An effective hydrodynamic description of marching locusts.

A fundamental question in complex systems is how to relate interactions between individual components ('microscopic description') to the global properties of the system ('macroscopic description'). Furthermore, it is unclear whether such a macroscopic description exists and if such a description can capture large-scale properties. Here, we address the validity of a macroscopic description of a complex biological system using the collective motion of desert locusts as a canonical example. One of the world's most devastating insect plagues begins when flightless juvenile locusts form 'marching bands'. These bands display remarkable coordinated motion, moving through semiarid habitats in search of food. We investigated how well macroscopic physical models can describe the flow of locusts within a band. For this, we filmed locusts within marching bands during an outbreak in Kenya and automatically tracked all individuals passing through the camera frame. We first analyzed the spatial topology of nearest neighbors and found individuals to be isotropically distributed. Despite this apparent randomness, a local order was observed in regions of high density in the radial distribution function, akin to an ordered fluid. Furthermore, reconstructing individual locust trajectories revealed a highly aligned movement, consistent with the one-dimensional version of the Toner-Tu equations, a generalization of the Navier-Stokes equations for fluids, used to describe the equivalent macroscopic fluid properties of active particles. Using this effective Toner-Tu equation, which relates the gradient of the pressure to the acceleration, we show that the effective 'pressure' of locusts increases as a linear function of density in segments with the highest polarization (for which the one-dimensional approximation is most appropriate). Our study thus demonstrates an effective hydrodynamic description of flow dynamics in plague locust swarms.

Molecular structure and conformations of 1,2-dimethoxycyclobutene-3,4-dione. An electron-diffraction investigation augmented by quantum mechanical and normal coordinate calculations.

The structure and conformations of 1,2-dimethoxycyclobutene-3,4-dione in the vapor at a temperature of 185 °C have been measured by gas-phase electron diffraction. The molecule exists in two forms, one of symmetry C2v with the methyl groups trans to the double bond, and one of Cs symmetry with a methyl group cis and the other trans to this bond (these forms hereafter designated as trans and cis). The molar ratio trans/cis is 68/32 with a 2σ uncertainty of about 24. Many of the parameter values for the two forms are very nearly alike and could not be measured experimentally. With the adoption of parameter differences calculated at the B3LYP/cc-pVTZ level, the following bond distances (r(g)/Å) and bond angles (∠/deg) with estimated 2σ uncertainties were obtained for trans/cis: C1═C2 = 1.381(9)/1.381, C1-C4 = 1.493(11)/1.495, C3-C4 = 1.543(20)/1.545, C═O = 1.203(4)/⟨1.200⟩, C1-O = 1.316(6)/⟨1.320⟩, O-CH3 = 1.444(9)/⟨1.443⟩, C═C-C3 = 93.1(5)/⟨93.1⟩, C3-C4═O = 136.7(29)/⟨136.9⟩, C═C-O = 131.0(23)/137.5, and 131.8, C-O-C = 117.2(12)/118.2 and 116.9; the individual angle values for the cis form listed as averages differ very little. The bond distances and bond angles are in excellent qualitative agreement with prediction based on conventional ideas about the effects of conjugation and hybridization, and their relative values agree very well with predictions from quantum mechanical calculations.