  We study the dynamics of asymmetric, deformable particles in oscillatory,
linear shear flow. By simulating the motion of a dumbbell, a ring polymer, and
a capsule we show that cross-stream migration occurs for asymmetric elastic
particles even in linear shear flow if the shear rate varies in time. The
migration is generic as it does not depend on the particle dimension.
Importantly, the migration velocity and migration direction are robust to
variations of the initial particle orientation, making our proposed scheme
suitable for sorting particles with asymmetric material properties.
