The Collective Movement Phase Transition In A Hierarchical Society

Collective motion is one of most spectacular and fascinating emergent behaviors in nature and human society,as exhibited from fish shoals,bird flocks,and large-scale migration of various mammals,even humans at macroscopic level,to the reproduction of bacteria and intracellular molecular cooperative motion at the microscopic level.While detailed case studies are preferred in general by biologists,physicists usually seek for minimal models with the hope that there are universal features behind seemingly diverse observations,and simple models are sufficient to capture the fundamental laws.A classical model,which considerably advanced our understanding of collective motion,is the Vicsek model inspired by statistical physics.The model captures the interaction between individuals with simple rules,where phase transitions between the ordered and disordered states of collective motion emerges caused by local alignment and external disturbances,a major concern in nonequilibrium statistical physics.However,Vicsek model assumes that these individuals are indistinguishable,and the collective movement can be seen as the result of an egalitarian democratic decision,as indeed observed in some species.While the collective movements for some species are through an equal consensus,many more are based on biased decision-making,where a fraction of individuals(or even a single one)lead the group movement.This is particularly true when hierarchical social structures are present.For example,recent experiments have revealed well-defined hierarchical structures among homing pigeons and migratory white storks,where a small number of leaders lead the group flight.Social hierarchy is also revealed in mammals such as African elephants,gray wolves,primates,as well as in fish schools and honeybee swarms etc.However,a generic model that interpolates from egalitarian to despotic swarms is still lacking.Revealing how the hierarchy impacts on the collective motion remains a crucial challenge for understanding hierarchical societies in general.In this thesis,we propose a hierarchical swarm model on the basis of Vicsek model.To stratify the population,a natural way is to relate the labeling with the hierarchy that we assign a higher ranking to the individual with a smaller label.For those with lower ranking,consider the impact with a weight of ?.We show that,as the hierarchy becomes more important,the swarming transition changes dramatically from the weak first-order phase transition observed for egalitarian populations,to a stronger first-order transition,and finally to a second-order phase transition for despotic societies.To understand this change,we analyse their spatial structures the double-peak structure of order parameters,the correlation between local order parameters and global order parameters,as well as the correlation between the density and velocity fields.Furthermore,a two group model and vectorial hierarchical Vicsek model are established to verify the robustness of these results.Finally,we turn to a network perspective to understand the enhancement of firstorder phase transition.There the swarming particles is considered as network nodes,and a link is established when two particles are in each other's neighborhood,where the collective motion is transferred into a synchronization problem on networks.It successfully reproduces the intermediate level of hierarchy impact a that generates the strongest discontinuity,giving a clear physical picture.On the theoretic side,ur results points out a wide possibility for swarming transitions given the ubiquitous hierarchy,fill the model gap from egalitarian to despotic swarms;On the experimental side,we expect specific case studies with diverse hierarchical impacts that confirm our conclusion and reveal other complexities that may arise from the hierarchy impact.