Issues in Gravitational Clustering and Cosmology
  Observations reveal that on large scales the universe is spanned by a percolating network of superclusters interspersed with large and almost empty regions -- voids. This thesis reports the construction of a sophisticated computational algorithm called SURFGEN which is used to determine the morphological and topological properties of the cosmic web. SURFGEN generates a triangulated surface from a discrete data set representing (say) the distribution of galaxies in real (or redshift) space. SURFGEN then determines, for this surface, the Minkowski functionals which provide us with an excellent diagnostic of three dimensional shapes of clusters, superclusters and voids. SURFGEN is applied to N-body simulations, mock galaxy catalogues as well as to galaxies in the Las Campanas Redshift Survey. In all cases the morphology of individual superclusters and voids is determined and the connectedness of the cosmic web is assessed by means of the Genus curve and percolation analysis. We demonstrate that SURFGEN can successfully discriminate between rival models of structure formation and is a very useful tool with which to quantify the geometrical and topological properties of large scale structure. 
Jatush V. Sheth