Spatio-temporal dynamics of an active, polar, viscoelastic ring

Area of Science:

• Physics
• Materials Science
• Biophysics

Background:

• Active, polar, viscoelastic materials exhibit complex behaviors.
• Understanding their constitutive equations is crucial for explaining phenomena in living matter.

Purpose of the Study:

• To derive constitutive equations for a one-dimensional, active, polar, viscoelastic liquid.
• To investigate the hydrodynamics and emergent behaviors of such materials.

Main Methods:

• Treating the strain field as a slow hydrodynamic variable.
• Incorporating symmetry-allowed couplings between strain and polarity.
• Deriving an evolution equation for the polarity field, generalizing the damped Kuramoto-Sivashinsky equation.

Main Results:

• The derived hydrodynamics include an evolution equation for polarity.
• Bifurcations occur beyond thresholds of active coupling coefficients.
• These bifurcations lead to stationary and then propagating waves in strain, stress, and polarity fields.

Conclusions:

• The results offer a theoretical framework for active, polar, viscoelastic materials.
• These findings may explain phenomena like rotating actomyosin rings in cells.
• The model provides insights into mechanical waves observed in epithelial cell monolayers.