Non-equilibrium Collective Behavior In Active Matters And Living Systems

Recently,the collective motion of active matters and living systems cause more and more peoples' concern.We can see a wide range of collective behavior and vari-ous self-organized structures in animal groups,such as moving locusts,travelling bird flocks,fish schools and some human behavior.In experimental observations,active matters also exhibit a complex phase behavior,such as microtubule organization,bac-terial colonies.These systems are always characterized by some self-propelled proper-ties.There is a great difference between the active systems and equilibrium systems.In equilibrium,the interaction between individuals obeys the law of momentum conser-vation.But in active systems or living systems,the interaction does not obey this law,which leads to a wide range of collective patterns.The goal to be achieved to study active matters and living systems is to understand the information transfer between in-dividuals,the accurate interaction and the dynamic mechanism of collective motion.In this thesis,we mainly focus on the computer simulation of the collective motion of active matters and living systems.We are trying to understand the dynamic mechanis-m of collective motion and compare our results with experimental observations.This would be helpful for understanding the interaction between individuals and designing some strategies to control the collective motion.In chapter 1,we briefly introduce the basic concept of collective behavior and show some experimental observations of active matters and living systems.We make a comparison between active systems and traditional equilibrium state systems.We understand the various behavior of these systems from the view of species diversity.In addition,we describe some methods that are introduced in equilibrium state systems to study the non-equifibrium state systems.At the end of this chapter,we introduce the goal to be achieved in our study of active matters and living systems.In chapter 2,we give a brief introduction of some experimental observations about active matters and living systems.There are two kinds of active systems.One is the living systems including bacterial colonies,insects,fish schools,bird flocks and human behavior.In this kind of systems,each individual is a self-propelled particle with some individual information.They interact with others to transfer information,which in turn leads to the collective behavior of the group.Another kind of active system is the non-living system that the self-propelled energy is obtained by environment.The information transfers between particles by contact interaction.Thus,the shape of particle plays an important role in collective motion.In conclusion,the behavior of individual has significant effect on collective motion.Its dynamic mechanism is still not clear that needs to be careful explored.In chapter 3,we introduce some basic models of active matters and living systems.The most famous one is the Vicsek model that was provided in 1995.In this model,each particle had self-propelled character with alignment interaction.For different control parameters such as density and noise intensity,the system exhibited a phase transition from ordered state to disordered one.At the same time,the critical exponents of phase transition could be also calculated in this model.It was a simple and minimal model that helped us to understand the collective motion of self-propelled particles.After that,people proposed some variant models based on original Vicsek model.In original Vicsek model,particles were regarded as a point without any volume.Some models considered the exclude-volume effect and showed the effect of particles' shapes on collective behavior of the system.In addition,attraction and repulsion were also introduced in Vicsek model,leading to a wide range of collective behavior.In chapter 4,we study the effect of local density on the collective motion of self-propelled systems.In experimental observations,the environment has significant im-pact on individual's behavior.Generally,when individual is in a group with more neighbors,it is easy to follow the group's moving direction.Otherwise,its behavior is much like random walker.Motivated by this phenomenon,we introduce the local den-sity dependent noise in Vicsek model.We study the self-propelled system for various strength of density dependent noise and find the existence of high density and high or-dered band structure.This band absorbs almost all the particles in background and only a small number of particles are outside the band.In conclusion,the density dependent effect enhances the alignment order and cohesion of the group.We can design some travelling strategies with density dependent interaction to enhance the group cohesion.In chapter 5,we study the Vicsek-front model by computer simulation.In original Vicsek model,each particle has a view angle of 360°.However in real situation,many animals have a view angle less than 3600°,some of them are even less than 180°.Peo-ple find the neighbors in front of the individual show a great impact on the individual's behavior.Motivated by this phenomenon,we introduce the view angle effect and dis-tinguish the particles in the front or on the back of the given particle.We give a weight on the front and back particles to choose an average moving direction of its neighbors.We find significant difference between original Vicsek model and Vicsek-front model.Firstly,when the particle only sees the neighbors in front of itself,we find a thin band state with very high density.At the same time,for different densities of the system,one band state is stable.Secondly,we find a new phase in the left-down corner of the phase diagram.We define it as banded-liquid state that some dense clusters form band-like structure.This structure is not stable that often splits into clusters,and clusters gradu-ally aggregate into this band-like structure.We also study the Vicsek-angle model that particles have a view angle from 0° to 360°.Its phase diagram is similar to the Vicsek-front model that we also observe the banded-liquid state and thin band state.Based on these two models,we have more information to understand Vicsek model and the collective behavior of living systems.In chapter 6,we study the collective motion of hierarchical system.In most of the cases,there are some leaders in a group.The leaders have more decision-making effect than others,and followers always obey the leaders' decision.In our hierarchical model,there are three levels.The interaction between different levels is also different.Thus,we can control the particle numbers in each level to modify the collective be-havior of the group.When the number of leaders increases and leaders' opinions reach agreement,the group rapidly becomes coherent with high alignment order.While the number of leaders decreases,especially lower than a critical value,many followers can not receive the information from the leaders.Our model can deal with the problem such as what structures of the group(how many leaders and follows)would be best to enhance the group cohesion.There is another problem remains to be solved,for the strict management style and mild management style,which management style is better.In chapter 7,we summarize this thesis and give an outlook for the future works in active matter field.