Variational bounds and nonlinear stability of an active nematic suspension

TL;DR

This paper employs the entropy method to establish nonlinear stability bounds for active nematic suspensions, revealing how activity influences organization and stability in particle suspensions.

Contribution

It introduces a variational bound on entropy fluctuations derived from the entropy method, linking stability to activity levels in active nematic suspensions.

Findings

Isotropic suspensions are nonlinearly stable at low activity.

Derived bounds on spatiotemporal averages in unstable regimes.

Activity influences the self-organization limits of particle suspensions.

Abstract

We use the entropy method to analyze the nonlinear dynamics and stability of a continuum kinetic model of an active nematic suspension. From the time evolution of the relative entropy -- an energy-like quantity in the kinetic model -- we derive a variational bound on relative entropy fluctuations that can be expressed in terms of orientational order parameters. From this bound we show isotropic suspensions are nonlinearly stable for sufficiently low activity, and derive upper bounds on spatiotemporal averages in the unstable regime that are consistent with fully nonlinear simulations. This work highlights the self-organizing role of activity in particle suspensions, and places limits on how organized such systems can be.