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近年来,人们发现大量真实网络都表现出小世界和无尺度的特性,由此复杂网络演化模型成为学术界研究的热点问题.本文基于Sierpinski分形垫,通过迭代的方式构造了两个确定性增长的复杂网络模型,即小世界网络模型(S-DSWN)和无尺度网络模型(S-DSFN);其次,给出了确定性网络模型的迭代生成算法,解析计算了其主要拓扑特性,结果表明两个网络模型在度分布、集聚系数和网络直径等结构特性方面与许多现实网络相符合;最后,提出了一个确定性的统一模型(S-DUM),将S-DSWN与S-DSFN纳入到一个框架之下,为复杂网络的相关研究提供理论基础.特别地,发现这些网络模型都是极大平面图. 相似文献
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根据经典Koch曲线的构造,利用四面体作为迭代基元构造了一种立体Koch网络并对其结构性质做了研究, 给出了该网络的度分布函数,计算了该网络的团簇系数、平均最短路径长度以及度关联函数.结果表明,所构建的网络是无标度网络,度分布临界指数γ≈332;其团簇系数趋向于常数值0870435;平均路径长度与网络尺寸的对数呈正比关系,说明该网络具有小世界网络特性.另外,计算结果表明knn(k)随k的变化而变化,说明该Koch网络具有一定的度关联性. 相似文献
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相依网络的相依模式(耦合模式)是影响其鲁棒性的重要因素之一.本文针对具有无标度特性的两个子网络提出一种全局同质化相依网络耦合模式.该模式以子网络的总度分布均匀化为原则建立相依网络的相依边,一方面压缩度分布宽度,提高其对随机失效的抗毁性,另一方面避开对度大节点(关键节点)的相依,提高其对蓄意攻击的抗毁性.论文将其与常见的节点一对一的同配、异配及随机相依模式以及一对多随机相依模式作了对比分析,仿真研究其在随机失效和蓄意攻击下的鲁棒性能.研究结果表明,本文所提全局同质化相依网络耦合模式能大大提高无标度子网络所构成的相依网络抗级联失效能力.本文研究成果能够为相依网络的安全设计等提供指导意义. 相似文献
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研究负荷作用下相依网络中的级联故障具有重要的现实意义, 可为提高相依网络的鲁棒性提供参考. 构建了双层相依网络级联故障模型, 主要研究了外部度和内部度对负荷贡献比、耦合因素、层内度-度相关性对相依网络级联故障的影响. 研究表明, 当外部度和内部度对负荷贡献比达到一定值时, 相依网络抵抗级联故障的鲁棒性最强. 而耦合因素的影响是多方面的, 为了达到较高鲁棒性, 建议采用异配耦合方式和尽可能大的平均外部度, 并尽量使外部度保持均匀分布. 另外, 与不考虑负荷作用时相反, 当表征层内度-度相关性的相关系数越大时, 其抵抗级联故障的能力越强. 相似文献
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为了研究人群中的一些基本的社会关系结构,如家庭、室友、同事等,对传染病传播过程的影响机制,本文建立了一个具有局部结构的增长无标度网络模型.研究表明,局部结构的引入使得该网络模型能够同时再现社会网络的两个重要特征:节点度分布的不均匀性以及节点度之间的相关性.首先,该网络的节点度和局部结构度均服从幂律分布,且度分布指数依赖于局部结构的大小.此外,局部结构的存在还导致网络节点度之间具有正相关特性,而这种正相关正是社会网络所特有的一个重要特性.接着,通过理论分析和数值模拟,我们进一步研究了该网络结构对易感者-感染
关键词:
复杂网络
无标度网络
局部结构
传染病建模 相似文献
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在具有网络结构的系统中度关联属性对于动力学行为具有重要的影响, 所以产生适当度关联网络的方法对于大量网络系统的研究具有重要的作用. 尽管产生正匹配网络的方法已经得到很好的验证, 但是产生反匹配网络的方法还没有被系统的讨论过. 重新连接网络中的边是产生度关联网络的一个常用方法. 这里我们研究使用重连方法产生反匹配无标度网络的有效性. 我们的研究表明, 有倾向的重连可以增强网络的反匹配属性. 但是有倾向重连不能使皮尔森度相关系数下降到-1, 而是存在一个依赖于网络参数的最小值. 我们研究了网络的主要参数对于网络度相关系数的影响, 包括网络尺寸, 网络的连接密度和网络节点的度差异程度. 研究表明在网络尺寸大的情况下和节点度差异性强的情况下, 重连的效果较差. 我们研究了真实Internet网络, 发现模型产生的网络经过重连不能达到真实网络的度关联系数. 相似文献
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选取2003—2012年期间半年度中国基金公司持上市公司股票份额面板数据为样本数据,以基金公司为节点,以同一时刻共持同一家上市公司股票关系为边,以同一时刻共持的上市公司数量为权重,构建中国基金公司共持关系结构等价加权网络(简称共持网络).结合统计物理学等方法,分析了共持网络的拓扑结构稳定性及具有不同拓扑特征值的节点随时间演变过程中与共持网络中三类节点集合持股行为波动相关性.三类节点集合分别为t-1时刻基于某一股票形成的共持关系完全连通子图节点集合(第一类节点集合)、t-1时刻共持网络中非完全连通子图的节点集合(第二类节点集合)、t时刻新进入共持网络的节点集合(第三类节点集合).分析结果显示:1)节点与第二类节点集合持股行为波动呈正相关,且相关系数随着节点集聚系数的增强而增大;2)只有当节点的度和点强度值较高时,节点与第一类和第二类节点集合的持股行为呈正相关;3)不同拓扑特征条件下的节点与第三类节点集合的持股行为均不存在波动相关性.本文提供了一个研究持股行为相关性的新思路,并为进一步研究股票市场结构等价网络及节点重要性差异提供了基础. 相似文献
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A cylindrically symmetric inhomogeneous cosmological model with electromagnetic field for perfect fluid distributions is obtained. To get a determinate solution, a supplementary conditionA=(BC)
n
between metric potentials is used whereA, B, andC are functions of bothx andt andn is a constant. Some physical and geometrical properties of the model and behavior of electromagnetic field tensors are also discussed. 相似文献
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Auto-correlation functions of the fluctuations in the electron velocities transverse and parallel to the applied electric field are calculated by the Monte Carlo method for GaAs and InP at three different values of field strength which are around three times the threshold field for negative differential mobility in each case. From these the frequency-dependent diffusion coefficients transverse and parallel to the applied field and the figure of merit for noise performance when used in a microwave amplifying device are determined. The results indicate that the transverse auto-correlation functionC
t
(s) falls nearly exponentially to zero with increasing intervals while the parallel functionC
p
(s) falls sharply, attains a minimum and then rises towards zero. In each case a higher field gives a higher rate of fall and makes the correlation functions zero within a shorter interval. The transverses diffusion coefficient falls monotonically with the frequency but the parallel diffusion coefficient generally starts with a low value at low frequencies, rises to a maximum and then falls. InP, with a larger separation between the central and the satellite valleys, has a higher value of the low frequency transverse diffusion coefficient and a lower value of its parallel counterpart. The noise performance of microwave semiconductor amplifying devices depends mainly on the low frequency parallel diffusion constant and consequently devices made out of materials like InP with a large separation between valleys are likely to have better noise characteristics. 相似文献
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The flourishing complex network theory has aroused increasing interest in studying the properties of real-world networks. Based on the traffic network of Chang--Zhu--Tan urban agglomeration in central China, some basic network topological characteristics were computed with data collected from local traffic maps, which showed that the traffic networks were small-world networks with strong resilience against failure; more importantly, the investigations of assortativity coefficient and average nearest-neighbour degree implied the disassortativity of the traffic networks. Since traffic network hierarchy as an important basic property has been neither studied intensively nor proved quantitatively, the authors are inspired to analyse traffic network hierarchy with disassortativity and to finely characterize hierarchy in the traffic networks by using the n-degree--n-clustering coefficient relationship. Through numerical results and analyses an exciting conclusion is drawn that the traffic networks exhibit a significant hierarchy, that is, the traffic networks are proved to be hierarchically organized. The result provides important information and theoretical groundwork for optimal transport planning. 相似文献
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Polyacrylamide (PAAm) hydrogels immersed in water and aqueous NaCl solutions were investigated for their structure and dynamics
using static and quasi-elastic laser light scattering (QELS) techniques. Ensemble-averaged electric field correlation function
f(q, t) obtained from the non-ergodic analysis of intensity-autocorrelation function for PAAm gel immersed in water and in 5 M NaCl
showed an exponential decay to a plateau with an initial decay followed by saturation at long times. The value of the plateau
was found to depend on NaCl concentration and was higher than that of water. Collective diffusion coefficient, D, of the polymer network of the hydrogel immersed in water and in different concentrations of NaCl was determined by analysing
f(q, t). The measured diffusion coefficient showed linear decrease with increase in concentration of NaCl. The characteristic network
parameters were obtained by analyzing f(q, t) with harmonically bound Brownian particle model and from static light scattering studies. 相似文献
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Bianchi Type-I magnetized bulk viscous fluid string dust cosmological model is investigated. To get a determinate model, we
have assumed the conditions σ ∝θ andζθ = constant where σ is the shear,θ the expansion in the model andζ the coefficient of bulk viscosity. The behaviour of the model in the presence and absence of magnetic field together with
physical and geometrical aspects of the model are also discussed. 相似文献
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B. O'Shaughnessy D. Vavylonis 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,6(3):363-372
We study the reaction kinetics of end-functionalized polymer chains dispersed in an unreactive polymer melt. Starting from
an infinite hierarchy of coupled equations for many-chain correlation functions, a closed equation is derived for the 2nd
order rate constant k after postulating simple physical bounds. Our results generalize previous 2-chain treatments (valid in dilute reactants limit)
by Doi [#!doi:inter2!#], de Gennes [#!gennes:polreactionsiandii!#], and Friedman and O'Shaughnessy [#!ben:interdil_all_aip!#],
to arbitrary initial reactive group density n0 and local chemical reactivity Q. Simple mean field (MF) kinetics apply at short times, .For high Q, a transition occurs to diffusion-controlled (DC) kinetics with (where xt is rms monomer displacement in time t) leading to a density decay . If n0 exceeds the chain overlap threshold, this behavior is followed by a regime where during which k has the same power law dependence in time, , but possibly different numerical coefficient. For unentangled melts this gives while for entangled cases one or more of the successive regimes ,t
-3/8
and t
-3/4
may be realized depending on the magnitudes of Q and n0. Kinetics at times longer than the longest polymer relaxation time are always MF. If a DC regime has developed before then the long time rate constant is where R is the coil radius. We propose measuring the above kinetics in a model experiment where radical end groups are generated
by photolysis.
Received: 2 June 1998 / Revised: 9 July 1998 / Accepted: 10 July 1998 相似文献
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We have investigated the algebraic structure of the Fokker-Planck equation with a variable diffusion coefficient and a time-dependent
mean-reverting force. Such a model could be useful to study the general problem of a Brownian walker with a space-dependent
diffusion coefficient. We also show that this model is related to the Fokker-Planck equation with a constant diffusion coefficient
and a time-dependent anharmonic potential of the form V(x, t) = ?a(t)x
2 + b ln x, which has been widely applied to model different physical and biological phenomena, e.g. the study of neuron models and stochastic resonance in monostable nonlinear oscillators. Using the Lie algebraic approach
we have derived the exact diffusion propagators for the Fokker-Planck equations associated with different boundary conditions,
namely (i) the case of a single absorbing barrier, and (ii) the case of two absorbing barriers. These exact diffusion propagators
enable us to study the time evolution of the corresponding stochastic systems.
Received 23 October 2001 and Received in final form 24 December 2001 相似文献
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Abstract: The relation between Raman scattering, resonance Raman scattering, and absorption is reviewed to determine to what extent quantitative analysis can be applied in resonance Raman spectroscopy. In addition, it is demonstrated experimentally that normal Raman spectra can be dramatically inhibited by absorption and resonance Raman effects. Raman spectra of toluene and heptane mixtures—with progressively increasing concentrations of heptane—were measured using 229-nm laser excitation. The results show that the characteristic band intensities are not directly proportional to the relative concentrations of the compounds and deviate due to absorption resonance effects. An approximated mathematical model is developed to demonstrate that the intensities of the normal Raman scattering bands are suppressed. An inhibition coefficient Ki is introduced to describe the situation and determine the penetration depth. Most remarkably, it is shown that the intensity of the resonance Raman scattering bands can be constant even when the concentration ratios differ substantially in the sampled mixtures. 相似文献