A spatio-temporal model of particle or star growth is defined, whereby new unit masses arrive sequentially in discrete time. These unit masses are referred to as candidate stars, which tend to arrive in mass-dense regions and then either form a new star or are absorbed by some neighbouring star of high mass. We analyse the system as time increases, and derive the asymptotic growth rate of the number of stars as well as the size of a randomly chosen star. We also prove that the size-biased mass distribution converges to a Poisson–Dirichlet distribution. This is achieved by embedding our model into a continuous-time Markov process, so that new stars arrive according to a marked Poisson process, with locations as marks, whereas existing stars grow as independent Yule processes. Our approach can be interpreted as a Hoppe-type urn scheme with a spatial structure. We discuss its relevance for and connection to models of population genetics, particle aggregation, image segmentation, epidemic spread, and random graphs with preferential attachment.

This paper is concerned with a meteoroid shape estimation technique based on statistical laws of distribution for fragment masses. The idea is derived from the experiments that show that brittle fracturing produces multiple fragments of size lesser than or equal to the least dimension of the body. The number of fragments depends on fragment masses as a power law with exponential cutoff. The scaling exponent essentially indicates the initial form of the fragmented body. We apply the technique of scaling analysis to the empirical data on the mass distributions for Košice, Almahata Sitta and Bassikounou meteorites.