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Scale-Free Correlations in Flocking Systems with Position-Based Interactions

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Abstract

We consider a model of self-propelled agents with spring-like interactions that depend only on relative positions, and not on relative orientations. We observe that groups of these agents self-organize to achieve collective motion (CM) through a mechanism based on the cascading of self-propulsion energy towards lower elastic modes. By computing the correlation functions of the speed and velocity fluctuations for different group sizes, we show that the corresponding correlation lengths are proportional to the linear size of the group and have no intrinsic length scale. We argue that such scale-free correlations are a natural consequence of the position-based interactions and associated CM dynamics. We hypothesize that this effect, acting in the context of more complex realistic interactions, could be at the origin of the scale-free correlations measured experimentally in flocks of starlings, instead of the previously argued proximity to a critical regime.

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Acknowledgments

The work of CH was supported by the National Science Foundation under Grant No. PHY-0848755. The work of EF, AT and TW was supported by the Research Foundation Flanders (Flemish Community of Belgium) and European Science Foundation (ESF) funded H2Swarm project as well as by the KU Leuven funded BioCo3 IDO Project. The work of AT was supported by the Scientific and Technological Council of Turkey (TUBITAK) 2219 Program. We also acknowledge support by the Max Planck Institute for the Physics of Complex Systems in Dresden, Germany, through the Advanced Study Group “Statistical Physics of Collective Motion”, where part of this work was conducted.

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Authors and Affiliations

  1. CHuepe Labs, 954 W. 18th Place, Chicago, IL, 60608, USA

    Cristián Huepe

  2. Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL, 60208, USA

    Cristián Huepe

  3. Laboratory of Socioecology and Social Evolution, KULeuven, Naamsestraat 59, 3000, Leuven, Belgium

    Eliseo Ferrante, Tom Wenseleers & Ali Emre Turgut

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  1. Cristián Huepe
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  2. Eliseo Ferrante
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  4. Ali Emre Turgut
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Correspondence to Cristián Huepe.

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Huepe, C., Ferrante, E., Wenseleers, T. et al. Scale-Free Correlations in Flocking Systems with Position-Based Interactions. J Stat Phys 158, 549–562 (2015). https://doi.org/10.1007/s10955-014-1114-8

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  • DOI: https://doi.org/10.1007/s10955-014-1114-8

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