Moving and staying together without a leader
Résumé
A microscopic, stochastic, minimal model for collective and cohesive motionof identical self-propelled particles is introduced. Even though the particles interact strictly locally in a very noisy manner, we show that cohesioncan be maintained, even in the zero-density limit of an arbitrarilylarge flock in an infinite space. The phase diagram spanned by thetwo main parameters of our model, which encode the tendencies forparticles to align and to stay together, contains non-moving "gas","liquid"' and "solid" phases separated from their moving counterpartsby the onset of collective motion.The "gas/liquid" and "liquid/solid" are shown to be first-order phase transitions in all cases. In the cohesive phases, we study alsothe diffusive properties of individuals and their relation tothe macroscopic motion and to the shape of the flock.
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