Ising-like critical behavior of vortex lattices in an active fluid

Abstract

Turbulent vortex structures emerging in bacterial active fluids can be organized into regular vortex lattices by weak geometrical constraints such as obstacles. Here we show, using a continuum-theoretical approach, that the formation and destruction of these patterns exhibit features of a continuous second-order equilibrium phase transition, including long-range correlations, divergent susceptibility, and critical slowing down. The emerging vorticity field can be mapped onto a two-dimensional (2D) Ising model with antiferromagnetic nearest-neighbor interactions by coarse-graining. The resulting effective temperature is found to be proportional to the strength of the nonlinear advection in the continuum model.

References in corpus (42)

• Active Particles in Complex and Crowded Environments
• The World of the Complex Ginzburg-Landau Equation
• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Motility-Induced Phase Separation
• Active Brownian Particles. From Individual to Collective Stochastic Dynamics
• Meso-scale turbulence in living fluids
• Universality classes in nonequilibrium lattice systems
• Fluid dynamics of bacterial turbulence
• Sedimentation of active colloidal suspensions
• The 2019 Motile Active Matter Roadmap
• Confinement Stabilizes a Bacterial Suspension into a Spiral Vortex
• Fluid Flows Created by Swimming Bacteria Drive Self-Organization in Confined Suspensions
• Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis
• Active Turbulence
• The effective temperature
• Self-Propelled Rods: Insights and Perspectives for Active Matter
• Directed percolation criticality in turbulent liquid crystals
• Generalized energy equipartition in harmonic oscillators driven by active baths
• Effective temperature of active matter
• Ferromagnetic and antiferromagnetic order in bacterial vortex lattices
• The rise of fully turbulent flow
• A Universal Transition to Turbulence in Channel Flow
• Onset of meso-scale turbulence in living fluids
• Mesoscopic Turbulence and Local Order in Janus Particles Self-Propelling under an AC Electric Field
• Activity induced synchronization: From Mutual Flocking to Chiral Self-Sorting
• Minimal continuum theories of structure formation in dense active fluids
• Vortex arrays and meso-scale turbulence of self-propelled particles
• Derivation of a hydrodynamic theory for mesoscale dynamics in microswimmer suspensions
• Geometry-driven collective ordering of bacterial vortices
• Hydrodynamic length-scale selection and effective viscosity in microswimmer suspensions
• Turbulence and turbulent pattern formation in a minimal model for active fluids
• Anomalous Topological Active Matter
• Dynamical self-assembly of dipolar active Brownian particles in two dimensions
• Geometry-dependent viscosity reduction in sheared active fluids
• Oscillatory chiral flows in confined active fluids with obstacles
• Vortex dynamics and Lagrangian statistics in a model for active turbulence
• Scaling Analysis of the Site-Diluted Ising Model in Two Dimensions
• Computation of Spiral Spectra
• Emergence and melting of active vortex crystals
• The Dynamical Dimension of Defects in Spatiotemporal Chaos
• Asymmetric pattern formation in microswimmer suspensions induced by orienting fields
• Percolation and Magnetization in the Continuous Spin Ising Model

Cited by in corpus (9)

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• Self-sustained patchy turbulence in shear-thinning active fluids
• Vortex pattern stabilization in thin films resulting from shear thickening of active suspensions
• Oscillating edge current in polar active fluid
• Geometric frustration and pairing order transition in confined bacterial vortices
• Emergence of rogue-like waves in a reaction-diffusion system: Stochastic output from deterministic dissipative dynamics
• Controlling Vortex Rotation in Dry Active Matter
• Optimal Turbulent Transport in Microswimmer Suspensions