Simple and faithful nonlinear field equations for aligning self-propelled rods

Abstract

We derive a set of minimal yet complete nonlinear field equations describing the collective properties of self-propelled rods from a simple microscopic starting point, the Vicsek model with nematic alignment. Analysis of their linear and nonlinear dynamics shows good agreement with the original microscopic model. In particular, we derive an explicit expression for the fronts forming density-segregated, banded solutions, allowing us to develop a more complete analytic picture of the problem at the nonlinear level.

References in corpus (11)

• Novel type of phase transition in a system of self-driven particles
• Collective motion of self-propelled particles interacting without cohesion
• Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis
• Minimal model for active nematics: quasi-long-range order and giant fluctuations
• Enhanced diffusion and ordering of self-propelled rods
• Hydrodynamics of self-propelled hard rods
• Pattern formation of microtubules and motors: inelastic interaction of polar rods
• A Reanalysis of the Hydrodynamic Theory of Fluid, Polar-Ordered Flocks
• Active nematics are intrinsically phase-separated
• Frozen steady states in active systems
• Continuous theory of active matter systems with metric-free interactions

Cited by in corpus (79)

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• Collective Motion of Self-Propelled Particles with Memory
• Boltzmann-Ginzburg-Landau approach for continuous descriptions of generic Vicsek-like models
• Collective behavior of penetrable self-propelled rods in two dimensions
• Mesoscopic theory for fluctuating active nematics
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• Minimal continuum theories of structure formation in dense active fluids
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• A particle-field representation unifies paradigms in active matter
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• Active Curved Polymers form Vortex Patterns on Membranes
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• Hydrodynamic length-scale selection and effective viscosity in microswimmer suspensions
• Self-propelled particles with selective attraction-repulsion interaction - From microscopic dynamics to coarse-grained theories
• Motility-induced phase separation of active particles in the presence of velocity alignment
• A kinetic model and scaling properties for non-equilibrium clustering of self-propelled particles
• Spontaneous motion and deformation of a self-propelled droplet
• Antipolar ordering of topological defects in active liquid crystals
• Mesoscale pattern formation of self-propelled rods with velocity reversal
• Understanding Collective Dynamics of Soft Active Colloids by Binary Scattering
• Pattern-induced local symmetry breaking in active matter systems
• Understanding dense active nematics from microscopic models
• Active phase separation: new phenomenology from non-equilibrium physics
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• Giant Kovacs-Like Memory Effect for Active Particles
• Active particles in heterogeneous media display new physics: existence of optimal noise and absence of bands and long-range order
• Phase Separation and Emergent Structures in an Active Nematic
• Active Matter Class with Second-Order Transition to Quasi-Long-Range Polar Order
• Exact fluctuating hydrodynamics of active lattice gases -- Typical fluctuations
• Active Brownian Rods
• Chapman-Enskog expansion for the Vicsek model of self-propelled particles
• A Critical Assessment of the Boltzmann Approach for Active Systems
• Role of particle conservation in self-propelled particle systems
• Towards a quantitative kinetic theory of polar active matter
• Numerical treatment of the Boltzmann equation for self-propelled particle systems
• Entropy production and its large deviations in an active lattice gas
• Confinement and collective escape of active particles
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• Sufficient conditions for wave instability in three-component reaction-diffusion systems
• Diversity of phase transitions and phase separations in active fluids
• Promoting collective motion of self-propelled agents by distance-based influence
• Giant vortex dynamics in confined active turbulence
• Casimir effect in swimmer suspensions
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• Additivity, density fluctuations, and nonequilibrium thermodynamics for active Brownian particles
• Theoretical approaches to the steady-state statistical physics of interacting dissipative units
• Dynamical Sub-classes of Dry Active Nematics
• A Finite Volume Method for Continuum Limit Equations of Nonlocally Interacting Active Chiral Particles
• Hydrodynamic Equations for Flocking Models without Velocity Alignment
• Large density expansion of a hydrodynamic theory for self-propelled particles
• Deriving hydrodynamic equations from dry active matter models in three dimensions
• Environment-stored memory in active nematics and extra-cellular matrix remodeling
• Microphase separation in active filament systems is maintained by cyclic dynamics of cluster size and order
• Comment on Ihle, "Towards a quantitative kinetic theory of polar active matter"
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• Transport coefficients of self-propelled particles. II. Numerics for vorticity fluctuations and the reverse perturbation method
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• Gaussian theory for spatially distributed self-propelled particles
• Supramolecular assemblies in active motor-filament systems: micelles, bilayers, and foams
• Nematic alignment of self-propelled particles in the macroscopic regime
• Fluctuating Hydrodynamics Describes Transport in Cellular Aggregates
• Critical assessment of von Mises distribution and an infinite series ansatz for self-propelled particles
• Activity-induced phase transition and coarsening dynamics in dry apolar active nematics
• Phase separation of self-propelled disks with ferromagnetic and nematic alignment
• A Data-Driven Statistical Description for the Hydrodynamics of Active Matter
• Snowdrift game induces pattern formation in systems of self-propelled particles