Study Of Tuning Clique Percolation On Complex Networks And Confined Self-propelled Particles

Complex systems in real world consist of functioning components and intricate interactions between components.One characteristic of complex system is that minor change of their components may exert major impact on properties of the system as a whole.The complex network is a competent tool to study complex systems,with the abstraction of nodes representing components and edges interactions between components.An important process on network is percolation,featuring the emergence of macroscopic components.Percolation,as a geometrical phase transition and lacking the dependence of metric space,has wide applications in physics such as conductivity materials,magnetic models,colloids,and spin quantum Hall effect.In cooperative networks like costar,scientific coauthor and patent networks,the unit added into system at an evolution step is a clique instead of an edge.Based on the empirical data from the cooperative networks,we establish a clique growth model.At every time step,a 3-clique is added into the system.The probability of a node to be selected is non-uniform and dynamically dependent on its degree at current step.The dependent function is of power law form,with exponent being a tunable controlling parameter.We take the generalized connectivity and consider both(3,1)and(3,2)cases.We find the(3,2)percolation can be tuned from continuous to discontinuous and vice versa,by varying the controlling parameter.Contrarily,(3,1)percolation remains continuous in all the range of the controlling parameter.The mechanism for discontinuous percolation in previous study is via the overtaking,i.e.,small clusters merging into a new largest cluster.However,the mechanism for(3,2)discontinuous percolation is via the direct growth of largest cluster.The largest cluster constantly grows by merging smaller clusters.Discontinuous percolation represents a more dramatic change of the system.The finding of new mechanism for discontinuous percolation is beneficial to the study of robustness of networks and other processes occurring on networks.Networks in real worlds often interact with each other,resulting in a multilayer network.Self-propelled particles moving on background network is an interesting example of multilayer network to study.The collective motion of self-propelled particles is ubiquitous in both living and artificial systems.Vicsek model is a simple model to describe these phenomena.We restrict Vicsek model on 2D square lattice and require the state space of particle directions be discrete.The discretizations of both moving space and direction state space allow us to define alignment network.In real world,self-propelled particles always move in some environment and may encounter obstacles.We apply percolation process upon the lattice to simulate the disorder of background environment and observe its impact on the alignment network.We find no significant change around the critical percolation point of underlying lattice.We incorporate the size of max alignment cluster other than the global alignment order parameter to describe the local structure of particle alignment.There is non-zero optimal noise that maximize the collective motion of self-propelled particles.This is due to that mediate noise can promote the merge of alignment clusters,resulting in much larger ones.Besides the translational motion,self-propelled particles can also undergo rotational motion,which also exhibits intriguing phenomena.When active rotors are confined in2 D disk,the oscillations of both particles density and velocity are observed in simulation.From Onsager variational principle,we construct its isothermal equivalence,Rayleighian and derive the equations of motion for active rotors.We find at steady state,rotors form annulus structure,resulting in the oscillation of density.In the equations of motion,velocity and density are coupled together.The oscillation of density brings the velocity to oscillate,too.