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Register a new userSpontaneous flow states in active nematics: a unified picture
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Continuum hydrodynamic models of active liquid crystals have been used to describe dynamic self-organising systems such as bacterial swarms and cytoskeletal gels. A key prediction of such models is the existence of self-stabilising kink states that spontaneously generate fluid flow in quasi-one dimensional channels. Using simple stability arguments and numerical calculations we extend previous studies to give a complete characterisation of the phase space for both contractile and extensile particles (ie pullers and pushers) moving in a narrow channel as a function of their flow alignment properties and initial orientation. This gives a framework for unifying many of the results in the literature. We describe the response of the kink states to an imposed shear, and investigate how allowing the system to be polar modifies its dynamical behaviour.
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We investigate the occurrence of topologically protected waves in classical fluids confined on curved surfaces. Using a combination of topological band theory and real space analysis, we demonstrate the existence of a system-independent mechanism behind topological protection in two-dimensional passive and active fluids. This allows us to formulate an index theorem linking the number of modes, determined by the topology of Fourier space, to the real space topology of the surface on which they are hosted. With this framework in hand, we review two examples of topological waves in two-dimensional fluids, namely oceanic shallow-water waves propagating on the Earths rotating surface and momentum waves in active polar fluids spontaneously flocking on substrates endowed with a ${rm U}(1)$ isometry (e.g. surfaces of revolution). Our work suggests some simple rules to engineer topological modes on surfaces in passive and active soft matter systems.
Using agent-based simulations of self-propelled particles subject to short-range repulsion and nematic alignment we explore the dynamical phases of a dense active material confined to the surface of a sphere. We map the dynamical phase diagram as a function of curvature, alignment strength and activity and reproduce phases seen in recent experiments on active microtubules moving on the surfaces of vesicles. At low driving, we recover the equilibrium nematic ground state with four +1/2 defects. As the driving is increased, geodesic forces drive the transition to a band of polar matter wrapping around an equator, with large bald spots corresponding to two +1 defects at the poles. Finally, bands fold onto themselves, followed by the system moving into a turbulent state marked by active proliferation of pairs of topological defects. We highlight the role of nematic persistence length and time for pattern formation in these confined systems with finite curvature.
We use continuum simulations to study the impact of anisotropic hydrodynamic friction on the emergent flows of active nematics. We show that, depending on whether the active particles align with or tumble in their collectively self-induced flows, anisotropic friction can result in markedly different patterns of motion. In a flow-aligning regime and at high anisotropic friction, the otherwise chaotic flows are streamlined into flow lanes with alternating directions, reproducing the experimental laning state that has been obtained by interfacing microtubule-motor protein mixtures with smectic liquid crystals. Within a flow-tumbling regime, however, we find that no such laning state is possible. Instead, the synergistic effects of friction anisotropy and flow tumbling can lead to the emergence of bound pairs of topological defects that align at an angle to the easy flow direction and navigate together throughout the domain. In addition to confirming the mechanism behind the laning states observed in experiments, our findings emphasise the role of the flow aligning parameter in the dynamics of active nematics.
We examine the scaling with activity of the emergent length scales that control the nonequilibrium dynamics of an active nematic liquid crystal, using two popular hydrodynamic models that have been employed in previous studies. In both models we find that the chaotic spatio-temporal dynamics in the regime of fully developed active turbulence is controlled by a single active scale determined by the balance of active and elastic stresses, regardless of whether the active stress is extensile or contractile in nature. The observed scaling of the kinetic energy and enstropy with activity is consistent with our single-length scale argument and simple dimensional analysis. Our results provide a unified understanding of apparent discrepancies in the previous literature and demonstrate that the essential physics is robust to the choice of model.
We study dry, dense active nematics at both particle and continuous levels. Specifically, extending the Boltzmann-Ginzburg-Landau approach, we derive well-behaved hydrodynamic equations from a Vicsek-style model with nematic alignment and pairwise repulsion. An extensive study of the phase diagram shows qualitative agreement between the two levels of description. We find in particular that the dynamics of topological defects strongly depends on parameters and can lead to ``arch solutions forming a globally polar, smectic arrangement of Neel walls. We show how these configurations are at the origin of the defect ordered states reported previously. This work offers a detailed understanding of the theoretical description of dense active nematics directly rooted in their microscopic dynamics.
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