Flocking dynamics with voter-like interactions

BAGLIETTO, GABRIEL; FEDERICO VAZQUEZ

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT

IOP PUBLISHING LTD

Año: 2018 vol. 2018

1742-5468

We study the collective motion of a large set of self-propelled particles subject to voter-like interactions. Each particle moves on a 2D space at a constant speed in a direction that is randomly assigned initially. Then, at every step of the dynamics, each particle adopts the direction of motion of a randomly chosen neighboring particle. We investigate the time evolution of the global alignment of particles measured by the order parameter phiv, until complete order $arphi=1.0$ is reached (polar consensus). We find that phiv increases as t 1/2 for short times and approaches 1.0 exponentially fast for longer times. Also, the mean time to consensus τ varies non-monotonically with the density of particles ρ, reaching a minimum at some intermediate density $ho_{{m min}}$ . At $ho_{{m min}}$ , the mean consensus time scales with the system size N as $au_{{m min}} sim N^{0.765}$ , and thus the consensus is faster than in the case of all-to-all interactions (large ρ) where $au=2N$ . We show that the fast consensus, also observed at intermediate and high densities, is a consequence of the segregation of the system into clusters of equally-oriented particles which breaks the balance of transitions between directional states in well mixed systems.