Engineering bacterial vortex lattice via direct laser lithography

Nishiguchi, Daiki; Aranson, Igor S.; Snezhko, Alexey; Sokolov, Andrey

doi:10.1038/s41467-018-06842-6

Cited by 109 publications

(97 citation statements)

References 43 publications

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“…Ref. [43] and Fig. 1(a)), however, only topologically trivial bands can appear due to the absence of a sublattice structure; this is why the kagome-lattice structure (as considered here) is crucial for realizing topological active matter.…”

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confidence: 91%

“…Our proposal is based on the simplest setup on a flat continuum space with assuming no internal degrees of freedom of active particles. This class of systems is directly relevant to many realistic setups of active systems [39][40][41][42][43] and our design principle is applicable beyond the minimal model proposed here.Emergent effective Hamiltonian for active matter.-To describe collective dynamics of active matter, we use the Toner-Tu equations [44][45][46][47], which are the hydrodynamic equations for active matter with a polar-type interaction:where ρ(r, t) is the density field of active matter and v(r, t) is the local average of velocities of self-propelled particles. Equation (1) presents the equation of continuity.…”

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confidence: 99%

“…In particular, the experimental setup realized by Ref. [43] is directly relevant to our model except for the lattice structure and thus, our theoretical results can be tested with current experimental techniques. Secondly, our work suggests a simple and general way to construct topological active matter by designing its periodic structure (steady-state flow) with making the analogy to a profile of a tight-binding lattice (gauge field) relevant to electronic topological materials.…”

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confidence: 99%

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Anomalous Topological Active Matter

Sone

Ashida

2019

Phys. Rev. Lett.

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Active systems exhibit spontaneous flows induced by self-propulsion of microscopic constituents and can reach to a nonequilibrium steady state without an external drive. Constructing the analogy between the quantum anomalous Hall insulators and active matter with spontaneous flows, we show that topologically protected sound modes can arise in a steady-state active system in the continuum space. We point out that the net vorticity of the steady-state flow, which acts as a counterpart of the gauge field in condensed-matter settings, must vanish under realistic conditions for active systems. As a consequence, the quantum anomalous Hall effect naturally provides design principles for realizing topological metamaterials. We propose and analyze the concrete minimal model and numerically calculate its band structure and eigenvectors, demonstrating the emergence of nonzero bulk topological invariants with the corresponding edge sound modes. This new type of topological active systems can potentially expand possibilities for their experimental realizations and may have broad applications to practical active metamaterials. Possible realization of non-Hermitian topological phenomena in active systems is also discussed.Topologically nontrivial bands, which have been at the forefront of condensed matter physics [1][2][3][4][5][6], can also appear in various classical systems such as photonic [7-10] and phononic systems [11][12][13][14][15][16][17]. Such topologically nontrivial systems exhibit unidirectional modes that propagate along the edge of a sample and are immune to disorder. The existence of edge modes originates from the nontrivial topology characterized by bulk topological invariants of underlying photonic or acoustic band structures. The topological edge modes give rise to novel functionalities potentially applicable to, e.g., sonar detection and heat diodes [11,15]. Furthermore, they are argued to be closely related to the mechanism of robustness in biological systems [18,19].On another front, active matter, a collection of self-driven particles, has attracted much interest as an ideal platform to study biological physics [20][21][22] and out-of-equilibrium statistical physics [23][24][25][26][27][28]. While a prototype of active matter has been originally introduced to understand animal flocking behavior [29,30], recent experimental developments have allowed one to manipulate and observe artificial active systems in a controlled manner by utilizing Janus particles [31], catalytic colloids [32] and external feedback control [33].The aim of this Letter is to show that a topologically nontrivial feature can ubiquitously emerge in a nonequilibrium steady state of active matter and demonstrate it by analyzing the concrete minimal model, which can be realized with current experimental techniques. Specifically, we first point out that the net vorticity of the steady-state flow must vanish under realistic conditions for active systems in the continuum space. Since the vorticity in active matter can act as a counterpart o...

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confidence: 99%

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confidence: 99%

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Anomalous Topological Active Matter

Sone

Ashida

2019

Phys. Rev. Lett.

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“…Taken together, concerted experiments and simulations reveal a system in which the interplay of conservative and active stresses can be used to form and control the formation of dynamic patterns. Such patterns can be manipulated by strain and geometry, thereby providing a new avenue to harness the energy of active particles [57][58][59][60][61] for controlled transport at the microscale.…”

Section: Introductionmentioning

confidence: 99%

Emergence of Radial Tree of Bend Stripes in Active Nematics

et al. 2019

Self Cite

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Living liquid crystals, a realization of active nematics where a lyotropic liquid crystal is combined with active bacteria, exhibit a plethora of out-of-equilibrium phenomena that range from active turbulence and dynamic spatiotemporal patterns to the creation and annihilation of motile topological defects. Experiments and hydrodynamic simulations are used here to report on the emergence of bend stripes, which arise as spontaneous undulations of the director field in circularly aligned lyotropic liquid crystals doped with bacteria. The interplay between bacterial-induced hydrodynamic flows and elastic forces in the material induces remarkable deformation patterns consisting of branched, radially elongated bands of a high curvature of the director field. The average number of such branches increases with the distance from the center of the circular alignment, leading to the formation of a radial tree of bands that is reminiscent of a snowflake structure. Hydrodynamic simulations, which are in agreement with the experiments, are used to explain the origin of such structures and to provide additional insights into regimes that are beyond the limit of experimental measurements. In particular, it is found that when activity is switched off in the early stages of pattern formation, a pronounced decay of bend-distortion energy ensues, with little change of the splay energy, serving to confirm that the bend stripes are an outcome of activity-driven bend-instability phenomena. Taken together, experiments and simulations demonstrate a system in which strain and geometry can be combined to dynamically manipulate pattern formation in active matter, paving the way to a deeper understanding and finer control of active colloidal systems.

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“…Some vortex arrays are spontaneously formed due to the hydrodynamic interaction between motile cells, as in the case of sperm cells [1], or the actively moving micro-particles can nematically align due to collisions, such as collectively moving microtubules driven by molecular motors [2]. In bacterial suspensions, vortex lattices can form due to hydrodynamic interactions between micro-organisms guided by the walls of the micro-fluidic channels [3], or the vortex lattice can be formed by introducing periodic obstacles (pillars) within the bacterial suspension [4]. Such highly ordered patterns as vortex lattices possess very different transport properties in comparison with disordered chaotic motion.…”

Section: Introductionmentioning

confidence: 99%

Generation of Vortex Lattices at the Liquid–Gas Interface Using Rotating Surface Waves

Xia

Nicolas

Gorce

et al. 2019

Fluids

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In this paper, we demonstrate experimentally that by generating two orthogonal standing waves at the liquid surface, one can control the motion of floating microparticles. The mechanism of the vortex generation is somewhat similar to a classical Stokes drift in linear progression waves. By adjusting the relative phase between the waves, it is possible to generate a vortex lattice, seen as a stationary horizontal flow consisting of counter-rotating vortices. Two orthogonal waves which are phase-shifted by π / 2 create locally rotating waves. Such waves induce nested circular drift orbits of the surface fluid particles. Such a configuration allows for the trapping of particles within a cell of the size about half the wavelength of the standing waves. By changing the relative phase, it is possible to either create or to destroy the vortex crystal. This method creates an opportunity to confine surface particles within cells, or to greatly increase mixing of the surface matter over the wave field surface.

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Engineering bacterial vortex lattice via direct laser lithography

Cited by 109 publications

References 43 publications

Anomalous Topological Active Matter

Anomalous Topological Active Matter

Emergence of Radial Tree of Bend Stripes in Active Nematics

Generation of Vortex Lattices at the Liquid–Gas Interface Using Rotating Surface Waves

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