基于多重分形去趋势波动分析法的交通流多重分形无标度区间自动识别方法

无标度区间是时间序列在统计意义上存在分形自相似性的尺度范围,是交通流多重分形特征研究中的重要组成部分.为解决交通流多重分形研究中多重分形去趋势波动分析法(multi-fractal detrended fluctuation analysis,MF-DFA)缺乏有效识别无标度区间方法的问题,本文在分析算法过程中交通流波动函数对数曲线突变点性质的基础上,结合传统无标度区间识别方法的构建思想,建立基于MF-DFA算法的无标度区间自动识别方法.以北京市二环快速路外环方向的部分道路为例开展实例研究,通过与传统无标度区间识别方法的结果对比,验证新方法的有效性.研究结果表明:本文方法能自动识别交通流多重分形无标度区间,且稳定性好;案例研究可知交通流短时间内波动较小、自相似性较强,随着研究时间段变长、交通流波动逐渐变大,自相似性逐渐消失,进一步解释了交通流无标度区间的有限性.     

Infrared dim target detection based on fractal dimension and third-order characterization

We propose an improved algorithm based on fractal dimension and third-order characterization to detect dim target with cluttered background in an infrared （IR） image. We also illustrate the performance and efficiency comparisons between the presented algorithm and the traditional fractal detection method on real IR images. The experimental results show that the proposed algorithm is robust and efficient for IR dim target detection.     

如何给工科学生讲分形物理——介绍华中科技大学非线性物理教学改革之一

本文介绍了作者在华中科技大学讲授分形物理的几个重要环节及做法;抓住分形本质特性,立足于物理、精选模型、上机实践。最后,所花学时甚少却能取得比较好的效果。     

用分形理论研究低温条件下Al-Al界面间的接触导热现象

界面形貌是固体界面间接触导热的最主要影响因素 ,传统的形貌表征参数与仪器的分辨率和取样长度密切相关 ,因而基于这些参数的常规接触导热模型显然是尺度相关的。分形网络模型利用粗糙表面处处连续却不可微的分形特征 ,采用与尺度无关的分形参数 ,揭示了接触导热的本质 ,为准确预测接触热导开辟了一条新的途径。实验测定了粗糙表面的分形参数和低温条件下 Al50 52 - Al50 52界面间的接触热导 ,将接触热导的实验值与分形网络模型的预测结果进行了比较 ,并就接触热导与压力、分形参数和温度之间的关系进行了分析 ,指出分形网络模型的预测精度与分形参数相关联。     

Numerical simulation and pattern characterization of nonlinear spatiotemporal dynamics on fractal surfaces for the whole-heart modeling applications

Engineered and natural systems often involve irregular and self-similar geometric forms,which is called fractal geometry. For instance, precision machining produces a visuallyflat surface, while which looks like a rough mountain in the nanometer scale under themicroscope. Human heart consists of a fractal network of muscle cells, Purkinje fibers,arteries and veins. Cardiac electrical activity exhibits highly nonlinear and fractalbehaviors. Although space-time dynamics occur on the fractal geometry, e.g., chemicaletching on the surface of machined parts and electrical conduction in the heart, most ofexisting works modeled space-time dynamics (e.g., reaction, diffusion and propagation) onthe Euclidean geometry (e.g., flat planes and rectangular volumes). This brings inaccurateapproximation of real-world dynamics, due to sensitive dependence of nonlinear dynamicalsystems on initial conditions. In this paper, we developed novel methods and tools for thenumerical simulation and pattern recognition of spatiotemporal dynamics on fractalsurfaces of complex systems, which include (1) characterization and modeling of fractalgeometry, (2) fractal-based simulation and modeling of spatiotemporal dynamics, (3)recognizing and quantifying spatiotemporal patterns. Experimental results show that theproposed methods outperform traditional modeling approaches based on the Euclideangeometry, and provide effective tools to model and characterize space-time dynamics onfractal surfaces of complex systems.     

Fractal Strings and Multifractal Zeta Functions

For a Borel measure on the unit interval and a sequence of scales that tend to zero, we define a one-parameter family of zeta functions called multifractal zeta functions. These functions are a first attempt to associate a zeta function to certain multifractal measures. However, we primarily show that they associate a new zeta function, the topological zeta function, to a fractal string in order to take into account the topology of its fractal boundary. This expands upon the geometric information garnered by the traditional geometric zeta function of a fractal string in the theory of complex dimensions. In particular, one can distinguish between a fractal string whose boundary is the classical Cantor set, and one whose boundary has a single limit point but has the same sequence of lengths as the complement of the Cantor set. Later work will address related, but somewhat different, approaches to multifractals themselves, via zeta functions, partly motivated by the present paper.     

基于显微CT图像的岩芯孔隙分形特征

采用国内自主开发的高分辨率显微CT设备,对岩芯样本进行图像采集,运用数字图像分析方法获得图像中的岩芯孔隙目标,并以此为基础重建三维模型。然后基于分形理论,分别从二维图像和重建的三维模型角度计算孔隙的分形维数。最后,再采用基于多孔介质的分形模型对岩芯孔隙分形特征进行验证,得出岩芯的二维分形维数和三维分形维数之间的差值均值为1.000 3,最大偏差为0.004,很好地满足多孔介质分形模型中关于二维和三维分形维数的关系。     

High Efficient Tunable Fractal Axicon Based on LCoS

Based on the Cantor function and phase modulation, a tunable fractal axicon is formed on a liquid crystal on silicon （LCoS） with an improved generating method. It has higher focusing efficiency in higher fractal stage and approaches to 100% theoretically. The on-axis intensity keeps its fractal structure unchanged in operation of fractal stages. The tunability of the axicon is demonstrated by tune fractal stage from 1 to 3 and focal length from 0.8 m to 1 m. We also provide details of theoretical analyses and experimental results.     

调制无线电信号的分形特征研究

调制方式的不同以及信号受到功率放大器的非线性变换决定了调制无线电信号的形状存在着差异,提取这些差异特征是信号识别的基础. 基于分形理论提取信号特征是一种新的方法,本文模拟了在不同信噪比条件下,通过计算调制无线电信号的方差分形维以及Mandelbrot奇异分形维谱,将信号的调制特征以及非线性变换特征投射到分形特征空间. 数值仿真结果表明,不同调制方式、非线性变换对应了分形特征空间中的不同位置. 这些结果表明分形理论能够有效提取无线电信号的调制特征以及功率放大器的特征,对信号的调制方式以及个体特征识别具有一定 关键词： 无线电 信号 分形特征 识别     

Fractal analysis on human dynamics of library loans

In this paper, the fractal characteristic of human behaviors is investigated from the perspective of time series constructed with the amount of library loans. The values of the Hurst exponent and length of non-periodic cycle calculated through rescaled range analysis indicate that the time series of human behaviors and their sub-series are fractal with self-similarity and long-range dependence. Then the time series are converted into complex networks by the visibility algorithm. The topological properties of the networks such as scale-free property and small-world effect imply that there is a close relationship among the numbers of repetitious behaviors performed by people during certain periods of time. Our work implies that there is intrinsic regularity in the human collective repetitious behaviors. The conclusions may be helpful to develop some new approaches to investigate the fractal feature and mechanism of human dynamics, and provide some references for the management and forecast of human collective behaviors.     

Fractal Analysis of Mobile Social Networks

Fractal and self similarity of complex networks have attracted much attention in recent years.The fractal dimension is a useful method to describe the fractal property of networks.However,the fractal features of mobile social networks(MSNs) are inadequately investigated.In this work,a box-covering method based on the ratio of excluded mass to closeness centrality is presented to investigate the fractal feature of MSNs.Using this method,we find that some MSNs are fractal at different time intervals.Our simulation results indicate that the proposed method is available for analyzing the fractal property of MSNs.     

Fractal communication system

Complex electromagnetic situation and the need in protecting information from unauthorized access require new engineering solutions in the development of communication system. One of such approaches is associated with fractal communication systems (FCSs) employing antijamming waveforms with fractal spectra as information carriers. Basic concepts of an FCS are considered and the results of its practical implementation for computer communication via an aerial or a coaxial cable are discussed.     

纹理高阶分形特征在海面舰船目标检测中的应用

针对复杂海面环境下的舰船目标检测，分析了高阶分形特征缝隙在纹理分类中的应用，提出了一种基于分形维与缝隙的目标检测新方法，并利用该方法对海面舰船目标进行了检测。实验结果表明利用纹理分形维与缝隙特征进行海面舰船目标检测，可以取得较单一分形维检测更高的准确率。     

密封界面微孔结构的三维分形重构技术与泄漏特性

基于分形粗糙表面的三维数值重构技术,对界面微孔结构的分形表征进行详细研究,并应用分形多孔介质输运理论构建界面泄漏机理模型,建立微观形貌与宏观泄漏率之间的理论关系式.用有限元分析法对单粗糙峰的接触变形进行模拟,获得最大孔径的变形位移,实现微观接触力学与微观泄漏模型的有效耦合.应用所提出的预测模型对金属垫片泄漏率进行计算,结果与已有实验结果相吻合.由预测模型可知,粗糙表面分形维数、特征尺度系数以及变形位移量对微孔几何结构影响显著,是影响界面泄漏率的关键因素.     

燃烧过程中煤焦颗粒的逾渗特性变化

本论文根据分形理论及测定得到的准格尔褐煤在燃烧过程中颗粒的物性参数建立表征煤焦颗粒的分形体模型。 通过分形体上突入逾渗和普通逾渗模拟,研究在燃烧过程中由于颗粒内部分形体结构的改变造成的传输特性和反应特性 的变化情况。结果表明,建立的分形体模型能够很好的表征煤焦颗粒结构特征,逾渗模拟的结果与实际情况基本相符。     

Electromagnetic reflection and transmission from a new version of Cantor fractal nonlinear multilayers

In this paper, we put forward a new version of Cantor fractal multilayers, which are nonlinear medium, and investigate its properties of reflection and transmission when a plane wave is obliquely incident upon it. A new exact self-similarity algorithm that make use of the self -similarity of these structure are developed. The results for different stages of fractal growth within the first-order nonlinear approximation are found. Compared with the traditional chain-matrix approach, the scheme provides the reflection and transmission coefficients for any stage (S) with much less calculation time on a personal computer.     

Rescaled Range and Transition Matrix Analysis of DNA Sequences

We treat some fractal and statistical features of the DNA sequences. First, a fractal record model of DNA sequence is proposed by mapping,DNA sequences to integer sequences, followed by the R/S analysis of the model and computation of the Hurst exponents. Second, we consider the transition between the four kinds of bases within DNA. The transition matrix analysis of DNA sequences shows that some measures of complexity based on transition proportion matrices are of interest.     

Computerised Perimeter Mapping and the Measurement of Fractal Dimensions

A method is described for mapping the perimeter of shapes as a sequence of connected X & Y coordinates. It operates by tracking, in tandem, along a dilated outline of the shape and the true outline, maintaining contact between both tracks. This combination permits the complete mapping of binary shapes regardless of their complexity. The resulting sequence of X & Y coordinates form an 8-connected map of the outline, which can then be used to obtain fractal dimensions using structured walks. The method requires a digitised image that has been converted into a binary form and the ability to read the values of individual pixels from the digitised binary image. In addition a number of approaches for increasing the efficiency of the twin tracking algorithm are outlined. Obtaining fractal dimensions from a structured walk based on a fully mapped perimeter increases the accuracy of the measured fractal dimensions, extends the range of step sizes over which measurements can be made and permits a highly detailed examination of the perimeter.     

Fractal and structural aspects of adhesion in particulate-filled polymer composites

Two types of composites based on poly(hydroxy ether) and graphite with various amounts of a filler have been investigated by various methods. The methods have been used to estimate the characteristics of adhesion and interfacial layer, including its thickness and tensile strength and interdependence between these values and adhesion. The results are treated on the basis of the theory of irreversible aggregation, cluster theory of the polymer structure and fractal analysis. It is established that all important characteristics of adhesion, interfacial layer and mechanical properties are interconnected with the difference between fractal dimensions of the surface of the aggregates of filler particles and of a polymer matrix, whose structure is distorted under the influence of the filler surface.     

Nonequilibrium statistical mechanics of preasymptotic dispersion

Turbulent transport in bulk-phase fluids and transport in porous media with fractal character involve fluctuations on all space and time scales. Consequently one anticipates constitutive theories should be nonlocal in character and involve constitutive parameters with arbitrary wavevector and frequency dependence. We provide here a nonequilibrium statistical mechanical theory of transport which involves both diffusive and convective mixing (dispersion) at all scales. The theory is based on a generalization of classical approaches used in molecular hydrodynamics and on time-correlation functions defined in terms of nonequilibrium expectations. The resulting constitutive laws are nonlocal and constitutive parameters are wavevector and frequency dependent. All results reduce to their convolution-Fickian quasi-Fickian, or Fickian counterparts in the appropriate limits.