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Viscoelastic and elastomeric active matter: Linear instability and nonlinear dynamics

We consider a continuum model of active viscoelastic matter, whereby an active nematic liquid-crystal is coupled to a minimal model of polymer dynamics with a viscoelastic relaxation time $τ_C$. To explore the resulting interplay between active and polymeric dynamics, we first generalise a linear stability analysis (from earlier studies without polymer) to derive criteria for the onset of spontaneous heterogeneous flows (strain rate) and/or deformations (strain). We find two modes of instability. The first is a viscous mode, associated with strain rate perturbations. It dominates for relatively small values of $τ_C$ and is a simple generalisation of the instability known previously without polymer. The second is an elastomeric mode, associated with strain perturbations, which dominates at large $τ_C$ and persists even as $τ_C\to\infty$. We explore the novel dynamical states to which these instabilities lead by means of direct numerical simulations. These reveal oscillatory shear-banded states in 1D, and activity-driven turbulence in 2D even in the elastomeric limit $τ_C\to\infty$. Adding polymer can also have calming effects, increasing the net throughput of spontaneous flow along a channel in a new type of "drag-reduction". Finally the effect of including strong, antagonistic coupling between nematic and polymer is examined numerically, revealing a rich array of spontaneously flowing states.