  We study the dynamic structure of lipid domain inclusions embedded within a
phase-separated reconstituted lipid bilayer in contact with a swarming flow of
gliding filamentous actin. Passive circular domains transition into
highly-deformed morphologies that continuously elongate, rotate, and pinch off
into smaller fragments, leading to a dynamic steady state with approximately
23x speed up in the relaxation of the intermediate scattering function compared
to passive membrane domains driven by purely thermal forces. To corroborate
experimental results, we develop a phase-field model of the lipid domains with
two-way coupling to the Toner-Tu equations. We report phase domains that become
entrained in the chaotic eddy patterns, with oscillating waves of domains that
correlate with the dominant wavelengths of the Toner-Tu flow fields.
