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arXiv · 1601.01924

Surprising mappings of 2D polar active fluids to 2D soap and 1D sandblasting

Leiming Chen·Chiu Fan Lee·John Toner
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Abstract

Active fluids and growing interfaces are two well-studied but very different non-equilibrium systems. Each exhibits non-equilibrium behavior quite different from that of their equilibrium counterparts. Here we demonstrate a surprising connection between these two: the ordered phase of incompressible polar active fluids in two spatial dimensions without momentum conservation, and growing one-dimensional interfaces (that is, the 1+1-dimensional Kardar-Parisi-Zhang equation), in fact belong to the same universality class. This universality class also includes two equilibrium systems : two-dimensional smectic liquid crystals, and a peculiar kind of constrained two-dimensional ferromagnet. We use these connections to show that two-dimensional incompressible flocks are robust against fluctuations, and exhibit universal long-ranged, anisotropic spatio-temporal correlations of those fluctuations. We also thereby determine the exact values of the anisotropy exponent $\zeta$ and the roughness exponents $\chi_{_{x,y}}$ that characterize these correlations.

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Leiming Chen, Chiu Fan Lee, John Toner. 2016-01-08. Surprising mappings of 2D polar active fluids to 2D soap and 1D sandblasting. https://doi.org/10.1038/ncomms12215

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