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Using high resolution N-body simulations, we investigate the density profiles and the morphologies of galaxy clusters in three models of structure formation. We show that these properties of clusters are closely related to the occurrence of significant merging event to a cluster in the recent past. The three models are: (1) the standard CDM model (SCDM) with $\Omega_0 = \Omega_{CDM} = 1$, $\Lambda_0=0$ and $h=0.5$; (2) a low-density flat model (LCDM) with $\Omega_0=\Omega_{CDM}=0.3$, $\Lambda_0=0.7$ and $h=0.75$; (3) a CDM dominated open model (OCDM) with $\Omega_0=\Omega_{CDM}= 0.1$, $\Lambda_0=0$. We find that the clusters in the OCDM model have the steepest density profiles, their density contours are the roundest and show the smallest center shifts, among the three models. The clusters in the SCDM model have contours that are most elongated and show the largest center shifts, indicating the existence of frequent mergers in the recent past. The clusters in the LCDM model have density profiles and center shifts (in their density contours) similar to those in the SCDM model, although the density contours tend to be rounder. Our results show that, although the density profiles and morphologies of clusters depend on models of structure formation, the LCDM model, which is currently considered as a successful alternative to the SCDM model, can do as well in producing a substantial fraction of clusters with substructures. This is in contrast to the conception that this model may have serious problem in this aspect.
