RT Journal Article
T1 Mean field theory of chaotic insect swarms
A1 González Albaladejo, Rafael
A1 López Bonilla, Luis Francisco
AB The harmonically confined Vicsek model displays qualitative and quantitative features observed in natural insect swarms. It exhibits a scale-free transition between single and multicluster chaotic phases. Finite-size scaling indicates that this unusual phase transition occurs at zero confinement [Phys. Rev. E 107, 014209 (2023)]. While the evidence of the scale-free-chaos phase transition comes from numerical simulations, here we present its mean-field theory. Analytically determined critical exponents are those of the Landau theory of equilibrium phase transitions plus dynamical critical exponent z=1 and a new critical exponent φ=0.5 for the largest Lyapunov exponent. The phase transition occurs at zero confinement and noise in the mean-field theory. The noise line of zero largest Lyapunov exponents informs observed behavior: (i) the qualitative shape of the swarm (on average, the center of mass rotates slowly at the rate marked by the winding number and its trajectory fills compactly the space, similarly to the observed condensed nucleus surrounded by vapor) and (ii) the critical exponents resemble those observed in natural swarms. Our predictions include power laws for the frequency of the maximal spectral amplitude and the winding number.
PB APS
SN 2470-0045
YR 2023
FD 2023-06
LK https://hdl.handle.net/10016/37881
UL https://hdl.handle.net/10016/37881
LA eng
NO This work has been supported by the FEDER/Ministerio de Ciencia, Innovación y Universidades-Agencia Estatal de Investigación Grants No. PID2020-112796RB-C21 ( R.G.-A.) and No. PID2020-112796RB-C22 (L.L.B.), by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors (EPUC3M23), and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation). R.G.-A. acknowledges support from the Ministerio de Economía y Competitividad of Spain through the Formación de Doctores program Grant No. PRE2018-083807 cofinanced by the European Social Fund.
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RD 16 jun. 2024