A Modified Vicsek Model For Moving Swarms With Exponential Neighbor Weight And Restricted Visual Field

In the first chapter of this thesis, we review the basic concepts of statistical physics, complexnetwork and mobile ad hoc network (MANET) briefly. And the phenomena of swarming motionwith correlated studies are introduced.In the second chapter, we build a new modified Vicsek model for self-propelled agents withexponential neighbor weight (ENW) and restricted visual field (RVF) to study the ubiquitouscollective motion in nature. Vicsek model and its new versions are useful for simulating andexplaining swarming motion of biological individuals with neither leader nor common global message.However, in these models, researchers always supposed that each individual has global visual field(VF), and it is affected by all its neighbors with un-weighted influence, which may not always fit tothe reality. In the present work, we take both RVF and ENW(power exponent) simultaneously intoaccount, investigate the combinatory effect of them. Based on this mechanism, through extensivenumerical simulations, we see that to increase visual field is not always advantageous to systemicenhancement of the direction consensus Va and individual clustering S. Moreover, stationarydirection consensus Va exhibits maximum or decreases with VF, and a minimum convergence timeT appears in RVF, which demonstrates that global VF is not necessary prerequisite to coordinatedmotion, while ENW is a reasonable factor in modeling it. In addition, we simulated various recipes foroptimizing Va and T in unfavorable cases, and found a phase boundary separating inverse-dependent variations of T. Our result can not only be used for the design of MANET, but alsofor the improvement the efficiency of direction consensus of large flocks of artificial individualsbesides the understanding of biological swarming motion in nature.In the third chapter, we study the connectivity of MANET and the relations between the statisticalcharacteristics of critical global connected network whose nodes move continuously on thetwo-dimensional (2D) plane. Comparing with the case in which nodes move on the2D triangle lattice,we find that both of them have the same property of network connectivity and degree distribution. Onthe other hand, different from that case, we find that the clustering coefficient for the nodes withsmaller degree becomes larger, and it decreases gradually until the degree arrives at the average value,then it keeps constant until cutoff degree. Besides, the linear behavior of positive assortativity withaveraged nearest-neighbor degree is only valid in the range of the degree being larger than3andsmaller than the cutoff degree.