Effects of Non-uniform Gaussian Curvature on the Collective Motion of Active Particles
Underlying curvature non-trivially affects the behaviour of active systems due to the incompatibility of order and non-zero curvature. While active particles on a plane have been extensively studied in the past, little work has been done to understand the effects of curvature on their collective behaviour. There are a wide range of active systems that move on curved surface, for example, cells in crypts in the gut, vortex patterns in the mammalian cornea or actively driven microtubule bundles on a droplet. Following a study (R. Sknepnek and S. Henkes, Phys. Rev. E91, 022306(2015)) of active swarms on spheres, we aim to expand the model to a range of closed surfaces of revolution, with position dependent Gaussian curvature. We explore how curvature of the surface affects the dynamics of the collective motion of the particles, coupled with the effects of orientational alignment and driving velocity. We run simulations of self propelled particles with pairwise repulsive interactions and XY-model type orientational dynamics with delta-correlated noise, on a variety of curved surfaces. We aim to characterise the different behaviours which emerge and relate particle motion patterns to geodesics and regions of maximum Gaussian Curvature on the surface.
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