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Application of statistical mechanics to collective motion in biology

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  • Vicsek, Tamás
  • Czirók, András
  • Farkas, Illés J.
  • Helbing, Dirk

Abstract

Our goal is to describe the collective motion of organisms in the presence of fluctuations. Therefore, we discuss biologically inspired, inherently non-equilibrium models consisting of self-propelled particles. In our models the particles corresponding to organisms locally interact with their neighbours according to simple rules depending on the particular situation considered. Numerical simulations indicate the existence of new types of transitions. Depending on the control parameters both disordered and long-range ordered phases can be observed. In particular, we demonstrate that (i) there is a transition from disordered to ordered motion at a finite noise level even in one dimension and (ii) particles segregate into lanes or jam into a crystalline structure in a model of pedestrians.

Suggested Citation

  • Vicsek, Tamás & Czirók, András & Farkas, Illés J. & Helbing, Dirk, 1999. "Application of statistical mechanics to collective motion in biology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 274(1), pages 182-189.
    • Handle: RePEc:eee:phsmap:v:274:y:1999:i:1:p:182-189
    DOI: 10.1016/S0378-4371(99)00317-9
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    References listed on IDEAS

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    1. Czirók, András & Vicsek, Mária & Vicsek, Tamás, 1999. "Collective motion of organisms in three dimensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 264(1), pages 299-304.
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    Cited by:

    1. Barbaro, Alethea B.T. & Taylor, Kirk & Trethewey, Peterson F. & Youseff, Lamia & Birnir, Björn, 2009. "Discrete and continuous models of the dynamics of pelagic fish: Application to the capelin," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(12), pages 3397-3414.
    2. Zheng, Xiaoping & Li, Wei & Guan, Chao, 2010. "Simulation of evacuation processes in a square with a partition wall using a cellular automaton model for pedestrian dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(11), pages 2177-2188.
    3. Ha, Vi & Lykotrafitis, George, 2012. "Agent-based modeling of a multi-room multi-floor building emergency evacuation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2740-2751.
    4. Goldsztein, Guillermo H., 2017. "Crowd of individuals walking in opposite directions. A toy model to study the segregation of the group into lanes of individuals moving in the same direction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 162-173.
    5. Baetens, J.M. & Van Nieuland, S. & Pauwels, I.S. & De Baets, B. & Mouton, A.M. & Goethals, P.L.M., 2013. "An individual-based model for the migration of pike (Esox lucius) in the river Yser, Belgium," Ecological Modelling, Elsevier, vol. 258(C), pages 40-52.

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