The Collective Motion Of Self-propelled Particles On A Spherical Substrate

The active system consists of active particles which can individually dissipate en-ergy from the environment and drive themself into spontaneous motion.The active system is far from equilibrium and has attracted much attention due to its rich dynamic phenomena.The self-propelled particles model can describe much dynamic phenom-ena in active systems.It was recently demonstrated that the self-propelled particles freeze at the sufficiently high packing fraction and low activity.The phase diagrams have been established to describe the crystallization process with a wide range of ac-tivity and packing fraction.However,these studies have mainly focused on the active system on planar surface without the geometrical constraint.For the dense packing of particles with no polar or nematic order,due to the geometrical constraint of a spher-ical substrate,the total disclination charge of the spherical crystal must be 12.These inevitable topological defects provide a unique insight into the physics of the spherical crystal.Recently,the interplay between one active particle and crystallographic defects has been numerically investigated.But how the activity influences the global structure and dynamic motion of self-propelled particles on spherical substrates remains elusive.By using numerical simulation,this work first explores the crystallization of self-propelled particles confined on the spherical surface.The self-propelled particles freeze from liquid to solid with the increase of the packing fraction.During the freezing pro-cess,the topological defect fraction decreases and the global order increases.Further-more,the distribution of topological defects changes with the self-propelled velocity.The simulation shows the pattern evolution of inevitable topological defects due to the geometric constraints of the spherical substrate.At middle packing fraction,there is a transition from twelve isolated grain boundaries to uniform distribution of disloca-tions with the increase of the self-propelled velocity.This transition also exists at high packing fraction if the self-propelled velocity is high enough.By calculating the slope of the cage-MSD,this study find the boundary between liquid and solid,and draw a phase diagram.With the increase of the self-propelled velocity,the correlated motion between the particle and its neighbors gradually weakens and the solid melts into liquid.Then this thesis explores the phase behavior of the self-propelled particles confined on the spherical surface.At high angular Peclet number,the self-propelled particles can separate into the coexistence of dense and gas phases on the spherical surface.The simulation indicates that the orientational correlation for the self-propelled particles in-creases with the increase of the packing fraction.The self-propelled particles tend to remain aligned orientation and collective motion.This work shows the critical role of the geometrical constraint in the collective mo-tion of the self-propelled particles.This study investigates the self-propelled particles confined on a spherical substrate and explore the structural and dynamic properties of self-propelled particles by controlling the packing fraction and activity.These results may deepen our understanding of the active particles in complex and crowded environ-ments.