小世界网络上的扩散限制的聚集-湮没反应动力学

通过Monte-Carlo模拟,研究了基于NW网络的两种类集团不可逆聚集-湮没过程的动力学行为.在系统中,两个同种类集团相遇,将不可逆地聚集成一个更大的集团;不同种类的两个集团相遇,则发生部分湮没反应.模拟结果表明,1)当捷径量化参数p相对较大或较小时,系统经较长时间演化后,集团密度c(t)和粒子密度g(t)呈现幂律形式,c(t)∝t^－α和g(t)∝t^－β,其中幂指数α和β满足α=2β的关系;2)当p为其他值时,集团密度和粒子密度随时间按非严格的幂 关键词： 聚集-湮没过程 小世界网络 反应动力学 Monte-Carlo模拟')" href="#">Monte-Carlo模拟     

手机通话网络度特征分析

手机通信数据详细记录了人们的通信行为, 成为研究人们社会关系、行为模式的重要资源. 通话号码个数、通话次数和时长是手机通信网络的基本属性. 本文在复杂网络理论基础上, 应用统计的方法研究了中国西部某城市三百余万手机用户不同节假日和工作日的 四天通话数据在不同尺度下的号码度、通话度、时长度的分布以及平均号码度、 平均通话度、平均时长度的特征.研究表明, 所有尺度下, 号码度、通话度、时长度均为幂律分布, 幂指数随尺度、日期和指标的不同而不同, 在[1.3, 4] 范围内波动.总体上, 号码度幂指数大于通话度和时长度幂指数, 入度幂指数大于出度幂指数;节假日幂指数大于相应指标的工作日幂指数, 休息时段幂指数大于工作时段幂指数;与工作日相比, 节假日的平均号码度和平均通话度较小, 平均时长度较大.揭示了绝大多数用户每日只接打1个号码的电话, 节假日期间接打电话的用户数、次数、时长减少, 但平均通话时长增大的特征. 关键词： 手机通话网络 复杂网络 度分布 通话模式     

基于超图结构的科研合作网络演化模型

基于科研论文作者的合作方式, 用超图理论构建了一个科研合作超网络演化模型. 利用平均场理论分析了作者发表论文的演化规律, 发现作者的超度 (即发表论文数) 分布符合幂律分布. 进一步理论分析得到分布的幂指数γ与合作领域作者增长速度相关. γ越大, 新作者增长速度越快, 且存在关系: γ=1+L/M (L/M为作者增长率). 并通过对《物理学报》与《中国科学》2003–2012年期间作者发表论文进行了数据分析, 实证结果与理论分析及模拟结果能很好地符合. 本文对科研合作网络的理论和实证研究有一定的借鉴意义. 关键词： 复杂网络 超图 科研合作网络 演化模型     

二维有限能量约束下最优导航问题的理论分析

最近，Li等研究了在Kleinberg导航模型中引入总能量／l=cⅣ约束后的最优导航问题，其中4为网络中所有长程连边的长度之和，C为正常数，Ⅳ为网络节点总数．他们通过在1维和2维导航模型中的模拟结果推测，在有限能量约束下Kleinberg导航模型中按照幂律方式添加长程连边的最优幂指数应该是α=d＋1，其中d为导航模型的维数．本文在平均场理论下，建立了2维有限能量约束下的导航过程的动态微分方程，通过对该方程进行数学分析以及数值求解，从理论上证明了当网络规模足够大且总能量相对较小时，2维有限能量约束下的最优导航幂指数确实为α=3，这一结果证实了Li等之前的推测．     

α-碘酸锂的电流弛豫和偏压场作用下表观介电常数弛豫行为

本工作较为详细地测定了静电场作用下α-碘酸锂的电流弛豫行为:在撤去c轴方向上的静电场后,从我们所用测量电流仪器的响应时间到某一t_k的区间内,放电电流服从(t/t₀)^-α的负幂次方律;而在t>t_k,其规律近似地为:(t/t₀)^{(-α′ln(t/t₀))}。相关的弛豫参数α,α′和t_k在有限的范围内,依赖于温度和施加电压的大小,也因样品不同而有差异。对将近十个样品进行了测试,结果表明,大多数晶体在尽可能小的电压下0.43≤α≤0.7,0.07<α′<0.09;上述的电流弛豫表达式与α-碘酸锂在偏压场作用下观察到的其它物理现象的弛豫行为,与在中子衍射加强和表观介电常数中的表现如出一辙;可以初步肯定各种现象的弛豫行为具有相同的物理根源。 关键词：     

Al2O3单晶三明治结构的高温热激发电流

以Al₂O₃单晶和具有三明治结构的Al₂O₃单晶-Bi₂O₃-Al₂O₃单晶试样为研究对象,测量了在室温到750℃之间升温过程和降温过程中这两种试样的热激发电流,仅在三明治结构试样中检测到了热激发电流.随测量过程中升温速率的增大,降温过程中的热激发电流逐渐减小.认为热激发电流是由缺陷离子的扩散所引起,通过扩散活化能的计算发现有两种缺 关键词： 热激发电流 缺陷 扩散     

富勒烯薄膜上二维金属渗流系统的电击穿现象

富勒烯（Ｃ_６０和Ｃ_7０）薄膜可外延生长在新鲜解理的云母（００１）平面．以这富勒烯层为衬底，将金属薄膜蒸镀在其上，便构成典型的二维渗流系统．蒸镀过程在超高真空系统中完成，并同时对样品的电阻特性进行原位测量．随着外加电压的增加，观测到样品电阻可逆的变化现象与不可逆的电击穿现象．在渗流阈值附近，击穿电流Ｉ_b与样品电阻Ｒ之间表现出幂指数关系：Ｉ_b～Ｒ^－α．指数α比前人实验给出的数值和Ｎｏｄｅｓ-Ｌｉｎｋｓ-Ｂｌｏｂｓ模型的预期值小得多，而且随着衬底材料的不同而不同．基于金属和富勒烯界面相互作用的理论，对这些现象作了解释 关键词：     

具有随机节点结构的复杂网络同步研究

针对具有随机节点结构的复杂网络, 研究其同步问题. 基于Lyapunov稳定性理论和线性矩阵不等式技术给出了复杂网络同步稳定的充分性条件, 该充分性条件不仅与复杂网络的状态时延有关, 还与节点结构的概率分布有关. 数值仿真表明本文方法的有效性. 关键词： 复杂网络 随机节点 同步稳定 时滞     

掺杂蓝青铜的低频电压噪声研究

通过对掺杂蓝青铜的低频宽带噪声(BBN)的研究,发现在掺杂样品中杂质和缺陷能大大的加强低频电压噪声,并且噪声的幅度、波形又强烈地与单晶在冷却过程中的初始电流状态有关,从而揭示出电荷密度波的宽带噪声可能来自于样品中宏观缺陷的微观实质。 关键词：     

一种基于分支过程的信息流行度动力学模型

Web 2.0时代,建模和预测在线信息流行度是信息传播中的重要问题.本文基于社交网络系统信息传播的机制,通过假设和简化,提出了分支过程的概率模型,来描述在线社交网络信息的流行度动力学过程.对典型在线社交网络系统的信息流行度数据和网络结构数据进行了分析,统计结果表明信息流行度衰减遵循幂律分布(幂指数为1.8),微博网络的入度和出度分布也均服从幂律分布(幂指数为1.5).模型仿真结果发现,该模型能够再现真实社交网络数据的若干特征,且信息流行度与网络结构相关.对模型方程进行求解得到理论预测的结果与仿真分析和实际数据结果相符合.     

Confined Crystallization in Polymer Blends: DSC Studies of the Behavior and Kinetics of Isothermal Crystallization of Polypropylene in Poly(cis-butadiene) Rubber Blends

Thermal properties of polypropylene with poly(cis-butadiene) rubber (iPP/PcBR) blends have been measured by differential scanning calorimetry (DSC), and the melting point T_m, crystallization temperature T_c, enthalpy Δ H (melting enthalpies and crystalline enthalpies), and equilibrium melting point T⁰ _m have been measured and calculated. The variation of T_m, T_c, Δ H and T⁰ _m with composition in the blends was discussed, showing that an interaction between phases is present in iPP/PcBR blends. The degree of supercooling characterizing the interaction between two phases in the blends and the crystallizability of the blends which bears a relationship to the composition of the blends was discussed. The kinetics of isothermal crystallization of the crystalline phase in iPP/PcBR blends was studied in terms of the Avrami equation, and the Avrami exponent n and velocity constant K were obtained. The Avrami exponent n is between 3 and 2, meaning that iPP has a thermal nucleation with two dimensional growths. The variation of the Avrami exponent n, velocity constant K, and crystallization rate G bear a relation to the composition of the blends, n increases with increasing content ofPcBR. K also increased with increasing content of PcBR. All of the K for the blends are greater than for pure iPP. The crystallization rate G (t_1/2) depends on the compositions in the blends; all G of the blends are greater than for iPP.     

Traffic dynamics based on an efficient routing strategy on scale free networks

In this paper, we propose a new routing strategy on the basis of the so-called next-nearest-neighbor search strategy by introducing a preferential delivering exponent α. It is found that by tuning the parameter α, the scale-free network capacity measured by the order parameter is considerably enhanced compared to the normal next-nearest-neighbor strategy. Traffic dynamics both near and far away from the critical generating rate R_c are discussed, and it is found that the behavior of 1/f-like noise of the load time series not only depends on the generating rate R but also on the parameter α. We also investigate R_c as functions of C (capacity of nodes), m (connectivity density) and N (network size). Due to the low cost of acquiring next-nearest-neighbor information and the strongly improved network capacity, our strategy may be useful for the protocol designing of modern communication networks.     

Statistical properties of visibility graph of energy dissipation rates in three-dimensional fully developed turbulence

We study the statistical properties of complex networks constructed from time series of energy dissipation rates in three-dimensional fully developed turbulence using the visibility algorithm. The degree distribution is found to have a power-law tail with the tail exponent α=3.0. The exponential relation between the number of the boxes N_B and the box size l_B based on the edge-covering box-counting method illustrates that the network is not self-similar, which is also confirmed by the hub-hub attraction according to the visibility algorithm. In addition, it is found that the skeleton of the visibility network exhibits excellent allometric scaling with the scaling exponent η=1.163±0.005.     

Sparse Hopfield network reconstruction with <Emphasis Type="Italic">ℓ</Emphasis><Subscript>1</Subscript> regularization

We propose an efficient strategy to infer sparse Hopfield network based on magnetizationsand pairwise correlations measured through Glauber samplings. This strategy incorporatesthe ? ₁ regularization into the Bethe approximation by aquadratic approximation to the log-likelihood, and is able to further reduce the inferenceerror of the Bethe approximation without the regularization. The optimal regularizationparameter is observed to be of the order ofM ^?ν where M is the numberof independent samples. The value of the scaling exponent depends on the performancemeasure. ν ? 0.5001 for root mean squared error measure whileν ? 0.2743 for misclassification rate measure. The efficiency of thisstrategy is demonstrated for the sparse Hopfield model, but the method is generallyapplicable to other diluted mean field models. In particular, it is simple inimplementation without heavy computational cost.     

空间网络上的随机游走

本文以一维均匀环为基础, 通过添加有限数量的长程连接构造出了一维有限能量约束下的空间网络, 环上任意节点i与j之间存在一条长程连接的概率满足p_ijα d_ij^-α (α≥ 0),其中d_ij为节点i与j之间的网格距离, 并且所有长程连接长度总和受到总能量∧=cN(c≥ 0)的约束, N为网络节点总数.通过研究该空间网络上的随机游走过程,存在最优幂指数α₀ 使得陷阱问题的平均首达时间最短.进一步研究发现,平均首达时间与网络规模N之间存在着幂律关系, 随着网络规模N和总能量∧的增加,最优幂指数α₀单调增加,并趋近最优值1.5.     

2D-to-3D percolation crossover of metal-insulator composites

Percolation properties and d.c. conductivity were determined for an L²×h-random resistor network model of metal-insulator composite films. The effects of the thickness h on the percolation threshold and conductivity were studied numerically in the limit of an infinite size of the L²-plane parallel to the film. For thicknesses ranging from h/L=0.01 to h/L=0.24, a crossover between a finite-size regime and a saturation regime was observed at h/L≈0.1. In the finite-size regime (h/L?0.01), the percolation threshold scales as pc(h)−pc3∝h−1/x, the exponent x being compatible with that of the critical exponent of the 3D correlation length, ν₃. The conductivity exponent t appeared to depend linearly on the ratio h/L with a slope νD compatible with 2+ν₂, where ν₂ is the 2D correlation length exponent. In the saturation regime, a scaling correction for the percolation threshold was found with an exponent 1+1/ν₃. In this regime we also observed a logarithmic dependence of the conductivity exponent on h/L.     

Corrections to scaling in the q-state Potts model within Gaussian closure approximation

Corrections to scaling in the q-state Potts model due to departures of the initial condition from scaling morphology are studied at zero temperature in phase-ordering kinetics within Gaussian closure approximation. When the corrections to scaling are included, the equal time correlation function has the form G(r,t) = g₀(r/L)+L^-ωg₁(r/L) + ..., where L is the coarsening length scale. Both the correction-to-scaling exponent ω and the correction-to-scaling function g₁(x) are calculated for different values of q. The correction-to-scaling exponent ω is found to be nontrivial and depends on q. The corrections to scaling are found to be large (relative to scaling function g₀(x) itself) at large scaling variable x.     

On the hydrodynamic theory of central peak in displacive structural phase transitions

A model involving nonlinear coupling between the overdamped phonon mode and temperature fluctuations is studied using the dynamic renormalization group method. It is shown that the behavior of the central peak in the dynamic form factor depends on the specific heat exponent α. For α < 0 and as T → T_c the central peak is found to merge with the over-damped phonon mode and the coupling goes to zero at T_c as (T ? T_c)^?α. An argument on the intensity of the central peak in the critical region in presented and it is concluded that the hydrodynamic coupling may not be the dominant mechanism of the central peak in SrTiO₃.     

Beam propagation factor of partially coherent Hermite-Gaussian beams through non-Kolmogorov turbulence

Based on extended Huygens-Fresnel principle, an analytical expression of M² factor for partially coherent Hermite-Gaussian (PCHG) beams through non-Kolmogorov turbulence is obtained. Our results show that M² factor of PCHG beams depends on coherence length, beam order m, wavelength, exponent value α, outer scale L₀ and inner scale l₀. The impact of the exponent's variation on the M² factor is analyzed in detail. When the propagation distance fixed, the M² factor of PCHG beams has a maximum for alpha values lower than 11/3.     

Endogenous and exogenous dynamics in the fluctuations of capital fluxes

A phenomenological investigation of the endogenous and exogenous dynamics in the fluctuations of capital fluxes is carried out on the Chinese stock market using mean-variance analysis, fluctuation analysis, and their generalizations to higher orders. Non-universal dynamics have been found not only in the scaling exponent α, which is different from the universal values 1/2 and 1, but also in the distributions of the ratio η= σ^exo / σ^endo of individual stocks. Both the scaling exponent α of fluctuations and the Hurst exponent H_i increase in logarithmic form with the time scale Δt and the mean traded value per minute 〈f_i 〉, respectively. We find that the scaling exponent α^endo of the endogenous fluctuations is independent of the time scale. Multiscaling and multifractal features are observed in the data as well. However, the inhomogeneous impact model is not verified.