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Speaker: Nicolai Brilliantov

Title: Kinetic Theory of Ballistic Aggregation and Fragmentation: Application to Planetary Rings.

Abstract: We develop a kinetic theory of ballistic aggregation and fragmentation. The theory is based on two basic parameters -- the energy thresholds, E_agg and E_frag, which demarcate different types of
impacts. If the kinetic energy of the relative motion of a colliding pair is smaller than E_agg, particles merge, if it is larger than E_frag, they break, otherwise particles rebound. We assume that particles are formed from monomers which cannot split any further. We consider a wide class of fragmentation models, including a
complete disaggregation into monomers and fragmentation with a power-law distribution of debris sizes. We start from the Boltzmann equation for the mass and velocity distribution function and derive Smoluchowski-like equations for concentrations of particles of different mass. We analyze these equations analytically,
solve them numerically and perform Monte Carlo simulations. For several models we obtain an analytical solution for the size distribution of the aggregates. In particular we show, that for any
fragmentation model with a predominance of small debris at a collision, the resulting size distribution n(R) obeys a power-law n(R) \sim R^beta with an exponential cutof. Moreover, the exponent of the power law \beta does not depend on a particular fragmentation model. These predictions for the particle size distribution, and es-
pecially for the exponent \beta = 2:75 are in a very good agreement with the observational data for the size distribution of particles in planetary rings