We explore the morphological and dynamical evolution of galaxy clusters in simulations using scalar and vector-valued Minkowski valuations and the concept of fundamental plane relations. In this context, three questions are of fundamental interest: 1. How does the average cluster morphology depend on the cosmological background model? 2. Is it possible to discriminate between different cosmological models using cluster substructure in a statistically significant way? 3. How is the dynamical state of a cluster, especially its distance from a virial equilibrium, correlated to its visual substructure? To answer these questions, we quantify cluster substructure using a set of morphological order parameters constructed on the basis of the Minkowski valuations (MVs). The dynamical state of a cluster is described using global cluster parameters: in certain spaces of such parameters fundamental band-like structures are forming indicating the emergence of a virial equilibrium. We find that the average distances from these fundamental structures are correlated to the average amount of cluster substructure for our cluster samples during the time evolution. Furthermore, significant differences show up between the high- and the low-Omega models. We pay special attention to the redshift evolution of morphological characteristics and find large differences between the cosmological models even for higher redshifts.
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