Statistical mechanics for natural flocks of birds

Proceedings of the National Academy of Sciences of the United States of America - Tập 109 Số 13 - Trang 4786-4791 - 2012
William Bialek1, Andrea Cavagna2,3, Irene Giardina2,3, Thierry Mora4, Edmondo Silvestri2,3, Massimiliano Viale2,3, Aleksandra M. Walczak5
1Joseph Henry Laboratories of Physics and Lewis—Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544;
2Dipartimento di Fisica, Universitá Sapienza, Rome, Italy;
3Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, Rome, Italy
4Laboratoire de Physique Statistique de l’École Normale Supérieure, Centre National de la Recherche Scientifique and University Paris VI, Paris, France; and
5Laboratoire de Physique Théorique de l’École Normale Supérieure, Centre National de la Recherche Scientifique and University Paris VI, Paris, France

Tóm tắt

Flocking is a typical example of emergent collective behavior, where interactions between individuals produce collective patterns on the large scale. Here we show how a quantitative microscopic theory for directional ordering in a flock can be derived directly from field data. We construct the minimally structured (maximum entropy) model consistent with experimental correlations in large flocks of starlings. The maximum entropy model shows that local, pairwise interactions between birds are sufficient to correctly predict the propagation of order throughout entire flocks of starlings, with no free parameters. We also find that the number of interacting neighbors is independent of flock density, confirming that interactions are ruled by topological rather than metric distance. Finally, by comparing flocks of different sizes, the model correctly accounts for the observed scale invariance of long-range correlations among the fluctuations in flight direction.

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Thông tin xuất bản

Proceedings of the National Academy of Sciences of the United States of America

Tập 109 Số 13

4786-4791

Thông tin tác giả