模糊聚类正交方法若干结果

本文提出一个新的模糊聚类方法:正交法,这种方法基于如下正交聚类原则:记截矩阵R_λ=(α₁,α₂,…,α_n),其中列向量α_j=(α_1j,α_2j,…,α_nj)^T,所谓向量α_i,α_j正交,指内积(α_i,α_j)=0。     

电网在三种边攻击方式下的级联失效

研究美国西部电网在三种边攻击方式下级联失效差异性.定义边ij的初始负载为(k_ik_j)^θ,k_i,k_j分别表示节点i和j的度,θ为一可调参数.三种边攻击方式分别为:最小负载边攻击方式(LL)、最大负载边攻击方式(HL)和容量比最小边攻击方式(SPC).通过分析电网的拓扑结构,研究三种攻击方式级联失效差异性.研究表明:HL和LL攻击方式下,受攻击边的范围不随θ而改变,HL的攻击效果随θ的增大而增强,LL的攻击效果随θ的增大而减弱.而SPC法选中的被攻击边随θ变化,当θ取值较小时,SPC攻击边是拓扑结构较特殊的一种最小负载边,随着θ的增大,SPC攻击边趋向于高负载边,因此θ较小时,SPC的攻击效果和LL接近,当θ较大时,SPC的攻击效果和HL接近.     

EV共聚物序列中的两种结构因素

系统描述了EV共聚物序列中两种结构因素对共聚物主链中亚甲基和次甲基¹³C NMR化学位移的贡献,将SCS方法与半经验方法结合起来,阐明了常数项δ_LE和δ₀的物理意义,提出了以聚乙烯链反式构象化学位移δ_t为基准计算上述亚甲基和次甲基化学位移的公式:δ_c=δ_t+Σn_iS_i+ΣP_jγ_j并在此基础上,讨论了聚乙烯,聚丙烯的特殊情况和乙丙共聚物的链结构.     

弹体尾部轴对称干扰流场数值模拟

绕弹体的超声速气流与发动机喷流相互作用,在尾部形成复杂的干扰流场。本文用有限差分法求解全N-S方程,对这一复杂流场进行了数值模拟,得到了实验观察到的各种流场结构及其随喷口压力比的变化规律。外流M_∞=1.94,R_e∞=2.2×10⁵,喷流M_j=3.0,喷口压力比p_j/p_∞分别为1.03,0.527,0.15三种。差分算法为一种改进的Beam-Warming格式。计算底部压力和激波在喷流中心的反射位置与实验数据进行了比较,吻合较好。     

周期磁场调制下的二维电子结构

基于有限差分方法,研究周期梯度磁场调制下二维电子气的电子性质.结果表明:由于周期梯度磁场的存在,体系展现出丰富的电子能带结构.其子带的宽度随|k_y|增大而不断变窄,|k_y|越大势阱越深;由于在k_y > 0和k_y < 0两个区域的有效势能不一样,其能带结构在两个区域不一致且在k_y > 0的区域中形成更多束缚态.通过改变磁条周期、磁条到2DEG的距离及磁化强度研究其对电子能带结构的影响.     

InGaAs/GaAs量子点阵列中的能级计算

根据八带k·p理论，在三维InGaAs/GaAs量子点阵列中求解k_x=k_y=k_z=0处的有效质量哈密顿H₀的本征值，得到InGaAs量子点中导带中电子基态E_C1，第一激发态E_C2和重空穴态E_{HH1关键词： InGaAs 量子点 带内跃迁 k·p理论')" href="#">八带k·p理论}     

高阶Adams公式的系数

当k的值不大时(例如k≤4),诸系数γiγi^*,β_kρ,β_kρ^*易于手工计算。但对大的k值(例如k≥5),手工计算已非易事。利用著名的计算机代数软件:REDUCE^[a],我们可以很容易地计算出诸系数γi,γi^*,β_kρ,β_kρ^*。     

相位角对容性耦合电非对称放电特性的影响

电非对称效应作为一种新兴技术,被广泛用于对离子能量和离子通量的独立调控.此外,在改善等离子体的径向均匀性方面,电非对称效应也发挥了重要作用.本文采用二维流体力学模型,并耦合麦克斯韦方程组,系统地研究了容性耦合氢等离子体中当放电由多谐波叠加驱动时,不同谐波阶数k下的电非对称效应,重点观察了相位角θ_n对自偏压以及等离子体径向均匀性的影响.模拟结果表明：在同一谐波阶数下,自偏压随相位角θ_n的变化趋势不尽相同,且当k增大（k>3）时,自偏压随最高频相位角θ_k的变化范围逐渐减小.此外,通过调节相位角θ_n,可以改变轴向功率密度和径向功率密度的相对关系,进而实现对等离子体径向均匀性的调节.研究结果对于利用电非对称效应优化等离子体工艺过程具有一定的指导意义.     

一维长程关联无序系统的局域性

研究了在紧束缚近似下,由de Moura和Lyra提出的一维长程关联无序模型的局域性. 分布在［-W/2,W/2］区间的格点位能,其关联函数〈ε_iεj〉的傅里叶变换满足S(k)∝k^-α,其中关联强度α>0. 利用participation ratio不仅证实了在α>2和W<4 关键词： 安德森局域化 长程关联 扩展态     

一类演化方程的高稳定性的差分格式

考虑一类演化方程u_t=au∂_2k+1(其中a是常数,u∂_2k+1=∂^2k+1u/∂x^2k+1,k=1,2……)的有限差分解法。构造了两类具有高稳定性的显式差分格式。并用引入耗散项的方法建立了两类半显式差分格式,它们是无条件稳定的且可显式地进行计算。     

A model for cascading failures in scale-free networks with a breakdown probability

Considering that not all overload nodes will be removed from networks due to some effective measures to protect them, we propose a new cascading model with a breakdown probability. Adopting the initial load of a node j to be L_j=[k_j(∑_m∈Γjk_m)]^α with k_j and Γ_j being the degree of the node j and the set of its neighboring nodes, respectively, where α is a tunable parameter, we investigate the relationship between some parameters and universal robustness characteristics against cascading failures on scale-free networks. According to a new measure originated from a phase transition from the normal state to collapse, the numerical simulations show that Barabási-Albert (BA) networks reach the strongest robustness level against cascading failures when the tunable parameter α=0.5, while not relating to the breakdown probability. We furthermore explore the effect of the average degree 〈k〉 for network robustness, thus obtaining a positive correlation between 〈k〉 and network robustness. We then analyze the effect of the breakdown probability on the network robustness and confirm by theoretical predictions this universal robustness characteristic observed in simulations. Our work may have practical implications for controlling various cascading-failure-induced disasters in the real world.     

Edge-based-attack induced cascading failures on scale-free networks

Most previous existing works on cascading failures only focused on attacks on nodes rather than on edges. In this paper, we discuss the response of scale-free networks subject to two different attacks on edges during cascading propagation, i.e., edge removal by either the descending or ascending order of the loads. Adopting a cascading model with a breakdown probability p of an overload edge and the initial load (k_ik_j)^α of an edge ij, where k_i and k_j are the degrees of the nodes connected by the edge ij and α is a tunable parameter, we investigate the effects of two attacks for the robustness of Barabási-Albert (BA) scale-free networks against cascading failures. In the case of α<1, our investigation by the numerical simulations leads to a counterintuitive finding that BA scale-free networks are more sensitive to attacks on the edges with the lowest loads than the ones with the highest loads, not relating to the breakdown probability. In addition, the same effect of two attacks in the case of α=1 may be useful in furthering studies on the control and defense of cascading failures in many real-life networks. We then confirm by the theoretical analysis these results observed in simulations.     

Attack vulnerability of scale-free networks due to cascading failures

In this paper, adopting the initial load of a node i to be with k_i being the degree of the node i, we propose a cascading model based on a load local redistribution rule and examine cascading failures on the typical network, i.e., the BA network with the scale-free property. We find that the BA scale-free network reaches the strongest robustness level in the case of α=1 and the robustness of the network has a positive correlation with the average degree 〈k〉, where the robustness is quantified by a transition from normal state to collapse. In addition, we further discuss the effects of two different attacks for the robustness against cascading failures on our cascading model and find an interesting result, i.e., the effects of two different attacks, strongly depending to the value α. These results may be very helpful for real-life networks to avoid cascading-failure-induced disasters.     

基于可调负载重分配的无标度网络连锁效应分析

为了深入研究复杂网络抵制连锁故障的全局鲁棒性,针对现实网络上的负载重分配规则常常是介于全局分配与最近邻分配、均匀分配与非均匀分配的特点,围绕负荷这一影响连锁故障发生和传播最重要的物理量以及节点崩溃后的动力学过程,提出了一种可调负载重分配范围与负载重分配异质性的复杂网络连锁故障模型,并分析了该模型在无标度网络上的连锁故障条件.数值模拟获得了复杂网络抵制连锁故障的鲁棒性与模型中参数的关系.此外,基于网络负载分配规则的分析以及理论解析的推导,验证了数值模拟结论,也证明在最近邻与全局分配两种规则下都存在负载分配均匀性参数等于初始负荷强度参数即β=τ使得网络抵御连锁故障的能力最强.     

Cascading Failures of Complex Networks Based on Two-Step Degree

We propose a new concept, two-step degree. Defining it as the capacity of a node of complex networks, we establish a novel capacity-load model of cascading failures of complex networks where the capacity of nodes decreases during the process of cascading failures. For scale-free networks, we find that the average two-step degree increases with the increase of the heterogeneity of the degree distribution, showing that the average two- step degree can be used for measuring the heterogeneity of the degree distribution of complex networks. In addition, under the condition that the average degree of a node is given, we can design a scale-free network with the optimal robustness to random failures by maximizing the average two-step degree.     

Mitigation strategies on scale-free networks against cascading failures

According to the dynamic characteristics of the cascading propagation, we introduce a mitigation mechanism and propose four mitigation methods on four types of nodes. By the normalized average avalanche size and a new measure, we demonstrate the efficiencies of the mitigation strategies on enhancing the robustness of scale-free networks against cascading failures and give the order of the effectiveness of the mitigation strategies. Surprisingly, we find that only adopting once mitigation mechanism on a small part of the overload nodes can dramatically improve the robustness of scale-free networks. In addition, we also show by numerical simulations that the optimal mitigation method strongly depends on the total capacities of all nodes in a network and the distribution of the load in the cascading model. Therefore, according to the protection strength for scale-free networks, by the distribution of the load and the protection price of networks, we can reasonably select how many nodes and which mitigation method to efficiently protect scale-free networks at the lower price. These findings may be very useful for avoiding various cascading-failure-induced disasters in the real world and for leading to insights into the mitigation of cascading failures.     

A limited resource model of fault-tolerant capability against cascading failure of complex network

We propose a novel capacity model for complex networks against cascading failure. In this model, vertices with both higher loads and larger degrees should be paid more extra capacities, i.e. the allocation of extra capacity on vertex i will be proportional to k_i ^γ , where k_i is the degree of vertex i and γ > 0 is a free parameter. We have applied this model on Barabási-Albert network as well as two real transportation networks, and found that under the same amount of available resource, this model can achieve better network robustness than previous models.     

Impact of core-periphery structure on cascading failures in interdependent scale-free networks

Core-periphery structure is a typical meso-scale structure in networks. Previous studies on core-periphery structure mainly focus on the improvement of detection methods, while the research on the impact of core-periphery structure on cascading failures in interdependent networks is still missing. Therefore, we investigate the cascading failures of interdependent scale-free networks with different core-periphery structures and coupling preferences in the paper. First, we introduce an evaluation index to calculate the goodness of core-periphery structure. Second, we propose a new scale-free network evolution model, which can generate tunable core-periphery structures, and its degree distribution is analyzed mathematically. Finally, based on a degree-load-based cascading failure model, we mainly investigate the impact of goodness of core-periphery structure on cascading failures in both symmetrical and asymmetrical interdependent networks. Through numerical simulations, we find that with the same average degree, the networks with weak core-periphery structure will be more robust, while the initial load on node will influence the improvement of robustness. In addition, we also find that the inter-similarity coupling performs better than random coupling. These findings may be helpful for building resilient interdependent networks.     

Dynamical robustness of networks based on betweenness against multi-node attack

We explore the robustness of a network against failures of vertices or edges where a fraction f of vertices is removed and an overload model based on betweenness is constructed. It is assumed that the load and capacity of vertex i are correlated with its betweenness centrality B_i as B_i~θ and(1 + α)Bθi(θ is the strength parameter, α is the tolerance parameter).We model the cascading failures following a local load preferential sharing rule. It is found that there exists a minimal αc when θ is between 0 and 1, and its theoretical analysis is given. The minimal αc characterizes the strongest robustness of a network against cascading failures triggered by removing a random fraction f of vertices. It is realized that the minimalαc increases with the increase of the removal fraction f or the decrease of average degree. In addition, we compare the robustness of networks whose overload models are characterized by degree and betweenness, and find that the networks based on betweenness have stronger robustness against the random removal of a fraction f of vertices.     

基于相继故障信息的网络节点重要度演化机理分析

分析了过载机制下节点重要度的演化机理.首先,在可调负载重分配级联失效模型基础上,根据节点失效后其分配范围内节点的负载振荡程度,提出了考虑级联失效局域信息的复杂网络节点重要度指标.该指标具有两个特点:一是值的大小可以清晰地指出节点的失效后果;二是可以依据网络负载分配范围、负载分配均匀性、节点容量系数及网络结构特征分析节点重要度的演化情况.然后,给出该指标的仿真算法,并推导了最近邻择优分配和全局择优分配规则下随机网络和无标度网络节点重要度的解析表达式.最后,实验验证了该指标的有效性和可行性,并深入分析了网络中节点重要度的演化机理,即非关键节点如何演化成影响网络级联失效行为的关键节点.