Mesoscopic theory for fluctuating active nematics

Abstract

The term active nematics designates systems in which apolar elongated particles spend energy to move randomly along their axis and interact by inelastic collisions in the presence of noise. Starting from a simple Vicsek-style model for active nematics, we derive a mesoscopic theory, complete with effective multiplicative noise terms, using a combination of kinetic theory and Itô calculus approaches. The stochastic partial differential equations thus obtained are shown to recover the key terms argued in EPL \textbf{62} (2003) 196 to be at the origin of anomalous number fluctuations and long-range correlations. Their deterministic part is studied analytically, and is shown to give rise to the long-wavelength instability at onset of nematic order (see arXiv:1011.5408). The corresponding nonlinear density-segregated band solution is given in a closed form.

24 pages, 1 figure, submitted to New. J. Phys

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Cited by in corpus (67)

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• Defect unbinding in active nematics
• Boltzmann-Ginzburg-Landau approach for continuous descriptions of generic Vicsek-like models
• Large-scale chaos and fluctuations in active nematics
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• Quantitative Assessment of the Toner and Tu Theory of Polar Flocks
• Self-Aligning Polar Active Matter
• Hydrodynamic interactions in dense active suspensions: from polar order to dynamical clusters
• Clustering of Magnetic Swimmers in a Poiseuille Flow
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• Vesicle shape transformations driven by confined active filaments
• Active phase separation: new phenomenology from non-equilibrium physics
• Active Viscoelastic Matter: from Bacterial Drag Reduction to Turbulent Solids
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• Comparison between Smoluchowski and Boltzmann approaches for self-propelled rods
• The low noise phase of a 2d active nematic
• Active Matter Class with Second-Order Transition to Quasi-Long-Range Polar Order
• Phase Separation and Emergent Structures in an Active Nematic
• Critical Phenomena in Active Matter
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• Finite-time adiabatic processes: derivation and speed limit
• Active matter invasion of a viscous fluid: unstable sheets and a no-flow theorem
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• Designing, Synthesizing and Modeling Active Fluids
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• Active matter beyond mean-field: Ring-kinetic theory for self-propelled particles
• Entropy production and its large deviations in an active lattice gas
• Bodies in an Interacting Active Fluid: Far-Field Influence of a Single Body and Interaction Between Two Bodies
• A Boltzmann model for rod alignment and schooling fish
• Aspects of the density field in an active nematic
• Flocking and reorientation transition in the 4-state active Potts model
• Gap statistics of two interacting run and tumble particles in one dimension
• Flocking with a $q$-fold discrete symmetry: band-to-lane transition in the active Potts model
• The Phase Synchronized State of Oriented Active Fluids
• Long-Range Nematic Order in Two-Dimensional Active Matter
• Active nematics with quenched disorder
• Dynamical Sub-classes of Dry Active Nematics
• Theoretical approaches to the steady-state statistical physics of interacting dissipative units
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• Order-disorder transition in active nematic: A lattice model study
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• Density large deviations for multidimensional stochastic hyperbolic conservation laws
• Deriving hydrodynamic equations from dry active matter models in three dimensions
• Data-driven discovery of stochastic dynamical equations of collective motion
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• Comment on Ihle, "Towards a quantitative kinetic theory of polar active matter"
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• Giant density fluctuations in locally hyperuniform states
• Emergent universal long-range structure in random-organizing systems
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