Topological Sound and Flocking on Curved Surfaces
arXiv:1704.05424 · doi:10.1103/PhysRevX.7.031039
Abstract
Active systems on curved geometries are ubiquitous in the living world. In the presence of curvature orientationally ordered polar flocks are forced to be inhomogeneous, often requiring the presence of topological defects even in the steady state due to the constraints imposed by the topology of the underlying surface. In the presence of spontaneous flow the system additionally supports long-wavelength propagating sound modes which get gapped by the curvature of the underlying substrate. We analytically compute the steady state profile of an active polar flock on a two-sphere and a catenoid, and show that curvature and active flow together result in symmetry protected topological modes that get localized to special geodesics on the surface (the equator or the neck respectively). These modes are the analogue of edge states in electronic quantum Hall systems and provide unidirectional channels for information transport in the flock, robust against disorder and backscattering.
15 pages, 6 figures
References in corpus (46)
- Topological Insulators
- Novel type of phase transition in a system of self-driven particles
- Topological insulators and superconductors: ten-fold way and dimensional hierarchy
- The Mechanics and Statistics of Active Matter
- Flocks, herds, and schools: A quantitative theory of flocking
- Spontaneous motion in hierarchically assembled active matter
- Topological Acoustics
- Analogs of quantum Hall effect edge states in photonic crystals
- Scale-free correlations in bird flocks
- Long-lived Giant Number Fluctuations in a Swarming Granular Nematic
- Topological Boundary Modes in Isostatic Lattices
- Topological mechanics of gyroscopic metamaterials
- Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
- Topology and Dynamics of Active Nematic Vesicles
- Collective Motion of Vibrated Polar Disks
- Phase transition in the collective migration of tissue cells: experiment and model
- Grain Boundary Scars and Spherical Crystallography
- Boltzmann and hydrodynamic description for self-propelled particles
- Two-Dimensional Matter: Order, Curvature and Defects
- Topological phonon modes and their role in dynamic instability of microtubules
- Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis
- Dynamics of Self-Propelled Particles Under Strong Confinement
- Hydrodynamics of self-propelled hard rods
- Interacting Topological Defects on Frozen Topographies
- Fluctuations and Pattern Formation in Self-Propelled Particles
- Vortices in Superfluid Films on Curved Surfaces
- Active particles with soft and curved walls: Equation of state, ratchets, and instabilities
- A Reanalysis of the Hydrodynamic Theory of Fluid, Polar-Ordered Flocks
- Sound waves and the absence of Galilean invariance in flocks
- Anomalous coupling between topological defects and curvature
- Emergent spatial structures in flocking models: a dynamical system insight
- Swim pressure on walls with curves and corners
- Morphology of Nematic and Smectic Vesicles
- Curvature Induced Activation of a Passive Tracer in an Active Bath
- Active swarms on a sphere
- Dynamics and density distribution of strongly confined noninteracting nonaligning self-propelled particles in a nonconvex boundary
- Pattern formation in flocking models: A hydrodynamic description
- Activating membranes
- Hydrodynamics of polar liquid crystals
- Hard Discs on the Hyperbolic Plane
- Role of disclinations in determining the morphology of deformable fluid interfaces
- Crystalline Particle Packings on Constant Mean Curvature (Delaunay) Surfaces
- Crystalline Order on Catenoidal Capillary Bridges
- Patterning of polar active filaments on a tense cylindrical membrane
- Quantification of myosin distribution predicts global morphogenetic flow in the fly embryo
- Active Particles on Curved Surfaces
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- Topological active matter
- Topological Sound
- Topological waves in fluids with odd viscosity
- Guided accumulation of active particles by topological design of a second-order skin effect
- Review: Topology of solitons and singular defects in chiral liquid crystals
- Sounds and hydrodynamics of polar active fluids
- Anomalous bulk-edge correspondence in continuous media
- Topological localization in out-of-equilibrium dissipative systems
- Soft self-assembly of Weyl materials for light and sound
- Topological Gaseous Plasmon Polariton in Realistic Plasma
- Dynamical patterns in active nematics on a sphere
- Anomalous Topological Active Matter
- Geometrical control of active turbulence in curved topographies
- Active crystals on a sphere
- Topological phase transition in coupled rock-paper-scissor cycles
- Active motion on curved surfaces
- Pattern Propagation Driven by Surface Curvature
- Topology protects chiral edge currents in stochastic systems
- Newton-Cartan Submanifolds and Fluid Membranes
- Mode-coupling theory for the steady-state dynamics of active Brownian particles
- Topology-driven ordering of flocking matter
- Topological elasticity of flexible structures
- Nontrivial topology in the continuous spectrum of a magnetized plasma
- Wave topology brought to the coast
- Degeneracies and symmetry breaking in pseudo-Hermitian matrices
- Spontaneous membrane formation and self-encapsulation of active rods in an inhomogeneous motility field
- Defect order in active nematics on a curved surface
- Spontaneous rotation of active droplets in two and three dimensions
- Wildebeest Herds on Rolling Hills: Flocking on Arbitrary Curved Surfaces
- Vortex Flows and Streamline Topology in Curved Biological Membranes
- Command of Collective Dynamics by Topological Defects in Spherical Crystals
- Topology of rotating stratified fluids with and without background shear flow
- A Simulation Algorithm for Brownian Dynamics on Complex Curved Surfaces
- Rayleigh Edge Waves in Two-Dimensional Crystals with Lorentz Forces -- from Skyrmion Crystals to Gyroscopic Media
- Hydrodynamics of Quantum Vortices on a Closed Surface
- From the geometry of Foucault pendulum to the topology of planetary waves
- A topological fluctuation theorem
- Geometric control of topological dynamics in a singing saw
- Orientational ordering of point dipoles on a sphere
- Complete absorption of topologically protected waves
- Generalized topological bulk-edge correspondence in bulk-Hermitian continuous systems with non-Hermitian boundary conditions
- Flocking turbulence of microswimmers in confined domains
- Bulk topological states in a new collective dynamics model
- Fractional and scaled Brownian motion on the sphere: The effects of long-time correlations on navigation strategies
- Locomotion without force, and impulse via dissipation: Robotic swimming in curved space via geometric phase
- Intrinsic Langevin dynamics of rigid inclusions on curved surfaces
- Oscillatory and chaotic pattern dynamics driven by surface curvature
- Hermitian and non-Hermitian topology in active matter
- Classifying topological floppy modes in the continuum
- Weakly nonlinear analysis of Turing pattern dynamics on curved surfaces
- Chiral topological phases in designed mechanical networks
- Topological edge flows drive macroscopic re-organization in magnetic colloids
- Mixing-demixing transition and void formation in quasi-2D binary mixtures on a sphere
- An optimal complexity spectral method for Navier--Stokes simulations in the ball
- Topological Flux on a Context Manifold Generates Nonreciprocal Collective Dynamics
- A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces
- Gauge theory for topological waves in continuum fluids with odd viscosity