  The collective behavior of self-propelled particles (SPPs) under the combined
effects of a circularly patterned substrate and circular confinement is
investigated through coarse-grained molecular dynamics simulations of polarized
and disjoint ring polymers. The study is performed over a wide range of values
of the SPPs packing fraction $\bar\phi$, motility force $F_D$, and area
fraction of the patterned region. At low packing fractions, the SPPs are
excluded from the system's center and exhibit a vortical motion that is
dominated by the substrate at intermediate values of $F_D$. This exclusion zone
is due to the coupling between the driving force and torque induced by the
substrate, which induces an outward spiral motion of the SPPs. For high values
of $F_D$, the SPPs exclusion from the center is dominated by the confining
boundary. At high values of $\bar\phi$, the substrate pattern leads to
reversals in the vorticity, which become quasi-periodic with increasing
$\bar\phi$. We also found that the substrate pattern is able to separate SPPs
based on their motilities.
