Active filaments on curved surfaces: from single filaments to dilute suspensions

Curvature plays a central organizational role in active polymer dynamics. Using large-scale Langevin-dynamics simulations, we study active semiflexible filaments confined to smooth curved surfaces and map how curvature, bending rigidity, and activity interact. We find geodesic alignment, curvature lensing, and curvature-induced trapping. In particular, regions of negative Gaussian curvature localize filaments and hinder global surface exploration. These results show how surface geometry can be used to control the organization and transport of active matter on curved substrates.