Topological Sound and Flocking on Curved Surfaces

Shankar, Sadasivan; Bowick, Mark J.; Marchetti, M. Cristina

doi:10.1103/physrevx.7.031039

Cited by 98 publications

(123 citation statements)

References 86 publications

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“…Ellis [16] studied the effect of self-propulsion and curvature on the degree of defect unbinding. On the other hand, curvature can induce spontaneous flow and flocking [22][23][24][25][26][27][28]. Sanchez and coworkers [22] experimentally studied selfpropelled microtubule bundles on curved surfaces and reported the spontaneous generation of a streaming flow.…”

Section: Introductionmentioning

confidence: 99%

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Collective transport of polar active particles on the surface of a corrugated tube

Zhu

Liao

2019

New J. Phys.

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We study collective transport of polar active particles on the surface of a corrugated tube. Particles can be rectified on the surface of the asymmetric tube. The system shows different motion patterns which are determined by the competition between alignment strength and rotational diffusion. For a given alignment strength, there exist transitions from the circulating band state to the travelling state, and finally to the disordered state when continuously changing rotational diffusion. The circulating band is a purely curvature-driven effect with no equivalent in the planar model. The rectification is greatly improved in the travelling state and greatly suppressed in the circulating band state. There exist optimal parameters (modulation amplitude, alignment strength, rotational diffusion, and selfpropulsion speed) at which the rectified efficiency takes its maximal value. Remarkably, in the travelling state, we can observe current reversals by changing translational diffusion.

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Section: Introductionmentioning

confidence: 99%

“…For high curvature, Bruss and coworkers [24] found that particles converge to a common orbit to form symmetrybreaking microswarms. Shankar et al [25] found that curvature and active flow together result in symmetryprotected topological modes that get localized to special geodesics on the surface.…”

Section: Introductionmentioning

confidence: 99%

Collective transport of polar active particles on the surface of a corrugated tube

Zhu

Liao

2019

New J. Phys.

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“…We numerically calculate its band structure and eigenvectors, and demonstrate that they exhibit nonzero topological invari-ants with the corresponding edge modes. Possible relation to non-Hermitian topological phenomena is also discussed.Topological edge modes of active matter have been recently discussed by several authors [19,[35][36][37]. There, the presence of nonzero net vorticity of the active flows, which can act as an effective magnetic field, was crucial to support topological edge modes reminiscent of the quantum Hall effect [1,38].…”

mentioning

confidence: 99%

“…To simplify the problem, we ignore the terms including λ 2,3 and also the diffusive terms that contain the second-order derivative. This condition can be met in a variety of active systems [35,36,50]. We also assume that the pressure P is proportional to ρ as appropriate for an ideal gas.…”

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confidence: 99%

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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“…We consider two geometries: a spherical surface in which the region of lower motility covers one hemisphere or a smaller surface area, and a 2D planar surface with periodic boundary conditions, in which one half of the surface is associated with a lower motility. We will focus mainly on the topology of the compact sphere, since it naturally gives rise to only a single interface, and has also recently attracted interest due to its rich curvature-and topology-induced active-particle dynamics [39][40][41][42][43][44][45][46]. However, for the membrane-formation process reported here, the spherical topology is not a crucial ingredient: indeed, we will show that self-encapsulation at the interface between two different motilities also occurs similarly for rod motion in the plane, and that in fact the aligning interactions are the crucial factor.…”

Section: Introductionmentioning

confidence: 99%

Spontaneous membrane formation and self-encapsulation of active rods in an inhomogeneous motility field

2018

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We study the collective dynamics of self-propelled rods in an inhomogeneous motility field. At the interface between two regions of constant but different motility, a smectic rod layer is spontaneously created through aligning interactions between the active rods, reminiscent of an artificial, semi-permeable membrane. This "active membrane" engulfes rods which are locally trapped in low-motility regions and thereby further enhances the trapping efficiency by self-organization, an effect which we call "self-encapsulation". Our results are gained by computer simulations of self-propelled rod models confined on a two-dimensional planar or spherical surface with a stepwise constant motility field, but the phenomenon should be observable in any geometry with sufficiently large spatial inhomogeneity. We also discuss possibilities to verify our predictions of active-membrane formation in experiments of self-propelled colloidal rods and vibrated granular matter.

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Topological Sound and Flocking on Curved Surfaces

Cited by 98 publications

References 86 publications

Collective transport of polar active particles on the surface of a corrugated tube

Collective transport of polar active particles on the surface of a corrugated tube

Anomalous Topological Active Matter

Spontaneous membrane formation and self-encapsulation of active rods in an inhomogeneous motility field

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