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

¹ Department of Modern Physics, University of Science and Technology of China - Hefei, 230026, China
² Department of Physics, University of Science and Technology of China - Hefei, 230026, China
³ China Satellite Maritime Tracking and Control Department - Jiangyin, 214400, China
⁴ The Research Center for Complex System Science, University of Shanghai for Science and Technology and Shanghai Academy of System Science - Shanghai, 200093, China

^a jinzhili@mail.ustc.edu.cn
^b bhwang@ustc.edu.cn

Received: 16 September 2010
Accepted: 21 February 2011

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.