Angular Diameter Distances in Clumpy Friedmann Universes
  Solving null-geodesic equations, behavior of angular diameter distances is studied in inhomogeneous cosmological models, which are given by performing N-body simulations with the CDM spectrum. The distances depend on the separation angle of ray pairs, the mass and the radius of particles cosisting of galaxies and dark matter balls, and cosmological model parameters. The calculated distances are compared with the Dyer- Roeder distance, and after many ray-shooting, the average, dispersion and distribution of the clumpiness parameter are derived. 
Kenji Tomita (Yukawa Institute for Theoretical Physics)