Mapping two-dimensional polar active fluids to two-dimensional soap and one-dimensional sandblasting.
Mapping two-dimensional polar active fluids to two-dimensional soap and one-dimensional sandblasting.
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DOI：
10.1038/ncomms12215
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发表时间：
2016-07-25
影响因子：
16.6
通讯作者：
Toner J
中科院分区：
文献类型：
--
作者：
Chen L;Lee CF;Toner J
活性流体和生长界面是两个研究得很好但又截然不同的非平衡系统。每一个都表现出与其均衡对应的不同的非平衡行为。在这里，我们展示了这两者之间令人惊讶的联系：在没有动量守恒的二维空间中不可压缩的极性活动流体的有序相，和增长的一维界面(即1+1维的Kardar-Parisi-Zhang方程)，实际上属于同一普适性类。这一普适性类还包括两个平衡系统：二维近晶液晶和一种特殊的约束二维铁磁体。我们使用这些联系来表明，二维不可压缩的群体对波动是健壮的，并且表现出这些波动的普遍的长程、各向异性的时空关联。由此，我们还确定了表征这些关联的各向异性指数ζ和粗糙度指数χx，y的精确值。在许多移动的有机体中，例如细菌群，它们的成分紧密地堆积在一起，密度不会改变。这里，Chen等人。将这种不可压缩的群体在二维上映射到一维界面的增长上，从而计算这种群体的远距离行为。
Active fluids and growing interfaces are two well-studied but very different non-equilibrium systems. Each exhibits non-equilibrium behaviour distinct 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 ζ and the roughness exponents χx,y that characterize these correlations. In many groups of moving organisms, such as swarms of bacteria, their constituents pack so tightly that density cannot change. Here, Chen et al. map such incompressible flocks in two dimensions onto the growth of a one-dimensional interface, and thereby compute the large-distance behaviour of such flocks.