Optimal view angle in the three-dimensional self-propelled particle model

Abstract

The three-dimensional Vicsek model is introduced to investigate the collective motion of self-propelled particles. In this model each particle has a limited view angle. We find that there exists an optimal value of view angle, leading to the quickest direction consensus. Our work shows that the optimal view angle is just a function of the absolute velocity and the particles density in the limit of large boundary size. We present a series of special results demonstrating more fundamental and practical rules in the daily-life pragmatic collective phenomena, which is of significance to the low-cost communication.