Flocking is a paradigmatic example of collective animal behaviour, where decentralized interaction rules give rise to a globally ordered state. In the emergence of order out of self-organization we find similarities between biological systems, as bird flocks, and some physical systems, as ferromagnets. In both cases, the tendency of individuals to align to their neighbours gives rise to a polarized state. There is, however, one crucial difference: the interaction network within an animal group is not necessarily fixed in time, as each individual moves and may change its neighbours. Therefore, the dynamical interaction mechanism in biological and physical system can be quite different, not only due to the gross disparity in the complexity of the individual entities, but also because of the potential role of inter-individual motion. To assess the relevance of this mechanism it is necessary to gain quantitative experimental information about how much individuals move with respect to each other within the group. Here, by using data from field observations on starlings, we study the diffusion properties of individual birds within a flock and investigate the effect of diffusion on the dynamics of the interaction network. We find that birds diffuse faster than Brownian particles (superdiffusion) and in a strongly anisotropic way. We also find that neighbours change in time exclusively as a consequence of diffusion, so that no specific mechanism to keep one's neighbours seems to be enforced. Finally, we study the diffusion properties of birds at the border of the flock. We find that these individuals remain on the border significantly longer than what would be expected on the basis of a purely diffusional model, suggesting that there is a sort barrier a bird must cross to make the transition from border to interior of the flock.
Comment on "Velocity and Speed Correlations in Hamiltonian Flocks" by M. Casiulis et al. [arXiv:1911.06042]
在arXiv：1911.06042v1 M. Casiulis等人研究了一个哈密顿模型，在该模型中，运动的团簇的刚性旋转引起速度和速度的无标度相关。M. Casiulis等人将他们模型中的相关性与在真实鸟群中观察到的相关性进行了比较，并声称刚体旋转提供了一种与先前提出的鸟群相关性解释相反的解释，即速度方向的Goldstone模式和速度的边缘（或近临界）模式。在这里，我们表明，刚性旋转的情况下是完全不一致的一个大的机构，建立了实验证据的真实鸟群，因此，它没有提供一个适当的解释所观察到的现象。
Flocking and turning: a new model for self-organized collective motion
a Istituto Sistemi Complessi (ISC--CNR), Via dei Taurini 19, 00185 Roma, Italy b Dipartimento di Fisica, ``Sapienza'' Universit\'a di Roma, P.le Aldo Moro 2, 00185 Roma, Italy c Initiative for the Theoretical Sciences, The Graduate Center, 365 Fifth Avenue, New York, NY 10016 USA d Instituto de Investigaciones Fisicoqu \' micas Te \'o ricas y Aplicadas (INIFTA)；Departamento de F \' sica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, c.c. 16, suc. 4, 1900 La Plata, Argentina e CONICET La Plata, Consejo Nacional de Investigaciones Cient \' ficas y T \'e cnicas, Argentina f Laboratoire de Physique Statistique de l' \' E cole Normale Sup\'erieure, CNRS；h Laboratoire de Physique Th\'eorique de l'\'Ecole Normale Sup\'erieure, CNRS；University Paris VI, 24 rue Lhomond, 75231 Paris Cedex 05, France
