  Group-level behaviour of particles undergoing a velocity jump process with
hard-sphere interactions is investigated. We derive $N$-particle transport
equations that include the possibility of collisions between particles and
apply different approximation techniques to get expressions for the dependence
of the collective diffusion coefficient on the number of particles and their
diameter. The derived approximations are compared with numerical results
obtained from individual-based simulations. The theoretical results compare
well with Monte Carlo simulations providing the excluded volume fraction is
small.
