Study Of Collective Motion And Self-organization Phenomenon In Pedestrian Flow

Active matter exists widely in nature,and the individual scale span of active matter is large,from micro-nano robots to bacteria,and to animals and humans.In addition to the dynamical properties of the active particles,people also focus on the self-organization phenomenon emerging from the active particle popula-tion,such as the formation of clusters of bacteria,the formation of eddies by the aggregation of fish and birds,the orderly migration of animals and the collective motion of pedestrian flow.In recent decades,people have collected a large amount of data through experimental observations and tried to model and understand their dynamic properties and the emergence of the corresponding self-organization phe-nomenon,hoping to finally achieve the preparation and regulation of natural or artificial active matter systems.In this dissertation,we mainly studied pedestrian dynamics in several basic scenarios,in which the competitive interaction and the way to solve the conflict between pedestrians are described by the evolutionary game framework.We ana-lyzed the impact of the game process on the collective motion of pedestrians,then revealed the mechanisms leading to some special phenomena that have emerged in current empirical research.Besides,we study the transport properties of a single active particle with self-aligned property and discuss whether this property can be extended to other active matter(such as pedestrians).The main research contents and achievements of this dissertation are summa-rized as follows.In the first chapter,we systematically introduced the basic concepts,develop-ment history,typical models,and analysis methods of active matter and pedestrian dynamics.In the second chapter,the evacuation dynamic of pedestrians in a square room with one single exit is studied.The movement of the pedestrians is guided by the static floor field model.Whenever multiple pedestrians are trying to move to the same target position,a game theoretical framework is introduced to address the conflict.The pedestrians can behave as either cooperators or defectors,depend-ing on whether they show gentle or aggressive in face of conflicts,respectively.When competing with cooperators,a defector always obtains a relatively greater payoff,characterizing the advantage of occupying the preferred vacant cell,while a reduced payoff factorδis introduced for mutual defection due to the possible in-juries by aggressiveness.Depending on the payoff matrix,the game in which the pedestrians are involved may be either a Hawk-Dove or Prisoner’s Dilemma,from which the reaped payoffs determine the capacities,or probabilities,of the pedes-trians occupying the preferred vacant sites.The pedestrians are allowed to adjust their strategies when competing with others,and a parameterκis utilized to char-acterize the extent of their self-interest regarding.It is found that self-interest may induce either positive or negative impacts on evacuation dynamics depending on whether it can facilitate the formation of collective cooperation in the population or not.Particularly,a resonance-like performance of average evacuation time is realized in the regime of the Prisoner’s Dilemma.The effects of placing an obsta-cle in front of the exit and the diversity of responses of the pedestrians to the space competition on evacuation dynamic are also discussed.Research results suggest that the diversity of individuals responding to environmental information may be the essential factor attributing to the discrepancy observed in empirical studies.In the third chapter,we study the bidirectional pedestrian flow in a straight corridor using a floor field cellular automaton model,where the game-theoretical framework is exclusively introduced to deal with conflicts in that multiple pedes-trians are trying to move to the same target position.We study how the pedestrian counterflow dynamics depend on the reduced payoff factorδ,the corridor width W,and the anticipation floor field strength k_A.It is found that the average separa-tion time of the pedestrians displays a resonance-like behavior as a function ofδ,irrespective of the width of the corridor as long as jam does not happen.The way of dealing with conflicts has no qualitative effect on the lane formation,where the jam probability mainly depends on the parameters W and k_Aas well as the pedestrian density.A large value of k_Ameans a strong tendency to avoid potential future collisions and suppress the overtaking motivation,but,at a cost,increases the average separation time of the two groups of pedestrians when the width of the corridor is not so narrow.Our results provide a meaningful perspective for understanding the process of lane formation and jam dissolution in bidirectional pedestrian flow,which provides a useful theoretical reference for designing effi-cient pedestrian traffic strategies.In the fourth chapter,we study the statistical properties of balanced and un-balanced bidirectional pedestrian flow in a straight corridor,while the above game theoretical model is adopted to solve the conflicts.The simulation results show that the complementary cumulative distribution of the time intervals for pedestrians to leave the corridor successively can be fitted by a stretched exponential distribution,and the statistical properties of the two types of pedestrian flows are affected dif-ferently by the flow ratio.Secondly,it is found that the jam probability exhibits a non-monotonic behavior with the flow ratio,where the maximum jam probability arises at an intermediate flow ratio of around 0.2.Finally,our simulation results are compared to those obtained by empirical studies and find good agreement be-tween the both,which suggests that the peculiar characteristics of the pedestrians originated from the anticipation mechanism of collision avoidance.These findings suggest a general rule that may be used to describe pedestrian counterflow,which may also be extended to the study of other human behaviors,providing a meaning-ful perspective for further understanding the lane formation process in bidirectional pedestrian flow.In the fifth chapter,for the more complex translational and angular dynam-ics of active particles,as well as a series of anomalous transport phenomena that can occur,we study the two-dimensional dynamics of a self-propelled pointlike particle with self-aligning property moving in Poiseuille flow.Such a model con-struction can also correspond to some special pedestrian motion scenarios.The re-sults show that with the change of the ratio of particle mass to self-driving force to viscosity,the type of long-term transport properties of the particle may change sig-nificantly(from normal diffusion to hyperdiffusion),while in the normal diffusion region,the effective diffusion coefficient of the particle exhibits a resonance-like behavior as a function of temperature.The relaxation property of moving speed and the position probability distribution function of the particle is also obtained.The transition of several types of anomalous diffusion and normal diffusion regime indicates the self-aligning property may be universal,which can be used as a the-oretical reference for future experiments analysis and modeling of active matter.Finally,we summarize the full text and propose some prospects for future empirical research and modeling improvements in pedestrian flow.