【作者】 李玉剑；

【导师】 汪秉宏； 席震东；

【作者基本信息】 中国科学技术大学 ， 理论物理， 2011， 博士

【摘要】 与人类活动息息相关的生态环境、社会组织、经济体系、信息传播、工程技术等,甚至作为生命体的人类本身,都属于复杂系统范畴。在人类文明史上,诸类现象的研究形成了多种知识体系和方法论。近年海量数据的积累,正孕育着对经典理论的全面挑战。当知识从直觉转换为数据时,人类对环境的认知是否会产生质的飞跃?观念的飞跃和数学化是否导致深层次普遍性规律的发现?类似物理理论的建立又能否从根本上提升人类掌控自然的能力?这都是复杂系统研究所面临的挑战。复杂系统研究的核心问题：构成系统的大量的子系统是如何通过相互作用而自组织成为一个具有涌现行为结构的新的开放的非平衡系统?复杂系统研究的科学目标是产生新的技术(包括新的软件),对于复杂系统科学中基本问题的更深层次的理解。统计力学作为研究多体系统微观与宏观之间相互联系的数学理论,在系统地整理各类测量数据、建立相应的动力学模型进而分析其特性、寻找系统运动的规律等方面可发挥主导作用。近年来复杂网络的研究显示,不同范畴的系统在组织结构上可有惊人的相似,暗示复杂系统深层次的共性。统计力学研究是揭示普适性规律的重要途径.本文利用统计力学的多种手段对复杂系统中若干集体行为和临界现象的动力学进行研究,并发现了一些有趣的结果。文中通过引进截断参数K和排队等待时间提出了两种建立在最近邻信息的局域路由策略,发现通过调节优先传递指数α和K,被序参量刻画的无标度网络处理能力显著提高,文中讨论了接近和远离临界产生率Rc的交通动力学,发现负载流的时间序列不仅依靠产生率R还与参数K和α有关,最后研究了临界产生率和连接密度m的函数关系。考虑到获得最近邻信息及显著改善网络处理能力的低花费,文中提出的策略将对现代通讯网络的协议设计很有意义。在原始的BML模型上我们改变网络的拓扑结构,试图探讨道路网络中反映网络拓扑结构的参量——平均的边和节点数目比值λ=E/N的变化对于交通拥堵出现的影响。考察了这上面车辆交通的动力学过程,发现道路结构对于交通拥堵的出现有着显著的关系,采取恰当的拓扑结构可以增加道路网络的吞吐量,为改善拥堵提出可能的理论依据。另外,讨论了复杂网络上的博弈。我们提出了基于收益的策略学习机制的囚徒博弈模型并研究了该模型在不同网络结构上(规则网络、小世界网络和无标度网络)的动力学性质,发现了在规则网络上的合作者倾向于分散,我们详细的讨论了无标度网络上的博弈行为,发现无标度网络上比起小度节点,度大的(?)节点不倾向于合作易于获得最大的收益,而度小的节点更频繁的变化自己的博弈策略。对于舆论动力学我们提出了一个引入移动机制的模型,并对其更新策略的机制进行了研究,找到了一个最佳的更新策略,并研究了系统由混合意见达到意见一致的相变过程的动力学问题。在三维Vicsek模型中引入粒子的视野角的概念,试图寻找系统是否存在着一个最佳的视野角使系统最快的达到同步,我们发现了这个最佳视野角,并研究了在热力学极限下,最佳视野角与系统粒子密度和初始速度之间的关系,给出了定量的分析。并利用序参量对系统从集体无序到集体有序这一集体行为进行刻画,对相关的临界现象进行了分析。最后,我们对Eden模型也作了进一步推广,提出来具有屏蔽效应的广义Eden模型,给出了相关的解析,这个结果可能对限制集聚扩散的生长机制给出解释。更多还原

【Abstract】 Complex system is a very broad domain, including social organizations, economic systems, information diffusion, industrial technology, human beings, etc, on which various knowledge systems and methodologies have been established. However, classical theories are facing a great challenge due to the emergence of huge amount of data. We are confronting many unknown questions when knowledge is transferred from intuition to data:whether our cognition of the environment can achieve a qualitative leap? Whether this leap and can lead to discovery of deep universal law? Whether the foundation of new theory improves our ability to control the nature?The core issues of complex system:how the emergence appears in a new non-equilibrium open-structure system self-organized by the large number of subsystems? The objectives of complex system science:to generate new technologies (including new software) and the deeper understanding about the basic problems of complex system.Statistical mechanics is a theory bridge micro and macro many-body system. It can play a important role in organizing all kinds of measurement data systematically, establishing appropriate kinetic model to obtain its properties and finding the law of movement and other aspects of the system. The studies of complex networks have shown that the organizational structure in different areas can have surprisingly similarity in recent years, which suggests the common underlying in complex system. Statistical mechanics is an important way to reveal the universal law. In this paper, we study a number of critical phenomena and collective behaviors in complex systems by various means of statistical mechanics and find some interesting results.We propose a effective routing strategy on the basis of the so-called nearest neighbor search strategy by introducing a preferential delivering exponent a and a waiting time exponentβ. We assume that the handling capacity of one vertex is proportional to its degree when the degree is smaller than a cut-off value K, and is infinite otherwise. Traffic dynamics both near and far away from the critical generating rate Rc are discussed. Simulation results demonstrate that the optimal a,βand K. Our strategy may be useful and reasonable for the protocol designing of modern communication networks.We study the traffic dynamics in two-dimensional Biham-Middleton-Levine(BML) traffic flow model based on the irregular lattice. It is found that a phase separation phenomenon, in which the system separates into coexistence of free flow and jam, could be observed in intermediate vehicle density range.We investigate the prisoner’s dilemma game based on a new rule:players will change their current strategies to opposite strategies with some probability if their neighbors’average payoffs are higher than theirs. Compared with the cases on regular lattices (RL) and Newman-Watts small world network (NW), cooperation can be best enhanced on the scale-free Barabasi-Albert network (BA). It is found that cooperators are dispersive on RL network, which is different from previously reported results that cooperators will form large clusters to resist the invasion of defectors. Cooperative behaviors on the BA network are discussed in detail.We generalize a majority-rule model on the opinion dynamics, where all mobile agents update their status based on Vicsek model. We find the existence of an optimal preferential rule for which the convergence to global consensus can be achieved much more rapidly than under other rules. Qualitative insights are obtained by examining the spatiotemporal evolution of the opinion clusters.The three-dimensional Vicsek model is introduced to investigate the collective motion of self-propelled particles. In this model each particle has a limited view angle. We find that there exists an optimal value of view angle, leading to the quickest direction consensus. Our work shows that the optimal view angle is just a function of the absolute velocity and the particles density in the limit of large boundary size. We present a series of special results demonstrating more fundamental and practical rules in the daily-life pragmatic collective phenomena, which is of significance to the low-cost communication.We generalize the Eden model to take into account of the screening effect, i.e., the end point grows much faster than the interior points do. Highly anisotropic clusters are obtained in our generalized Eden model. It is found that the length in the long direction scales differently than that in the short direction does as the number of site increases.更多还原