  Networks of caustics can occur in the distribution of particles suspended in
a randomly moving gas. These can facilitate coagulation of particles by
bringing them into close proximity, even in cases where the trajectories do not
coalesce. We show that the long-time morphology of these caustic patterns is
determined by the Lyapunov exponents lambda_1, lambda_2 of the suspended
particles, as well as the rate J at which particles encounter caustics. We
develop a theory determining the quantities J, lambda_1, lambda_2 from the
statistical properties of the gas flow, in the limit of short correlation
times.
