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Title: Dynamic critical exponent of natural insect swarms
Plain: 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: 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.
Settled by: A renormalization-group value of z consistent with measurements on independent swarm data sets, together with matching static exponents.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: partially-resolved
Status note: 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.
Posed since: 2017