Flocking dynamics with voter-like interactions

• Published in: arXiv.org
• Main Authors: Baglietto, Gabriel, Vazquez, Federico
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 11.04.2019
• Subjects: Noise; Order disorder; Order parameters; Phase transitions; Physics - Physics and Society; Physics - Statistical Mechanics
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1608.08231

We study the collective motion of a large set of self-propelled particles subject to voter-like interactions. Each particle moves on a two-dimensional 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 \(\varphi\), until complete order \(\varphi=1.0\) is reached (polar consensus). We find that \(\varphi\) increases as \(t^{1/2}\) for short times and approaches exponentially fast to \(1.0\) for long times. Also, the mean time to consensus \(\tau\) varies non-monotonically with the density of particles \(\rho\), reaching a minimum at some intermediate density \(\rho_{\tiny \mbox{min}}\). At \(\rho_{\tiny \mbox{min}}\), the mean consensus time scales with the system size \(N\) as \(\tau_{\tiny \mbox{min}} \sim N^{0.765}\), and thus the consensus is faster than in the case of all-to-all interactions (large \(\rho\)) where \(\tau=2N\). 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.