Collective motion of polar active particles on a sphere

Collective motion of active particles with polar alignment is investigated on a sphere. We discussed the factors that affect particle swarm motion and define an order parameter that can show the degree of particle swarm motion. In the model, we added a polar alignment strength, along with Gaussian curvature, affecting particles swarm motion. We find that when the force exceeds a certain limit, the order parameter will decrease with the increase of the force. Combined with our definition of order parameter and observation of the model, the reason is that particles begin to move side by side under the influence of polar forces. In addition, the effects of velocity, rotational diffusion coefficient, and packing fraction on particle swarm motion are discussed. It is found that the rotational diffusion coefficient and the packing fraction have a great influence on the clustering motion of particles, while the velocity has little influence on the clustering motion of particles.