Dynamic critical exponent of natural insect swarms
In plain words
In midge swarms, the time over which fluctuations die out grows with the correlation length according to a power set by one number, the dynamic exponent. Its measured value, about 1.4, differs from standard theories of moving groups.
Precise statement
In wild midge swarms the relaxation time of velocity fluctuations scales as $\tau \sim \xi^z$ with measured $z = 1.37 \pm 0.11$ (Cavagna and co-workers, 2023; $1.12 \pm 0.16$ in the 2017 analysis), below $z = 2$ for overdamped dynamics. Determine the universality class: compute z in a field theory with inertial, spin-like velocity coupling and self-propulsion, and check it with the measured static and dynamic exponents.
What would settle it
A renormalization-group value of z consistent with measurements on independent swarm data sets, together with matching static exponents.
Status in the literature
A 2023 renormalization-group calculation for an active inertial model gave $z = 1.35$, matching the measured $1.37 \pm 0.11$ (Nature Physics, doi 10.1038/s41567-023-02028-0); confirmation on independent swarm data and of the static exponents is open.
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