Flocking dynamics with voter-like interactions
Abstract
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 φ, until complete order \varphi=1.0 is reached (polar consensus). We find that φ 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 ρmin . At ρmin , the mean consensus time scales with the system size N as τmin ∼ N0.765 , and thus the consensus is faster than in the case of all-to-all interactions (large ρ) where τ=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.
- Publication:
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Journal of Statistical Mechanics: Theory and Experiment
- Pub Date:
- March 2018
- DOI:
- 10.1088/1742-5468/aaac3e
- arXiv:
- arXiv:1608.08231
- Bibcode:
- 2018JSMTE..03.3403B
- Keywords:
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- Physics - Physics and Society;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 18 pages, 8 figures