Giant number fluctuations in dry active polar fluids: A shocking analogy with lightning rods

Abstract

The hydrodynamic equations of dry active polar fluids (i.e., moving flocks without momentum conservation) are shown to imply giant number fluctuations. Specifically, the rms fluctuations < (δN) 2 > of the number N of active particles in a region containing a mean number of active particles < N > scales according to the law < (δN) 2 > = K ′ < N > φ(d)

Hydrodynamic theory of flocking at a solid-liquid interface: long range order and giant number fluctuations

“…Very interestingly, the experiments of [22] found giant fluctuations of the active particle number in a fixed volume, with a standard deviation that scaled with N 0.8 in the ordered phase, where N is the mean number in the volume. Although the exponent of 0.8 is the value predicted [17,18] for dry polar active fluids, we will argue here that this is a coincidence, and that in fact polar fluids at a solid-liquid interface belong to an entirely different and heretofore unstudied universality class, with number fluctuations scaling like N 0.75 , which probably lies within experimental error of the 0.8 exponent found in the experiments.…”

“…These intrinsically nonequilibrium systems often display orientationally ordered phases, both in living [1][2][3][4][5] and nonliving [6][7][8][9][10] systems. Such phases of active fluids exhibit many phenomena impossible in equilibrium orientationally ordered phases (e.g., nematics [11]), among them spontaneous breaking of continuous symmetries in two dimensions [12][13][14][15], instability in the extreme Stokesian limit [16], and giant number fluctuations [17][18][19].…”

“…Pulling a factor of q 2 out of the numerator of each of these expressions, and a factor of q 4 out of their denominators, gives the scaling forms (I.13), (I.16), and (I. 18) , with the scaling functions (I.14) and ((I.17)) for these correlation functions given in the introduction, and plot-ted there in figure (3).…”

A novel nonequilibrium state of matter: a $d=4-ε$ expansion study of Malthusian flocks

“…In any spatial dimension d, these correlations decay too rapidly to give rise to giant number fluctuations (GNF) [8,19]; that is, they are not sufficiently long-ranged to make the rms number fluctuations δN ≡ (N − N ) 2 in a large region grow more rapidly than the square root of the mean number N . However, they are sufficiently long-ranged to make δN depend on the shape of the region in which the particle number N is being counted [20].…”

Swarming bottom feeders: Flocking at solid-liquid interfaces

“…This occurs both in living [1][2][3][4][5] and synthetic [6][7][8][9][10] systems. Such "active orientationally ordered phases" exhibit many phenomena impossible in their equilibrium analogs (e.g., nematics [11]),including spontaneous breaking of continuous symmetries in two dimensions [12][13][14][15], instability in the extreme Stokesian limit [16], and giant number fluctuations [17][18][19].…”