Studying the Dynamical Properties of 20 Nearby Galaxy Clusters
  Using SDSS-DR7, we construct a sample of 42382 galaxies with redshifts in the
region of 20 galaxy clusters. Using two successive iterative methods, the
adaptive kernel method and the spherical infall model, we obtained 3396
galaxies as members belonging to the studied sample. The 2D projected map for
the distribution of the clusters members is introduced using the 2D adaptive
kernel method to get the clusters centers. The cumulative surface number
density profile for each cluster is fitted well with the generalized King
model. The core radii of the clusters' sample are found to vary from 0.18 Mpc
$\mbox{h}^{-1}$ (A1459) to 0.47 Mpc $\mbox{h}^{-1}$ (A2670) with mean value of
0.295 Mpc $\mbox{h}^{-1}$.
  The infall velocity profile is determined using two different models, Yahil
approximation and Praton model. Yahil approximation is matched with the
distribution of galaxies only in the outskirts (infall regions) of many
clusters of the sample, while it is not matched with the distribution within
the inner core of the clusters. Both Yahil approximation and Praton model are
matched together in the infall region for about 9 clusters in the sample but
they are completely unmatched for the clusters characterized by high central
density. For these cluster, Yahil approximation is not matched with the
distribution of galaxies, while Praton model can describe well the infall
pattern of such clusters.
