Active cluster crystals with Vicsek-like alignment interaction

Our aim is to mix together the Vicsek model, that settled the basis of the understanding of the
movement of swarming animals, with a model that performs active crystal clusters. To include
interactions that depend on the orientation is a simple way of generalizing the usual isotropic forces
associated to the crystal clusters formation. Moreover, the two models lead to the non-trivial
emergence of collective phenomena, besides stressing the relevance of the non-equilibrium nature
intrinsically linked with the active movement of the particles. We study how the pattern formation
affects the well-known results from the Vicsek model and under which conditions it is possible to
induce a coherent motion on the crystal structure. Through the process of building the model,
we enter in fundamental questions about active matter, in particular, we seek for a microscopic
argument that can tell us why active matter is out of equilibrium. Our method is based on the
numerical integration of the equations of motion, we will either study single realizations and develop
a statistical study.