Abstract
Vicsek Model is widely recognized as one of the classic models for studying flocking problems. The presence of discontinuous phase transitions in the Vicsek Model under vector noise has been widely recognized, while there is no accepted consensus on whether the Vicsek Model under scalar noise has discontinuous phase transitions until now. The Eigen Microstate method has been applied to study complex systems such as natural climate, and it is suitable for studying both equilibrium systems and non equilibrium systems. The method of Eigen Microstate is used in this article to study the phase transition of the Vicsek model with scalar noise at small and medium-sized scales, and concludes that the standard Vicsek model has discontinuous phase transitions. And quantitative analysis was conducted to calculate the critical point of phase transition in the standard Vicsek model, and the relationship between the critical point and cluster density was summarized.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Butt, T., Mufti, T., Humayun, A., et al.: Myosin motors drive long range alignment of actin filaments. J. Biol. Chem. 285(7), 4964–4974 (2010). https://doi.org/10.1074/jbc.M109.044792
Herbert-Read, J.E., Perna, A., et al.: Inferring the rules of interaction of shoaling fish. Proc. Natl. Acad. Sci. 108(46), 18726–18731 (2011). https://doi.org/10.1073/pnas.1109355108
Becco, C., Vandewalle, N., Delcourt, J., et al.: Experimental evidences of a structural and dynamical transition in fish school. Physica A: Stat. Mech. Appl. 367, 487–493 (2006). https://doi.org/10.1016/j.physa.2005.11.041
Ballerini, M., Calbibbo, N., Candeleir, R., et al.: Interaction ruling animal collective behavior depends on topological rather than metric distance: evidence from a field study. Proc. Nat. Acad. Sci. USA 105(4), 1232–1237 (2008). https://doi.org/10.1073/pnas.0711437105
Nagy, M., Ákos, Z., Biro, D., Vicsek, T.: Hierarchical group dynamics in pigeon flocks. Nature 464, 890–893 (2010). https://doi.org/10.1038/nature08891
Dalmao, F., Mordecki, E.: Cucker-Smale flocking under hierarchical leadership and random interactions. J. SLAM J. Appl. Math. 71(4), 1307–1316 (2011). https://doi.org/10.1137/100785910
Jia, Y., Vicsek, T.: Modelling hierarchical flocking. New J. Phys. 21(9), 093048 (2019). https://doi.org/10.1088/1367-2630/ab428e
Reynolds, C.W.: Flocks, herds, and schools: a distributed behavioral model. ACM SIGGRAPH Comput. Graph. 21(4), 25–34 (1987). https://doi.org/10.1145/37402.37406
Vicsek, T., Czirok, A., Ben-Jacob, E., Cohen, I., Shochet, O.: Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75(6), 1226–1229 (1995). https://doi.org/10.1103/PhysRevLett.75.1226
Cucker, F., Smale, S.: Emergent behavior in flocks. IEEE Trans. Autom. Control 52(2), 852–862 (2007). https://doi.org/10.1109/TAC.2007.895842
Barbaro, A.B.T., Canizo, J.A., Carrillo, J.A., Degond, P.: Phase transitions in a kinetic flocking model of Cucker-Smale type. Multi-scale Model. Simul. 14(3), 1063–1088 (2016). https://doi.org/10.1137/15m1043637
Aldana, M., Huepe, C.: Phase transitions in self-driven many-particle systems and related non-equilibrium models: a network approach. J. Stat. Phys. 112(1–2), 135–153 (2003). https://doi.org/10.1023/A:1023675519930
Barbaro, A.B.T., Degond, P.: Phase transition and diffusion among socially interacting self-propelled agents. Discret. Continuous Dyn. Syst.-Ser. B 19(5), 1249–1278 (2014). https://doi.org/10.1371/journal.pone.0027950
Pattanayak, S., Mishra, S.: Collection of polar self-propelled particles with a modified alignment interaction. J. Phys. Commun. 2(4), 045007 (2018). https://doi.org/10.1088/2399-6528/aab8cc
Escaff, D., Delpiano, R.: Flocking transition within the framework of Kuramoto paradigm for synchronization: clustering and the role of the range of interaction. J. Chaos 30(8), 083137 (2020). https://doi.org/10.1063/5.0006218
Grégoire, G., Chaté, H., et al.: Onset of collective and cohesive motion. Phys. Rev. Lett. 92(2), 25702 (2004). https://doi.org/10.1103/physrevlett.92.025702
Nagy, M., Duruka, I., Vicsek, T.: New aspects of the continuous phase transition in the scalar noise model (SNM) of collective motion. Phys. A: Stat. Mech. Appl. 373, 445–454 (2007). https://doi.org/10.1016/j.physa.2006.05.035
Baglietto, G., Albano, E.V.: Nature of the order-disorder transition in the Vicsek model for the collective motion of self-propelled particles. J. Phys Rev E. 80(5 pt 1), 050103 (2009). https://doi.org/10.1103/PhysRevE.80.050103
Binder, K.: Finite size scaling analysis of Ising model block distribution functions. J. Zeitschrift furPhysik B Condensed Matter. 43(2), 119–140 (1981). https://doi.org/10.1007/BF01293604
Sun, Y., Hu, G., Zhang, Y., et al.: Eigen microstates and their evolutions in complex systems. Commun. Theor. Phys. 73(6), 065603 (2021). https://doi.org/10.1088/1572-9494/abf127
Li, X., Xue, T., Sun, Y., et al.: Discontinuous and continuous transitions of collective behaviors in living systems. China Phys. B 30(12), 128703 (2021). https://doi.org/10.1088/1674-1056/ac3c3f
Hu, G.K., Liu, T., Liu, M.X., et al.: Condensation of eigen microstate in statistical ensemble and phase transition. Sci. China (Phys. Mech. Astron.) 62(09), 45–52 (2019). https://doi.org/10.1007/s11433-018-9353-x
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Jia, Y., Han, J., Li, Q. (2024). Phase Transition at Small-Medium Scales Vicsek Model Based on Eigen Microstate Method. In: Wang, Q., Dong, X., Song, P. (eds) Proceedings of 2023 7th Chinese Conference on Swarm Intelligence and Cooperative Control. CCSICC 2023. Lecture Notes in Electrical Engineering, vol 1205. Springer, Singapore. https://doi.org/10.1007/978-981-97-3328-6_2
Download citation
DOI: https://doi.org/10.1007/978-981-97-3328-6_2
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-97-3327-9
Online ISBN: 978-981-97-3328-6
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)