各向异性超导体电阻转变的修正Kosterlitz-Thouless相变模型

从二维系统的Kosterlitz-Thouless (KT) 相变理论出发，在关联长度中引入热激活能和平均钉扎高度，提出了修正的KT相变模型.该模型与库伦气体标度理论和Halperin-Nelson关系具有一致性.应用修正的KT相变模型研究磁场下Tl₂Ba₂CaCu₂O_x(Tl-2212)薄膜电阻转变的标度行为，发现由电阻转变计算得到的平均钉扎高度与温度具有线性依赖关系，实验结果支持修正的KT相变模型. 关键词： 标度行为 各向异性超导体 电阻转变     

Exact solutions for network rewiring models

Evolving networks with a constant number of edges may be modelled using a rewiring process. These models are used to describe many real-world processes including the evolution of cultural artifacts such as family names, the evolution of gene variations, and the popularity of strategies in simple econophysics models such as the minority game. The model is closely related to Urn models used for glasses, quantum gravity and wealth distributions. The full mean field equation for the degree distribution is found and its exact solution and generating solution are given.     

Recursive weighted treelike networks

We propose a geometric growth model for weighted scale-free networks, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks, which are partially determined by the parameters. Analytical results indicate that the resulting networks have power-law distributions of degree, strength, weight and betweenness, a scale-free behavior for degree correlations, logarithmic small average path length and diameter with network size. The obtained properties are in agreement with empirical data observed in many real-life networks, which shows that the presented model may provide valuable insight into the real systems.     

Scaling,Renormalization and Statistical Conservation Laws in the Kraichnan Model of Turbulent Advection

We present a systematic way to compute the scaling exponents of the structure functions of the Kraichnan model of turbulent advection in a series of powers of ξ, adimensional coupling constant measuring the degree of roughness of the advecting velocity field. We also investigate the relation between standard and renormalization group improved perturbation theory. The aim is to shed light on the relation between renormalization group methods and the statistical conservation laws of the Kraichnan model, also known as zero modes.     

Inevitable self-similar topology of binary trees and their diverse hierarchical density

Self-similar topology, which can be characterized as power law size distribution, has been found in diverse tree networks ranging from river networks to taxonomic trees. In this study, we find that the statistical self-similar topology is an inevitable consequence of any full binary tree organization. We show this by coding a binary tree as a unique bifurcation string. This coding scheme allows us to investigate trees over the realm from deterministic to entirely random trees. To obtain partial random trees, partial random perturbation is added to the deterministic trees by an operator similar to that used in genetic algorithms. Our analysis shows that the hierarchical density of binary trees is more diverse than has been described in earlier studies. We find that the connectivity structure of river networks is far from strict self-similar trees. On the other hand, organization of some social networks is close to deterministic supercritical trees.     

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.     

Height and roughness distributions in thin films with Kardar-Parisi-Zhang scaling

We study height and roughness distributions of films grown with discrete Kardar-Parisi-Zhang (KPZ) models in a small time regime which is expected to parallel the typical experimental conditions. Those distributions are measured with square windows of sizes 8 ? r ? 128 gliding through a much larger surface. Results for models with weak finite-size corrections indicate that the absolute value of the skewness and the value of the kurtosis of height distributions converge to 0.2 ? ∣S∣ ? 0.3 and 0 ? Q ? 0.5, respectively. Despite the low accuracy of these results, they give additional support to a recent claim of KPZ scaling in oligomer films. However, there are significant finite-size effects in the scaled height distributions of models with large local slopes, such as ballistic deposition, which suggests that comparison of height distributions must not be used to rule out KPZ scaling. On the other hand, roughness distributions of the same models show good data collapse, with negligible dependence on time and window size. The estimates of skewness and kurtosis for roughness distributions are 1.7 ? S ? 2 and 3 ? Q ? 7. A stretched exponential tail was found, which seems to be a particular feature of KPZ systems in 2 + 1 dimensions. Moreover, the KPZ roughness distributions cannot be fitted by those of 1/f^α noise. This study suggests that the roughness distribution is the best option to test KPZ scaling in the growth regime, and provides quantitative data for future comparison with other models or experiments.     

Local Thermodynamic Equilibrium for some Stochastic Models of Hamiltonian Origin

We consider a class of 1-D stochastic models that are realizations of Hamiltonian models of heat conduction and prove that in the infinite volume limit local thermodynamic equilibrium is attained with linear energy profile.     

两个四维混沌系统广义投影同步

利用主动控制同步法设计合适的非线性反馈控制器，实现两个相同的四维混沌系统的同结构广义投影同步，以及实现两个不同的新型四维混沌系统异结构广义投影同步.通过改变广义投影同步的比例因子，获得任意比例于原驱动混沌系统输出的混沌信号.数值仿真表明了所设计的控制器有效性和理论推导的正确性.