Publication: Scale free chaos in swarms
Loading...
Official URL
Full text at PDC
Publication Date
2022-08-18
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Citations
Exportar
Abstract
Swarms are examples of collective behavior of insects, which are singular among manifestations of flocking. Swarms possess strong correlations but no global order and exhibit finite-size scaling with a dynamic critical exponent z ≈ 1. We have discovered a phase transition of the three-dimensional harmonically confined Vicsek model that exists for appropriate noise and small confinement strength. On the critical line of confinement versus noise, swarms are in a state of scale-free chaos that can be characterized by minimal correlation time, correlation length proportional to swarm size and topological data analysis. The critical line separates dispersed single clusters from confined multicluster swarms. Susceptibility, correlation length, dynamic correlation function and largest Lyapunov exponent obey power laws. Their critical exponents agree with those observed in natural midge swarms, unlike values obtained from the order-disorder transition of the standard Vicsek model which confines particles by artificial periodic boundary conditions.
Description
Unesco subjects
Keywords
Citation
1 T. Mora, W. Bialek, Are Biological Systems Poised at Criticality? J. Stat. Phys. 144, 268-302 (2011).
2 W. S. Bialek, Biophysics: Searching for Principles (Princeton University Press, Princeton, 2012).
3 Q.-Y. Tang, Y. Y. Zhang, Y. Wang, W. Wang, D. R. Chialvo, Critical fluctuations in the native state of proteins. Phys. Rev. Lett. 118, 088102 (2017).
4 D. J. T. Sumpter, Collective Animal Behavior (Princeton University Press, 2010).
5 M. Azaïs, S. Blanco, R. Bon, R. Fournier, M.-H. Pillot, J. Gautrais, Traveling pulse emerges from coupled intermittent walks: A case study in sheep. PLoS ONE 13(12), e0206817 (2018).
6 A. Cavagna, I. Giardina, T.S. Grigera, The physics of flocking: Correlation as a compass from experiments to theory. Phys. Rep. 728, 1-62 (2018).
7 K. Huang, Statistical Mechanics. 2nd ed (Wiley, NY, 1987).
8 A. Okubo, Dynamical aspects of animal grouping: Swarms, schools, flocks, and herds. Adv. Biophys. 22, 1-94 (1986).
9 A. Okubo, S. A. Levin, Diffusion and Ecological Problems: Modern Perspectives, 2nd ed (Springer, NY, 2001).
10 J. G. Puckett, N. T. Ouellette, Determining asymptotically large population sizes in insect swarms. J. Roy. Soc. Interface 11, 20140710 (2014).
11 A. Attanasi, A. Cavagna, L. Del Castello, I. Giardina, S. Melillo, L. Parisi, O. Pohl, B. Rossaro, E. Shen, E. Silvestri, M. Viale, Collective Behaviour without Collective Order in Wild Swarms of Midges. PLoS Comput. Biol. 10(7), e1003697 (2014).
12 A. Attanasi, A. Cavagna, L. Del Castello, I. Giardina, S. Melillo, L. Parisi, O. Pohl, B. Rossaro, E. Shen, E. Silvestri, M. Viale, Finite-Size Scaling as a Way to Probe Near-Criticality in Natural Swarms. Phys. Rev. Lett. 113, 238102 (2014).
13 A. Cavagna, D. Conti, C. Creato, L. Del Castello, I. Giardina, T. S. Grigera, S. Melillo, L. Parisi, M. Viale, Dynamic scaling in natural swarms. Nat. Phys. 13(9), 914-918 (2017).
14 B. I. Halperin, P. C. Hohenberg, Scaling laws for dynamic critical phenomena. Phys. Rev. 177, 952-971 (1969).
15 D. J. Amit, V. Martin-Mayor, Field Theory, The Renormalization Group and Critical Phenomena, 3rd ed (World Scientific, Singapore, 2005).
16 D. Gorbonos, R. Ianconescu, J. G. Puckett, R. Ni, N. T. Ouellette, N. S. Gov, Long-range acoustic interactions in insect swarms: an adaptive gravity model. New J. Phys. 18, 073042 (2016).
17 T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, O. Shochet, Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75, 1226-1229 (1995).
18 T. Vicsek, A. Zafeiris, Collective motion. Phys. Rep. 517, 71-140 (2012).
19 M. C. Marchetti , J. F. Joanny, S. Ramaswamy, T.B. Liverpool, J. Prost, M. Rao and R.A. Simha, Hydrodynamics of soft active matter. Rev. Mod. Phys. 85, 1143-1189 (2013).
20 H. Chaté, Dry aligning dilute active matter. Ann. Rev. Cond. Matter Phys. 11, 189-212 (2020).
21 G. Benettin, M. Casartelli, L. Galgani, A. Giorgilli, J. M. Strelcyn, Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 2: Numerical application. Meccanica 15, 21-30 (1980).
22 E. Ott, Chaos in dynamical systems (Cambridge University Press, Cambridge UK 1993).
23 M. Cencini, F. Cecconi, A. Vulpiani, Chaos. From simple models to complex systems (World Scientific, New Jersey 2010).
24 J. B. Gao, Z. M. Zheng, Direct dynamical test for deterministic chaos and optimal embedding of a chaotic time series. Phys. Rev. E 49, 3807-3814 (1994).
25 J. B. Gao, J. Hu, W. W. Tung, Y. H. Cao, Distinguishing chaos from noise by scale-dependent Lyapunov exponent. Phys. Rev. E 74, 066204 (2006).
26 T. Bohr, Chaos and turbulence, in p. 157 of Applications of Statistical and Field Theory Methods to Condensed Matter, D. Baeriswyl, A. R. Bishop, J. Carmelo, eds. (Plenum, New York, 1990).
27 M. C. Cross, P. C. Hohenberg, Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851-1112 (1993).
28 H. G. Schuster, W. Just, Deterministic chaos. An introduction. 4th ed (Wiley-VCH, Weinheim, 2005).
29 A. Cavagna, L. Di Carlo, I. Giardina, L. Grandinetti, T. S. Grigera, G. Pisegna, Renormalization group crossover in the critical dynamics of field theories with mode coupling terms. Phys. Rev. E 100, 062130 (2019).
30 A. Cavagna, L. Di Carlo, I. Giardina, T. S. Grigera, G. Pisegna, and M. Scandolo, Dynamical Renormalization Group for Mode-Coupling Field Theories with Solenoidal Constraint. J. Stat. Phys. 184, 26 (2021).
31 G. Baglietto, E. V. Albano, Finite-size scaling analysis and dynamic study of the critical behavior of a model for the collective displacement of selfdriven individuals. Phys. Rev. E 78, 021125 (2008).
32 V. Holubec, D. Geiss, S. A. M. Loos, K. Kroy, F. Cichos, Finite-Size Scaling at the Edge of Disorder in a Time-Delay Vicsek Model. Phys. Rev. Lett. 127, 258001 (2021).
33 J. K. Hale, Theory of Functional Differential Equations (Springer, New York 1977).
34 L. L. Bonilla, A. Liñán, Relaxation Oscillations, Pulses and Traveling Waves in the Diffusive Volterra Delay-Differential Equation. SIAM Journal on Applied Mathematics 44, 369-391 (1984).
35 A. Zomorodian, G. Carlsson, Computing persistent homology. Discrete Comput. Geom. 33, 249-274 (2002).
36 H. Edelsbrunner, J. Harer, Computational Topology: An Introduction (American Mathematical Society, 2010).
37 M. Sinhuber, N. T. Ouellette, Phase Coexistence in Insect Swarms. Phys. Rev. Lett. 119, 178003 (2017).
38 J. Glimm, A. Jaffe, Quantum Physics. A Functional Integral Point of View, 2nd ed (Springer, 1987).
39 J. M. Yeomans, Statistical Mechanics of Phase Transitions (Oxford Science Publications, Oxford UK, 1992).
40 Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, 3rd ed. (Springer, New York 2004).
41 G. Dangelmayr, E. Knobloch, The Takens-Bogdanov bifurcation with O(2)-symmetry. Phil. Trans. R. Soc. Lond. A 322, 243-279 (1987).
42 T. Ihle, Kinetic theory of flocking: Derivation of hydrodynamic equations. Phys. Rev. E 83, 030901(R) (2011).
43 L. L. Bonilla, C. Trenado, Crossover between parabolic and hyperbolic scaling, oscillatory modes and resonances near flocking. Phys. Rev. E 98, 062603 (2018).
44 C. Trenado, L. L. Bonilla, A. Marquina, Bifurcation theory captures band formation in the Vicsek model of flock formation. arXiv:2203.14238.
45 A.P. Solon, H. Chaté, J. Tailleur, From Phase to Microphase Separation in Flocking Models: The Essential Role of Nonequilibrium Fluctuations. Phys. Rev. Lett. 114, 068101 (2015).
46 R. Kürsten, T. Ihle, Dry Active Matter Exhibits a Self-Organized Cross Sea Phase. Phys. Rev. Lett. 125, 188003 (2020).
47 L. L. Bonilla, Two nonequilibrium phase transitions: Stochastic Hopf bifurcation and onset of relaxation oscillations in the diffusive sine-Gordon model, in p. 75 of Far from equilibrium phase transitions, L. Garrido, ed. (Lecture Notes in Physics 319, Springer, Berlin 1988)