distribution of the height are given. For large width, the fan structure is shown to be contained in a cone with semivertical angle thetac of about 20^∘{}. The limiting density is around 0.5.