多重分形谱在材料分析中的应用研究

基于多重分形谱的物理意义，通过图像分析与处理技术，利用Delphi语言设计了图像结构的多重分形谱的计算程序。通过程序中图像黑白二值化转化阈值的设定，实现了从材料组织结构形貌图像上提取其相应的概率测度和标度指数的功能，并计算了它们的多重分形谱。分析表明：在对材料的组织结构进行研究的问题中，多重分形谱是一种有意义的表征参数，能够从多分形角度对材料的组织结构开展定量化的分析与解释。     

Multifractal Spectrum and Calculation

多重分形理论是进行信号奇异性处理的有用工具 ,由于只有少数集合的多重分形谱可以有解析表达式 ,多重分形谱的计算是其中重要而又较难处理的问题 .简要介绍了多重分形理论的一种形式体系 ,提出了一种采用动态链表来进行多重分形谱计算的方法 ,大幅度地降低了对存储器容量的要求 .用所提出的方法对康托集进行了计算 ,计算结果与理论结果相符 ,表明了算法的有效性 .     

Universal scaling laws for fully-developed magnetic field turbulence near and far upstream of the Earth’s bow shock

We analyze the multifractal scaling of the modulus of the interplanetary magnetic field near and far upstream of the Earth’s bow shock, measured by Cluster and ACE, respectively, from 1 to 3 February 2002. The maximum order of the structure function is carefully estimated for each time series using two different techniques, to ensure the validity of our high-order statistics. The first technique consists of plotting the integrand of the pth order structure function, and the second technique is a quantitative method which relies on the power-law scaling of the extreme events. We compare the scaling exponents computed from the structure functions of magnetic field differences with the predictions obtained by the She–Lévêque model of intermittency in anisotropic magnetohydrodynamic turbulence. Our results show a good agreement between the model and the observations near and far upstream of the Earth’s bow shock, rendering support for the modelling of universal scaling laws based on the Kolmogorov phenomenology in the presence of sheet-like dissipative structures.     

基于小波的网络连接层流量模型

最近研究表明网络流量的统计特性在不同尺度上表现出很大的差异,由大量具有高斯性的网络流量和少量的突发性网络流量组成.为了更好地理解这种复杂的网络流量统计特性,引入多尺度分析工具小波,在多尺度分析的基础上提出一种新的基于小波的网络连接层流量模型,有机地结合了独立小波模型和多重分形小波模型的优点,即保持了独立小波模型在不同尺度对高斯性方差的拟合,同时保持了多重分形小波模型对突发性的拟合.真实网络流量的仿真结果表明这个模型能够灵活地适应网络流量在不同尺度下所表现出的高斯特性和突发行为.     

多重分形谱及其计算

多重分形理论是进行信号奇异性处理的有用工具,由于只有少数集合的多重分形谱可以有解析表达式,多重分形谱的计算是其中重要而又较难处理的问题.简要介绍了多重分形理论的一种形式体系,提出了一种采用动态链表来进行多重分形谱计算的方法,大幅度地降低了对存储器容量的要求.用所提出的方法对康托集进行了计算,计算结果与理论结果相符,表明了算法的有效性.     

基于小波多重分形的通信信号调制识别

针对非平稳、信噪比变化范围较大的通信信号,采用小波多重分形的方法进行调制类型识别。先利用小波变换把通信信号进行分解,再对得到的细节信号计算多重分形维数。仿真结果表明,该方法对噪声和调制参数不敏感,可对通信中的数字调制信号进行有效识别。     

Chaos and multifractals in the solar wind

By using the false-nearest-neighbours method, we have argued that the deterministic component of solar wind plasma dynamics should be low-dimensional. In fact, the results we have obtained using the method of topological embedding indicate that the behaviour of the solar wind can be approximately described by a low-dimensional chaotic attractor in the inertial manifold, which is a subspace of system phase space. We have also shown that the multifractal spectrum of the solar wind attractor is consistent with that for the multifractal measure of the self-similar generalized weighted Cantor set with two different scaling parameters and one probability measure parameter responsible for nonuniform compression in phase space and multifractality. The values of the parameters fitted also demonstrate that the complex solar wind system could only be weakly non-conservative (small dissipation) and quantify nonlinear dynamics; some parts of the attractor in phase space are visited much more frequently than other parts. In addition, to quantify the multifractality of space plasma intermittent turbulence, we consider that generalized Cantor set also in the context of scaling properties of solar wind turbulence. We investigate the resulting multifractal spectrum of a one-dimensional phenomenological model of turbulence cascade depending on its parameters, especially for asymmetric scaling. In particular, we have shown that intermittent pulses are stronger for the cascade model with two different scaling parameters. Even thought solar wind turbulence appears to be rather space filling, a better agreement with the data is obtained, especially for the negative index of generalized dimensions. Therefore we argue that there is a need to use a two-scale asymmetric cascade model. We hope that this generalized multifractal model will be a useful tool for analysis of intermittent turbulence in space plasmas. We thus believe that fractal analysis of chaotic systems could lead us to a deeper understanding of their nature, and maybe even to predict their seemingly unpredictable behaviour.