Flocking dynamics with voter-like interactions: fast nematic consensus by spatial segregation

FEDERICO VAZQUEZ; GABRIEL BAGLIETTO

Workshop; SOFIA: Latin American School and Workshop on Data Analysis and Mathematical Modeling of Social Sciences; 2016

We study the collective motion of self-propelled particles with voter-like interactions. Each particle moves at a constant speed on a two-dimensional space and, in a single step of the dynamics, it aligns its direction of motion with that of a randomly chosen neighboring particle. Directions are also perturbed by an external noise of amplitude η. We find that, in the absence of a noise η=0, the system ultimately reaches full nematic (orientational) order. However, in the thermodynamic limit, a very small amount of noise η > 0 is enough to keep the system totally disordered. Besides, at zero noise the dynamics of ordering is much slower than in the standard Vicsek model, and is characterized by an order parameter φ that increases as φ~ t1/2 for short times, and approaches exponentially fast to 1 for long times. Also, at zero noise, the mean convergence time to complete order is non-monotonic with the density of particles, and for high densities the convergence is faster than in the case of all-to-all interactions. We show that the fast nematic consensus is a consequence of the segregation of the system into clusters of equally-oriented particles, breaking the balance of transitions between directional states observed in well mixed systems.