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Collective motion of self-propelled particles with density-dependent switching effect
M. Ballerini, N. Calbibbo, R. Candeleir, A. Cavagna, E. Cisbani, I. Giardina, V. Lecomte, A. Orlandi, G. Parisi, A. Procaccini, M. Viale, and V. Zdravkovic, Proc. Natl. Acad. Sci. U. S. A. 105, 1232 (2008).
C. Liu, X. Fu, L. Liu, X. Ren, C. K. L. Chau, S. Li, L. Xiang, H. Zeng, G. Chen, L. Tang, P. Lenz, X. Cui, W. Huang, T. Hwa, and J. Huang, Science 334, 238 (2011).
N. C. Makris, P. Ratilal, S. Jagannathan, Z. Gong, M. Andrews, I. Bertsatos, O. R. Godo, R. W. Nero, and J. M. Jech, Science 323, 1734 (2009).
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We study the effect of density-dependent angular response on large scale collective motion, that particles are more likely to switch their moving direction within lower local density region. We show that the presence of density-dependent angular response leads to three typical phases: polar liquid, micro-phase separation and disordered gas states. In our model, the transition between micro-phase separation and disordered gas is discontinuous. Giant number fluctuation is observed in polar liquid phase with statistically homogeneous order. In the micro-phase separation parameter space, high order and high density bands dominate the dynamics. We also compare our results with Vicsek model and show that the density-dependent directional switching response can stabilize the band state to very low noise condition. This band stripe could recruit almost all the particles in the system, which greatly enhances the coherence of the system. Our results could be helpful for understanding extremely coherent motion in nature and also would have practical implications for designing novel self-organization pattern.
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