Constitutive equations for a one-dimensional, active, polar, viscoelastic
liquid are derived by treating the strain field as a slow hydrodynamic
variable. Taking into account the couplings between strain and polarity allowed
by symmetry, the hydrodynamics of an active, polar, viscoelastic body include
an evolution equation for the polarity field that generalizes the damped
Kuramoto-Sivashinsky equation. Beyond thresholds of the active coupling
coefficients between the polarity and the stress or the strain rate,
bifurcations of the homogeneous state lead first to stationary waves, then to
propagating waves of the strain, stress and polarity fields. I argue that these
results are relevant to living matter, and may explain rotating actomyosin
rings in cells and mechanical waves in epithelial cell monolayers.Comment: 9 pages, 4 figure
