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When interacting motile units self-organize into flocks, they realize one of the most robust ordered state found in nature. However, after twenty five years of intense research, the very mechanism controlling the ordering dynamics of both living and artificial flocks has remained unsettled. Here, combining active-colloid experiments, numerical simulations and analytical work, we explain how flocking liquids heal their spontaneous flows initially plagued by collections of topological defects to achieve long-ranged polar order even in two dimensions. We demonstrate that the self-similar ordering of flocking matter is ruled by a living network of domain walls linking all $pm 1$ vortices, and guiding their annihilation dynamics. Crucially, this singular orientational structure echoes the formation of extended density patterns in the shape of interconnected bow ties. We establish that this double structure emerges from the interplay between self-advection and density gradients dressing each $-1$ topological charges with four orientation walls. We then explain how active Magnus forces link all topological charges with extended domain walls, while elastic interactions drive their attraction along the resulting filamentous network of polarization singularities. Taken together our experimental, numerical and analytical results illuminate the suppression of all flow singularities, and the emergence of pristine unidirectional order in flocking matter.
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We report flocking in the dry active granular matter of millimeter-sized two-step-tapered rods without an intervening medium. The system undergoes the flocking phase transition at a threshold area fraction ~ 0.12 having high orientational correlations between the particles. However, the one-step-tapered rods do not flock and are used as the motile dissenters in the flock-forming granular matter. At the critical fraction of dissenters ~ 0.3, the flocking order of the system gets completely destroyed. The variance of the systems order parameter shows a maximum near the dissenter fraction f ~ 0.05, suggesting a finite-size crossover between the ordered and disordered phases.
Controlling the phases of matter is a challenge that spans from condensed materials to biological systems. Here, by imposing a geometric boundary condition, we study controlled collective motion of Escherichia coli bacteria. A circular microwell isolates a rectified vortex from disordered vortices masked in bulk. For a doublet of microwells, two vortices emerge but their spinning directions show transition from parallel to anti-parallel. A Vicsek-like model for confined self-propelled particles gives the point where two spinning patterns occur in equal probability and one geometric quantity governs the transition as seen in experiments. This mechanism shapes rich patterns including chiral configurations in a quadruplet of microwells, thus revealing a design principle of active vortices.
This article summarizes some of the open questions in the field of active matter that have emerged during Active20, a nine-week program held at the Kavli Institute for Theoretical Physics (KITP) in Spring 2020. The article does not provide a review of the field, but rather a personal view of the authors, informed by contributions of all participants, on new directions in active matter research. The topics highlighted include: the ubiquitous occurrence of spontaneous flows and active turbulence and the theoretical and experimental challenges associated with controlling and harnessing such flows; the role of motile topological defects in ordered states of active matter and their possible biological relevance; the emergence of non-reciprocal effective interactions and the role of chirality in active systems and their intriguing connections to non-Hermitian quantum mechanics; the progress towards a formulation of the thermodynamics of active systems thanks to the feedback between theory and experiments; the impact of the active matter framework on our understanding of the emergent mechanics of biological tissue. These seemingly diverse phenomena all stem from the defining property of active matter - assemblies of self-driven entities that individually break time-reversal symmetry and collectively organize in a rich variety of nonequilibrium states.
Turbulence in driven stratified active matter is considered. The relevant parameters characterizing the problem are the Reynolds number Re and an active matter Richardson-like number,R. In the mixing limit,Re>>1, R<<1, we show that the standard Kolmogorov energy spectrum 5/3 law is realized. On the other hand, in the stratified limit, Re>>1,R>>1, there is a new turbulence universality class with a 7/5 law. The crossover from one regime to the other is discussed in detail. Experimental predictions and probes are also discussed.
How fast must an oriented collection of extensile swimmers swim to escape the instability of viscous active suspensions? We show that the answer lies in the dimensionless combination $R=rho v_0^2/2sigma_a$, where $rho$ is the suspension mass density, $v_0$ the swim speed and $sigma_a$ the active stress. Linear stability analysis shows that for small $R$ disturbances grow at a rate linear in their wavenumber $q$, and that the dominant instability mode involves twist. The resulting steady state in our numerical studies is isotropic hedgehog-defect turbulence. Past a first threshold $R$ of order unity we find a slower growth rate, of $O(q^2)$; the numerically observed steady state is {it phase-turbulent}: noisy but {it aligned} on average. We present numerical evidence in three and two dimensions that this inertia driven flocking transition is continuous, with a correlation length that grows on approaching the transition. For much larger $R$ we find an aligned state linearly stable to perturbations at all $q$. Our predictions should be testable in suspensions of mesoscale swimmers [D Klotsa, Soft Matter textbf{15}, 8946 (2019)].
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