Multi-defect Dynamics in Active Nematics

Abstract

Recent experiments and numerical studies have drawn attention to the dynamics of active nematics. Two-dimensional active nematics flow spontaneously and exhibit spatiotemporal chaotic flows with proliferation of topological defects in the nematic texture. It has been proposed that the dynamics of active nematics can be understood in terms of the dynamics of interacting defects, propelled by active stress. Previous work has derived effective equations of motion for individual defects as quasi-particles moving in the mean field generated by other defects, but an effective theory governing multi-defect dynamics has remained out of reach. In this paper, we examine the dynamics of 2D active nematics in the limit of strong order and overdamped compressible flow. The activity-induced defect dynamics is formulated as a perturbation of the manifold of quasi-static nematic textures explicitly parameterized by defect positions. This makes it possible to derive a set of coupled ordinary differential equations governing defect (and therefore texture) dynamics. Interestingly, because of the non-orthogonality of textures associated with individual defects, their motion is coupled through a position dependent "collective mobility" matrix. In addition to the familiar active self-propulsion of the +1/2 defect, we obtain new collective effects of activity that can be interpreted in terms of non-central and non-reciprocal interactions between defects.

Floating flocks: Two-dimensional long-range uniaxial order in three-dimensional active fluids

“…Since −1/2 defects have a three-fold symmetry, ±1/2 defectpairs in active nematics generically unbind at low noise strengths [86]. While a full examination of defect dynamics in the interfacial nematic phase, including their advection by the active flow leading to non-reciprocal defect interactions [13,91], is beyond the scope of this paper, I now argue that the long-range interaction that stabilises the ordered phase to director fluctuations also makes the separation of ±1/2 defect much less likely than in other active nematic systems, both wet and dry.…”

“…ii. In addition to this, defects in an active system are also dragged by the velocity field generated by other defects [95] which leads to non-reciprocal interaction between defects [13,91,96]. A consideration of these complexities will be discussed elsewhere.…”

The role of fluid flow in the dynamics of active nematic defects

“…Recent work has focused on formulating an effective description of defects in active nematics as quasiparticles [18,25,19,21,26,20,27,28]. This approach parallels wellestablished work in equilibrium systems, where defects can be described as a gas of Coulomb charges and are known to drive order-disorder transitions in 2D [29].…”

“…Shankar et al [20] have shown that the dynamics of the gas of unbound defects can be mapped onto that of a mixture of self-propelled (the +1/2 defects) and passive (the −1/2 defects) quasiparticles with Coulomb interactions and aligning torques, provided that the texture gradients generated at the core of one defect by the other defects can be treated as quasistationary. More recently, the inclusion of multi-defect interactions, within the same quasistatic approximation, has revealed new non-central and non-reciprocal forces in multi-defect textures [28]. Important corrections to the effective dynamics also arise from the fact that the phase field induced at the core of a defect by all the others depends on all the defect velocities, as well as on their past history of accelerations, but including such effects remains a formidable challenge.…”

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.…”