Dynamics of self-aligning polar active matter

Abstract

Active matter systems consist of self-propelled particles that continuously convert energy into motion, maintaining a state of constant non-equilibrium. In many cases, the orientation of a particle’s propulsion becomes misaligned with its actual velocity, creating an angle between the two vectors. This can happen during interactions with external confining potentials or collisions with other particles. By incorporating self-alignment dynamics, a torque emerges to align the particle’s orientation with its velocity. This phenomenon is observed in both biological and synthetic systems, and significantly alters the dynamics both in the individual particle level and in the collective behaviors of the system. For a single particle, it can lead to orbital motion in confining potentials, while at the collective level, it leads to phenomena such as flocking transitions and self-organization, depending on the system’s geometry. This work begins with a review of existing results for individual particle systems and progresses to explore the impact of self-alignment torque on collective dynamics. First, flocking behavior is investigated in systems without confinement, identifying a critical torque threshold for the onset of flocking. Introducing obstacles leads to spontaneous lane formation along the symmetry directions of the substrate. By adding a harmonic confinement to the system, several new phases emerge, including: a magnetized state where all particles align in the same direction and orbit the potential center; a compact vortex state where particles share the same angular velocity, resulting in a collective rotation around the potential; a hollow vortex state displaying shear banding between the inner and outer layers; and a state in which the system splits into several small clusters. To support these findings, a rigid-body model was developed to complement numerical results and a phase diagram was constructed to characterize the emergence of these phases.