| Abstract: |
| We study collective motion of active particles on three prescribed surfaces with distinct topological
and geometrical properties. Kinematics of the active particles on the surfaces is driven by selfpropelling,
particle-particle interaction, surface constraining and under-damped stochastic forces described
by Ornstein-Uhlenbeck processes. We demonstrate the prevailing collective patterns in the active
particle systems on the three types of surfaces: a sphere, a torus and a hill and valley landscape
with distinct topological and geometrical properties. We note that all the sustainable, spatial-temporal
patterns are profoundly affected by the curvature of the surfaces as well as their symmetry. In particular,
we find that the large magnitude of curvature in the hill and valley landscape coupled with certain surface
symmetry warrants a spatial-temporal periodic traveling rings pattern which synchronizes the collective
movement of the active particles with the symmetry in the landscape. However, the large magnitude
of curvature alone without the necessary surface symmetry is not sufficient to sustain such a periodic,
spatial-temporal pattern, instead collective motion settles into cyclic rotation. |
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