Long-Range Nematic Order in Two-Dimensional Active Matter

Abstract

Working in two space dimensions, we show that the orientational order emerging from selfpropelled polar particles aligning nematically is quasi-long-ranged beyond r, the scale associated to induced velocity reversals, which is typically extremely large and often cannot even be measured. Below r, nematic order is long-range. We construct and study a hydrodynamic theory for this de facto phase and show that its structure and symmetries differ from conventional descriptions of active nematics. We check numerically our theoretical predictions, in particular the presence of π-symmetric propagative sound modes, and provide estimates of all scaling exponents governing long-range space-time correlations.

Phase separation of self-propelled disks with ferromagnetic and nematic alignment

“…While it is now clear that true long-range order can arise for ferromagnetic interactions, numerical and analytical results have not convincingly yield a conclusion in this respect for the nematic case [52,77]. However, a very recent study shows that very large systems need to be explored in order to grasp the asymptotic quasi-longrange order nature of the ordered state [55]. Finite, yet large, systems of linear size smaller than a characteristic length scale (which can be made very large) feature instead long-range order.…”

“…Many extensions of the Vicsek model have been considered, accounting for different kinds of alignment rules [25]. In particular, the case in which particles align along a preferred axis with head-tail nematic symmetry has received considerable attention [52][53][54][55], as being models of self-propelled elongated objects, such as most swimming bacteria (third column Fig. 1).…”

Defect Spirograph: Dynamical Behavior of Defects in Spatially Patterned Active Nematics

“…Active nematics have drawn considerable interest, and a general understanding of their behavior has begun to emerge from observations across a wide range of experimental systems that include in vitro assemblies of filamentous proteins [8][9][10][11], dense suspensions of elongated bacteria [12,13], living nematics [14], and dense colonies of elongated cellular tissues [15][16][17][18]. These experiments have been accompanied by theoretical studies that have sought to explain or anticipate their properties [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. In active nematics, active stresses lead to a constant generation and annihilation of topological defects, giving rise to a loss of longrange nematic ordering.…”