Dry, aligning, dilute, active matter: A synthetic and self-contained overview

These notes are based on lectures given during the Summer School `Active Matter and Nonequilibrium Statistical Physics', held in Les Houches in September 2018. Dry, aligning, dilute, active matter (DADAM), with its many adjectives, refers to a corner of the multidimensional, fast-growing field of active matter studies. This corner, however, has both historical and theoretical importance for the entire field. These lectures notes first describe this particular status of DADAM. We then provide an overview of our current knowledge of DADAM in a synthetic and coherent manner. This constitutes the bulk of these notes. For convenience, we first describe the phenomenology of simple active particle models representing the basic DADAM classes, limiting ourselves to two spatial dimensions, where most work has been performed. Then we discuss the continuous hydrodynamic theories derived from these models using the Boltzmann-Ginzburg-Landau approach. We show in particular that they are largely faithful to the microscopic level, albeit qualitatively. In the conclusion, we come back to the nodal situation of DADAM within active matter studies and provide perspectives on how one can expand DADAM knowledge into various directions, approaching more realistic and more complex situations in a controlled way.