Phase Transition Analysis And Kinetics Models For Collective Motion

The collective behaviors in nature have attracted extensive attention due to their various self-organization structures.Collective ordered motion with distinct patterns are discovered in many real-life situations,ranging from the colony of bacteria,organization of cells,migration of animals to the traffic of human beings,etc.Specifically,it was observed in these multi-body systems that simple local-scale interactions among individuals usually lead to complex structures macro-scopically,such like vortex in sardines,marching queues in spiny lobsters,tide of surging horses and lanes in pedestrians.Researches are concerning the process of emergence and dissipation of macro order,therefore in recent decades,they building models by plenty of observations and experiments to reproduce these phenomena,analyze the phase transition and propose reasonable explanationIn this dissertation,we have analyzed the inner dynamics,ordered phenom-ena and phase transition for different type of nature collective.We study the orientation alignment behavior for fish schools and bird flocks in second and third chapters,which including inner factors and potential interactions of align-ment phenomena.And we investigate the reasonable models for more complex pedestrian crowds to match various pedestrian motions in forth chapter.Find-ing the common features of different nature collectives in the same scenario for animals,meanwhile finding the general models of pedestrian crowds in different scenarios for pedestrian motions,are the different ways for searching inner rules in collective motion studiesThe main research contents and achievements are summarized as followsIn the first chapter,we show the nature phenomena of collective motion and its research information background,most concerned phase transition in this field and brief derivation of state distribution equations.At last for the most important Vicsek model of collective motion field,its basic concepts,devel-opment history,discussion of phase transition types,analysis of self-organization structure,latest findings and analytical calculation are introducedIn the second chapter,we find some common features from the models of collective motions which could present the phenomena of macro order phase after reading various studies of collective behavior(such as birds,fishes and sheep)By exploring a compact,steady and ordered system,we find the two necessary conditions for alignment order(analogue to ferromagnetic phase),one of them is an interaction as well as a potential well in every agent’s orientation,and another is a steady spatial structure formatted among agents which similar to crystal lattice.Then,we analyze the phase transition behavior of full-connected system near the critical point through the approach of mean field approximation.After theoretical derivation,we find the critical exponent and critical point for most models in generally with the interaction of potential well,and these models belong to the same universal class.At last,according to simulations and numerical calculations,and these results are consisting with our theoretical derivation,it confirms the universal critical behavior among different modelsIn the third chapter,after studying of the model with potential well in an-gular direction,we subsequently turning our focus into multiple phase transition in this kind of model.In this part,the phase transition behavior between the three phases,such as polar liquid,density band and disorder gas in quasi Vicsek model is introduced.We analyze and calculate the peak density scale of band structure,find the non-monotonic feature of peak density with different param-eters,and demonstrate the influence of noise intensity and interaction ranges for phase transition.At the last,the transform of phase transition types from first order to second order has been found by changing the interaction range,and we draw the dividing line of those phase transition and transition types based on simulative result and semi-analytical solutionIn the fourth chapter,we propose model and take simulations for anoth-er common collective behavior,the pedestrian motion.It is different from the way of modeling in Vicsek model which conjecturing the interaction between individuals is based on some macro alignment phenomena,our pedestrian dy-namics model with the consideration of two heuristic mechanisms of anticipation and attraction is inspired by logic of daily behavior.The former interaction en-ables the individuals to anticipate potential collisions in terms of the state of surrounding environment and slow down their moving speed accordingly,while the latter reflects the tendency of the individuals following(or being attracted by)those peer partners with high moving speeds,trying to reach their destina-tions as quickly as possible.By tuning the interaction ranges of anticipation and attraction,we explore the collection motion behavior of the pedestrians in three common movement scenarios,i.e.,the bidirectional pedestrian flows in a straight corridor,the crossing pedestrian flows in a square and the crowd evacua-tion in a room.Interestingly,with appropriate combinations of the anticipation distance and attraction distance,we reproduce the typical collective motion pat-terns of the pedestrians observed in the empirical studies,such as the formation and separation of global pedestrian flow lanes,the stop-and-go waves,and the vortex-like patterns as well.Particularly,we find that a strong attraction effect by the fast-moving pedestrian flows benefits the efficient passing only in the cor-ridor case,whereas in the case of crossing pedestrians the avoidance behavior due to anticipation will play a dominating role in guaranteeing an ordered collective motion.The conclusion of this dissertation and some prospects for the future works in this field is given in the last chapter.