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Dynamic scaling in natural swarms


Collective behaviour in biological systems presents theoretical challenges beyond the borders of classical statistical physics. The lack of concepts such as scaling and renormalization is particularly problematic, as it forces us to negotiate details whose relevance is often hard to assess. In an attempt to improve this situation, we present here experimental evidence of the emergence of dynamic scaling laws in natural swarms of midges. We find that spatio-temporal correlation functions in different swarms can be rescaled by using a single characteristic time, which grows with the correlation length with a dynamical critical exponent z ≈ 1, a value not found in any other standard statistical model. To check whether out-of-equilibrium effects may be responsible for this anomalous exponent, we run simulations of the simplest model of self-propelled particles and find z ≈ 2, suggesting that natural swarms belong to a novel dynamic universality class. This conclusion is strengthened by experimental evidence of the presence of non-dissipative modes in the relaxation, indicating that previously overlooked inertial effects are needed to describe swarm dynamics. The absence of a purely dissipative regime suggests that natural swarms undergo a near-critical censorship of hydrodynamics.

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Figure 1: Experiment and temporal correlation.
Figure 2: Dynamic scaling and critical exponent.
Figure 3: Non-dissipative relaxation.


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We thank S. Caprara, F. Cecconi, F. Ginelli and J. G. Lorenzana for important discussions. This work was supported by IIT-Seed Artswarm, European Research Council Starting Grant 257126, US Air Force Office of Scientific Research Grant FA95501010250 (through the University of Maryland) and ERANET-LAC grant CRIB. T.S.G. was supported by grants from CONICET, ANPCyT and UNLP (Argentina).

Author information




A.C. and I.G. designed the study. S.M. coordinated the experiment. C.C., L.D.C. and S.M. performed the experiment. L.P. and S.M. adapted the tracking algorithm and produced the 3D trajectories. S.M. and D.C. calculated the experimental correlation functions. T.S.G. wrote the code and ran the numerical simulations. A.C., D.C., I.G., T.S.G., S.M. and M.V. performed the theoretical analysis. A.C. wrote the paper.

Corresponding authors

Correspondence to Andrea Cavagna or Stefania Melillo.

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The authors declare no competing financial interests.

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Cavagna, A., Conti, D., Creato, C. et al. Dynamic scaling in natural swarms. Nature Phys 13, 914–918 (2017).

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