Active nematics on a substrate: Giant number fluctuations and long-time tails

  title={Active nematics on a substrate: Giant number fluctuations and long-time tails},
  author={Sriram Ramaswamy and R. Aditi Simha and John Toner},
We construct the equations of motion for the coupled dynamics of order parameter and concentration for the nematic phase of driven particles on a solid surface, and show that they imply i) giant number fluctuations, with a standard deviation proportional to the mean in dimension d = 2 of primary relevance to experiment, and ii) long-time tails $\sim t^{-d/2}$in the autocorrelation of the particle velocities despite the absence of a hydrodynamic velocity field. Our predictions can be tested in… 

Low-noise phase of a two-dimensional active nematic system.

This work systematically study the two-dimensional fluctuating ordered phase in a coarse-grained hydrodynamic description involving both the nematic director and the conserved density field, showing that the system always displays only quasi-long-ranged orientational order beyond a crossover scale.

Aspects of the density field in an active nematic

The growth kinetics of the density domains is shown to be faster than the law expected for variables governed by a conservation law, and the suppression of density fluctuations in the stationary ordered nematic by the imposition of an orienting field.

Long-Range Nematic Order in Two-Dimensional Active Matter.

Working in two space dimensions, we show that the orientational order emerging from self-propelled polar particles aligning nematically is quasi-long-ranged beyond ℓ_{r}, the scale associated to

Long-Lived Giant Number Fluctuations in a Swarming Granular Nematic

Working with a fluidized monolayer of macroscopic rods in the nematic liquid crystalline phase, giant number fluctuations consistent with a standard deviation growing linearly with the mean are found, in contrast to any situation where the central limit theorem applies.

Mesoscopic theory for fluctuating active nematics

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

Banding, excitability and chaos in active nematic suspensions

Motivated by the observation of highly unstable flowing states in suspensions of microtubules and kinesin, we analyse a model of mutually propelled filaments suspended in a solvent. The system

Active nematics are intrinsically phase separated.

Numerically it is shown that the steady state of two-dimensional nonequilibrium nematic steady states in granular-rod monolayers or films of orientable amoeboid cells is macroscopically phase separated, yet dominated by fluctuations, as in the Das-Barma model.

A dynamic renormalization group study of active nematics

We carry out a systematic construction of the coarse-grained dynamical equation of motion for the orientational order parameter for a two-dimensional active nematic, that is a nonequilibrium steady

Swimmer Suspensions on Substrates: Anomalous Stability and Long-Range Order.

It is shown that, depending on the sign of a single parameter, a state with polar orientational order is anomalously stable (or anomalously unstable), with a nonzero relaxation rate for angular fluctuations, not parallel to the ordering direction, at zero wave number.



Algebraic Decay of Velocity Fluctuations in a Confined Fluid

Computer simulations of a colloidal particle suspended in a fluid confined by rigid walls show that, at long times, the velocity correlation function decays with a negative algebraic tail. The

Active membrane fluctuations studied by micropipet aspiration.

It is shown that a natural choice of the parameters quantifying the strength of the active noise explains both the large amplitude of the observed effects and its remarkable insensitivity to the active-center density in the investigated range.

Collective motion in a system of motile elements.

A mathematical model of cluster motion seen in nature, including collective rotation, chaos, wandering, occur in computer simulations of this deterministic model by introducing a set dimensionless parameters.

Directed transport may arise even in absence of a macroscopic bias provided that both parity and time reversal symmetry are broken. P. Curie

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UCSB (NSF Grant PHY99-07949) for partial support. JT acknowledges support from NSF grant #DMR-9980123

  • SR and JT thank the Aspen Center for Physics, and SR the Institute for Theoretical Physics

* Electronic address: † Electronic address: ‡ Electronic address: jjt@darkwing

    ) ; R . Kemkemer , D . Kling , D . Kaufmann , and H . Gruler

    • Eur . Phys . J . E
    • 1999

    Of course, in d = 2, there are no components of δn ⊥ perpendicular to q ⊥ , since there is only one direction perpendicular to z. We include δn T here to generalize the model to systems in d > 2

      and D . J . Durian , in preparation . [ 5 ] See , for example , T . Vicsek , Phys . Rev . Lett . 75 ( 1995 ) 1226 ; A . Czirok , H . E . Stanley , and T . Vicsek , J . Phys . A 30 ( 1997 ) 1375

      • P . Curie , J . Phys . ( Paris ) 3 o Série ( théorique et appliqué ) t . III , 393 (
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