Collective Motion And Critical Behavior Of The Self-propelled Particle System

The motion of groups of animals in nature can be regarded as active matter(or self-propelled particles)systems,such as shoals of fish,flocks of birds,bac-terial colony,crowds and so on.It is well known that these systems can produce a variety of motion patterns under different conditions,like congregations,highly cooperative and organized movements,and occasional leadership.These common and interesting phenomena fascinate scientists all the time,but the original mech-anism and nature problem of collective motion is still incompletely resolved.In order to unveil the riddle,a large number of physical workers have put forward many agent-based models in the past few decades,and the study of the collective motion is on the rise In a pioneer work,Reynolds proposed three interaction rules,say,separation,alignment,and cohesion,to study the collective motion of flocks.With these three simple rules,the flock moves in an extremely realistic way,creating complex mo-tion and interaction that would be extremely hard to create otherwise.Perhaps the most popular model of collective motion is by Vicsek et al.,the Vicsek mod-el.In this model,all particles move at the same speed and every particle adjusts its direction of motion at each time step in order to align with the mean direction of its neighboring particles.A noise term is introduced in this model to simu-late those uncertain factors in real environment,and it has been found that the motion patterns of the system depend on both the noise level and the density of particles,with a transition from an ordered to a disordered state by tuning the t-wo parameters.Strombom had come up with a model containing only attraction and showed that three different patterns of motion,swarms,undirected mills,and moving aligned groups,can emerge.Chate et al.introduced the attraction between individuals on the basis of the Vicsek model and studied the phenomenon of cel-1 sorting.Recently,by introducing aggregation interaction and other constraints,Barberis et al.and Cheng et al.investigated the nonequilibrium dynamic patterns of self-propelled particle systems using statistical mechanics methods and showed abundant patterns of collective motion In this work,we combine the velocity alignment and aggregation mechanisms to study the collective motion of active agents in noisy circumstances.The agents are located on a two-dimensional square plane,and the proportion of velocity align-ment and aggregation interactions are,respectively,set to be k and 1-k.In the case of k= 1 our model is similar to the classical Vicsek Model,while it degen-erates to the view angle model for k= 0.By tuning the intensity of the external noise η and the proportional coefficient k,and carrying out extensive numerical simulations,we find that the system can exhibit diverse dynamic patterns widely observed in real biological systems.By means of finite-size scaling analysis,we confirm that the presence of the aggregation interaction affects not only the posi-tion of the critical noise ηc(beyond which the agents display disordered motion),but also the type of the phase transition of the collective motion.In particular,under weak external noise environment,the transition from disordered to ordered state by increasing k(i.e.,by decreasing the proportion of aggregation interaction)is found to be of first order.Besides,for moderate external noise,we also find the existence of the optimal proportion of the aggregation interaction for the system to achieve the highest degree of order.Our results highlights the important role of the aggregation interaction in the collective motion and may have promising potential applications in natural self-propelled particles and artificial multi-agent systems.