(111d) Curvature-Controlled Geometrical Lensing Behavior in Self-Propelled Colloidal Particle Systems

In many biological systems, the curvature and topology of the surfaces, cells or other organisms live on, influence their collective properties. Using molecular dynamics simulations we find that Gaussian curvature (both positive and negative) likewise influences active colloidal systems. We show that for self-propelled particles confined to curved surfaces the curvature acts as a geometrical lens and shifts the critical density of motility-induced phase separation (MIPS) to lower values for positive curvature and higher values for negative curvature, which we explain theoretically by the nature of parallel lines in spherical and hyperbolic space. Curvature also fluidizes dense MIPS clusters due to the emergence of defect patterns disrupting the crystalline order inside the clusters. Based on our results we also design a new non-equilibrium behavior (cyclic phase separation). Here, the particles are restricted to surfaces which feature binary/trinary curvature profiles (like spherocylinders), which leads to local differences in the stability of phase separation and induces a steady loop of cluster formation and cluster dissolution.