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We consider a confined sheared active polar liquid crystal with a uniformorientation and study the effect of variations in the magnitude ofpolarization. Restricting our analysis to one-dimensional geometries, wedemonstrate that with asymmetric boundary conditions, this system ischaracterized, macroscopically, by a linear shear stress vs. shear strainrelationship that does not pass through the origin: At a zero strain rate, thefluid sustains a non-zero stress. Analytic solutions for the polarization,density, and velocity fields are derived for asymptotically large or smallsystems and are shown by comparison with precise numerical solutions to be goodapproximations for finite-size systems.

Exact results for sheared polar active suspensions with variable liquid crystalline order