In this thesis, we study systems of active particles interacting via generic torques of different nature. We analyze the phase behavior of these systems, which results from the interplay between self-propulsion, excluded-volume and torques.We tackle the problem from two different perspectives. On the one hand, we derive a continuum field theory that describes a system of self-propelled particles subjected to generic torques. At the mean-field level, the linear stability analysis of the field equations unveils different instabilities of the homogeneous and isotropic state, leading to pattern formation and phase separation.On the other hand, we explore the phase diagrams of collections of aligning active Brownian particles by means of numerical simulations. We specifically focus on understanding what happens to motility-induced phase separation in the presence of different types of velocity alignment interactions. We study Vicsek-like alignment rules as well as dipolar interactions, which can be regarded as an alternative way of introducing effective alignment to the system. We extend the numerical simulations to also explore the phase behavior of mixtures of aligning active particles with different motilities. Here, we report a coupling between the fast and slow species, by which the fast species enhances the slow-species' motility. Finally, we address, at a fundamental level, what are the minimal ingredients leading to the emergence of a polarized phase in systems of aligning active particles. To do so, we propose a Hamiltonian model that could admit a transition to collective motion fulfilling the conservation of total linear momentum and derive a suitable algorithm to properly integrate the equations of motion.
EPFL2022
