Substructure in clusters of galaxies and the value of Ω

We investigate the formation of clusters of galaxies in an expanding universeusing a new code that regrids at a region of high density. In particular weinvestigate two models for the initial conditions, both with the standard CDMpower spectrum - one has $\Omega = 1$ and the other $\Omega = 0.2$. Bothuniverses have $H_0 = 100 \kms\mpc^{-1}$ and $\Lambda = 0$. The level ofsubstructure in the final cluster can be used as a discriminant of the cosmicdensity. We discuss various statistics which can be measured observationallyfrom clusters of galaxies, that can be used to discriminate between the twomodels. We find that most of the statistics that use the clusters' membergalaxies may not be the best measures of substructure. Statistics that relymore on X-ray maps and other observables depending more directly on the massdistribution could be better discriminants of $\Omega$.Comment: 7 pages, uuencoded gzipped postscript file, figures included. Accepted for publication to the M.N.R.A.