We study with semi-analytical methods the statistics of pronounced arcs caused by lensing of galaxies by foreground galaxy clusters. For the number density and redshift distribution of rich clusters we use Press-Schechter theory, normalized on the basis of empirical data. For the background sources we make use of observational results in the Hubble Deep Field. We present results for three diffe...

,where 84, 16, 95, and 5 represent the phi values at 84, 16, 95, and 5 percentiles. Folk (1968) presented a verbal classification scale for sorting: <0.350: very well sorted; 0.35-0.500: well sorted; 0.5-0.710: moderately well sorted; 0.71-1.00: moderately sorted; 1.00-2.00: poorly sorted; 2.00-4.00: very poorly sorted; and, >4.00: extremely poorly sorted. 4. "skewness" measures the degree to w...

There are two popular ways to speed up simulations of planet formation via increasing the collision probability: ({\it i}) confine motion 2D, ii}) artificially enhance physical radii bodies by an expansion factor. In this paper I have performed 100 each containing $10^4$ interacting and computed parameters from results runs. Each run was executed for a lower higher accuracy parameter. The main ...