Many dynamical problems, particularly in the solar system, feature physical collisions of particles as a major component. Detecting all possible collisions over a fixed (short) interval is comparable in complexity to computing gravity between these particles, with the brute force work scaling as the square of the number of particles N. Tree techniques can reduce both of these operations to order Nlog(N). I will describe our particular implementation in the context of solar system problems, with examples from planet formation, asteroid evolution, planetary ring dynamics, and granular dynamics.
For planet formation, we include for the first time explicit treatment of planetesimal collision outcomes assuming self-gravity dominates over material strength. For asteroid evolution, we find that asteroid family properties are best explained by reaccumulation of debris following catastrophic disruption. Reaccumulation can also account for the recently recognized existence of asteroids with satellites. For planetary ring dynamics, we show that details of the nature of interparticle collisions can have a profound effect on large-scale observable ring properties. For granular dynamics, we present a new technique for modelling the collisional and gravitational interaction of fractal aggregates.
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