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

TL;DR

This paper develops equations describing active nematics on a substrate, predicting giant number fluctuations and long-time tails in velocity autocorrelations, which can be tested in biological and granular systems.

Contribution

It introduces a theoretical framework for active nematics on a substrate, revealing novel fluctuation behaviors without hydrodynamic flow.

Findings

Giant number fluctuations with standard deviation proportional to mean

Long-time tails in velocity autocorrelation decay as t^{-d/2}

Predictions applicable to biological and granular active matter

Abstract

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 and (ii) long-time tails $\sim t^{-d/2}$ in the autocorrelation of the particle velocities in $d$ dimensions despite the absence of a hydrodynamic velocity field. Our predictions can be tested in experiments on aggregates of amoeboid cells as well as on layers of agitated granular matter.