湍流大气中的准直激光束III.分形结构与相位不连续点饶瑞中

 利用数值方法研究了不同起伏条件下准直激光束在湍流大气中的传播，分析了光斑的分形维数以及相位不连续点数目的统计特征。结果表明：随着起伏条件的增大，光斑的分形维数以及相位不连续点数目增大；光斑的分形维数与锐度（描述光斑质量的参量）有一定的关系，但相位不连续点数目与光斑质量不存在确定的关系。在本文的计算条件下，分形维数一直随起伏条件的增大而增大，没有出现类似于闪烁饱和的现象。在一定的起伏条件下，相位不连续点数目具有一定的统计分布，而不是一个确定的值，并且具有相当的发散性。     

激光大气闪烁饱和的孔径平均效应

理论分析了湍流介质中一定孔径内光强起伏（闪烁）的频谱特征，在6.8km的大气传播距离上同时测量了激光在针孔和φ260mm孔径内的闪烁，根据两者功率谱特征的对比分析结果以及两者闪烁均方差间的关系，指出孔径平均效应可以在一定程度上消除激光大气闪烁的饱和效应，从而可以利用孔径平均效应在临界强起伏条件下测量湍流强度。     

激光大气闪烁的间歇特征

 以小波变换法观察了湍流大气中激光光强起伏的间歇特征, 并用奇性测度进行了定量的描述。根据间歇性参量的周日变化规律发现：激光大气闪烁的间歇性存在于所有的时间和起伏条件下,并且保持稳定,间歇性参量约为0.1,基本不随起伏条件和时间变化。     

采用投影光学估计弱起伏条件下的大气闪烁指数

在远场散斑投影成像系统上整合大气闪烁指数测量功能,有助于全面分析激光大气传输特性及其对光电系统性能的影响。但是在大口径接收时,大气闪烁会因孔径平滑效应而变得微弱,光源稳定性引起的强度起伏会更为明显。针对这一问题,基于光源强度起伏和大气闪烁的乘性调制假设,建立了考虑光源强度起伏的大气闪烁指数的测量模型。利用光源强度起伏不随孔径变化而大气闪烁随孔径变化这一差异性,通过投影光学在同一时刻测量两个不同接收孔径上的光强闪烁,结合弱起伏条件下的孔径平滑因子来求解测量模型,从而分别估计大气闪烁指数和光源强度闪烁指数。实验结果表明,在孔径0.05m至0.4m之间,实测值和理论估计值的最大相对误差小于9.685%,理论模型与实验符合度较高。采用该方法可以在投影光学上实现弱起伏条件下的大气闪烁指数估计。     

激光大气闪烁的高频谱特性

 采用三波长闪烁仪进行了大气边界层的光传输实验，结果表明：在相同的传播条件下，非平面波激光大气闪烁功率谱的高频部分与波长存在着一定的关系，功率谱无标度区间的斜率即标度指数是一个与湍流强度、波长等因素有关的函数，在满足弱起伏的条件下，标度指数一般与波长呈负相关，波长愈长则标度指数愈小，频谱下降的趋势愈快；波长愈短则标度指数愈大，频谱下降的趋势愈慢。     

近地层大气光学湍流的分形和间歇性特征分析

利用光纤湍流测量系统获得了合肥西郊科学岛上气象观测场内下垫面平坦的水面上方0.48m、草地上方1.8m和23m高处的大气折射率起伏的观测数据,采用R/S分析法计算了近地层大气光学湍流的赫斯特指数和分形维数,统计分析了分形维数的日变化特征及概率分布特征。结果表明:对于一天的不同时段,分形维数在一定范围内动态变化,且中午时段相对稳定;在三种下垫面条件下,全天分形维数的值大多在1.3~1.4之间,其最可几概率位于1.35处,从均值来看,草地上方1.8m的分形维数最大,水面上方0.48m次之,草地上方23m处最小。最后,初步探讨了近地层大气光学湍流分形维数、间歇性指数和湍流发展程度的相关性。     

孔径接收下大气闪烁频谱的理论和实验研究

 基于孔径接收下的对数振幅时间相关函数，推导了弱湍流起伏条件下大气闪烁频谱的表达式，分析了接收孔径对大气闪烁频谱的影响。通过完成水平大气传输实验，实际测量了孔径接收下的大气闪烁频谱。实验结果验证了理论计算。结果表明，孔径接收下的大气频谱分为低频段和高频段两部分，低频谱为常数，高频谱呈幂指数关系变化，且幂指数为-11/3；随着接收孔径增大，频谱在各频率点上的幅值逐渐减小，其形状保持不变。     

城市路径下激光光强起伏特性测量及链路余量估算

 在城市环境下进行了3.5 km的激光大气传输实验。实验中对光强起伏和到达角起伏进行了同步测量，分析了接收光强起伏的统计特性以及传输路径上大气折射率结构常数的特性。基于实验结果，对自由空间光通信中不同闪烁指数下的衰落冗余以及不同探测阈值下的衰落概率进行了估算，从而为空间光通信系统的设计提供可靠的实验基础。     

基于大气湍流效应的双波长激光传输特性实验研究

为研究大气湍流作用下不同波长激光信号的传输特性,建立了基于双波长条件下的激光光束传输实验测试系统,在此基础上进行了室外实验测量,得到了双波长光束同信道传输时的光束漂移和光强起伏变化的测试数据。实验结果表明,大气湍流对激光信号的传输具有较大的影响,且光强的闪烁系数与波长有很大的关系,选择波长较长的激光束可减少湍流对光强起伏的影响;光束质心漂移具有很大的随机性,且其质心变化与波长之间无明显的直接联系。实验测试数据结果与大气湍流理论相符合,对空间大气通信具有一定的参考价值。     

上下行传输孔径接收光强起伏特性分析

为了研究地星上行和星地下行激光链路孔径内接收光强信号的典型特征,基于大气湍流理论和位相屏方法,计算了短波和中波红外激光在特定大气相干长度条件下,孔径内接收激光功率与总功率的比值及起伏情况。根据统计结果讨论了上下行大气通道传播特性的差异,结果表明相同外界条件下,直径50 cm孔径内接收的下行激光信号强度大于上行激光信号强度1个数量级以上,其信号的起伏程度也低于上行激光;中等湍流下,下行激光孔径接收光强的概率分布函数服从对数正态分布,最大概率接收功率比与无湍流条件下的功率比值一致,分别为0.42%(1.315 m)和 0.26%(3.8 m)。     

Evidence of self-affine multiplicity fluctuation of target residues in 84Kr-AgBr interactions at 1.7 AGeV

Self-afline multiplicity scaling is investigated in the framework of a two-dimensional factorial mo-ment methodology using the concept of the Hurst exponent (H). Analyzing the experimental data of target evaporated fragments emitted in84Kr-AgBr interactions at 1.7 AGeV revealed that the best power law behav-ior is exhibited for H = 0.3 indicating a self-affine multiplicity fluctuation pattern. A signal of multifractality is also observed from knowledge of the anomalous fractal dimension dq extracted from the intermittency exponent aq of the anisotropic phase space scenario.     

湍流折射率谱型对大气闪烁和相位起伏功率谱的影响

基于Taylor湍流冻结假设理论,在不同湍流折射率谱型条件下,推导得出了光波闪烁和相位起伏频谱的表达式;数值计算了湍流谱型中折射率标度指数、内尺度以及外尺度变化时对光波频谱的影响。结果表明:随着折射率起伏标度指数的增大,闪烁频谱的低频段不再仅为常数,高频段下降的幂率逐渐增大,同时相位频谱在整个起伏频率段下降的幂率越来越大;湍流内尺度的增加将引起光波频谱的高频段下降的幂率越来越大;而随外尺度的减小,闪烁频谱低频段的振幅减小,这种影响在大口径接收时较为明显,相位谱的低频段幂率减小。     

Fractals in DNA sequence analysis

Fractal methods have been successfully used to study many problems in physics,mathematics,engineering,finance,and even in biology,There has been an increasing interest in unravelling the mysteries of DNA;for example,how can we distinguish coding and noncoding sequences,and the problems of classification and evolution relationship of organisms are key problems in bioinformatics,Although much research has been carried out by taking into consideration the long-range correlations in DNA sequences,and the global fractal dimension has been used in these works by other people,the models and methods are somewhat rough and the results are not satisfactory.In recent years,our group has introduced a time series model(statistical point of view)and a visual representation (geometrical point of view) to DNA sequence analysis.We have also used fractal dimension,correlation dimension,the Hurst exponent and the dimension spectrum (multifractal analysis)to discuss problems in this field.In this paper,we introduce these fractal models and methods and the results of DNA sequence analysis.     

Characterization of electrodeposited nickel film surfaces using atomic force microscopy

Microstructures of nickel surfaces electrodeposited on indium tin oxides coated glasses are investigated using atomic force microscopy. The fractal dimension D and Hurst exponent H of the nickel surface images are determined from a frequency analysis method proposed by Aguilar et al. [J. Microsc. 172 (1993) 233] and from Hurst rescaled range analysis. The two methods are found to give the same value of the fractal dimension D∼2.0. The roughness exponent α and growth exponent β that characterize scaling behaviors of the surface growth in electrodeposition are calculated using the height-difference correlation function and interface width in Fourier space. The exponents of α∼1.0 and β∼0.8 show that the surface growth does not belong to the universality classes theoretically predicted by statistical growth models.     

An accurate algorithm to calculate the Hurst exponent of self-similar processes

In this paper, we introduce a new approach which generalizes the GM2 algorithm (introduced in Sánchez-Granero et al. (2008) [52]) as well as fractal dimension algorithms (FD1, FD2 and FD3) (first appeared in Sánchez-Granero et al. (2012) [51]), providing an accurate algorithm to calculate the Hurst exponent of self-similar processes. We prove that this algorithm performs properly in the case of short time series when fractional Brownian motions and Lévy stable motions are considered.We conclude the paper with a dynamic study of the Hurst exponent evolution in the S&P500 index stocks.     

Correlation of optical properties with the fractal microstructure of black molybdenum coatings

Coating is commonly used for improving the optical properties of surfaces for solar collector applications. The coating morphology depends on the deposition conditions, and this determines the final optical characteristics. Coating morphologies are irregular and of fractal nature, so a suitable approach for its characterization should use methods borrowed from fractal analysis. The aim of this work is to study the fractal characteristics of black molybdenum coatings on copper and to relate the fractal parameters to the optical properties. To this end, coating surfaces were prepared via immersion in a solution of ammonium paramolybdate for different deposition periods. The fractal analysis was carried out for SEM and AFM images of the coating surface and the fractal properties were obtained with a recently developed high-dimensional extension of the well-known detrended fluctuation analysis (DFA). The most salient parameter drawn from the application of the DFA is the Hurst index, a parameter related to the roughness of the coating surface, and the multifractality index, which is related to the non-linearity features of the coating morphology. The results showed that optical properties, including absorptance and emittance, are decreasing functions of the Hurst and multifractality indices. This suggests that coating surfaces with high absorptance and emittance values are related to complex coating morphologies conformed within a non-linear structure.     

Experimental determination of Hurst exponent of the self-affine fractal patterns with optical fractional Fourier transform

The extension of ordinary Fourier transform to the fractional Fourier transform (FRFT) was first accomplished by Namias in 1980. He gave a complete mathematical definition and discussed the eigenfunction of the transform. Using a system of lenses Lohmann et al.[1] first successfully realized the FRFT optically and designed the single lens mode and double lens mode for the realization of the FRFT of continuously variable fractional order. The concept of fractals was first proposed by Man…     

Dynamical generalized Hurst exponent as a tool to monitor unstable periods in financial time series

We investigate the use of the Hurst exponent, dynamically computed over a weighted moving time-window, to evaluate the level of stability/instability of financial firms. Financial firms bailed-out as a consequence of the 2007–2008 credit crisis show a neat increase with time of the generalized Hurst exponent in the period preceding the unfolding of the crisis. Conversely, firms belonging to other market sectors, which suffered the least throughout the crisis, show opposite behaviors. We find that the multifractality of the bailed-out firms increase at the crisis suggesting that the multi fractal properties of the time series are changing. These findings suggest the possibility of using the scaling behavior as a tool to track the level of stability of a firm. In this paper, we introduce a method to compute the generalized Hurst exponent which assigns larger weights to more recent events with respect to older ones. In this way large fluctuations in the remote past are less likely to influence the recent past. We also investigate the scaling associated with the tails of the log-returns distributions and compare this scaling with the scaling associated with the Hurst exponent, observing that the processes underlying the price dynamics of these firms are truly multi-scaling.     

How fast do stock prices adjust to market efficiency? Evidence from a detrended fluctuation analysis

In this paper we analyse price fluctuations with the aim of measuring how long the market takes to adjust prices to weak-form efficiency, i.e., how long it takes for prices to adjust to a fractional Brownian motion with a Hurst exponent of 0.5. The Hurst exponent is estimated for different time horizons using detrended fluctuation analysis–a method suitable for non-stationary series with trends–in order to identify at which time scale the Hurst exponent is consistent with the efficient market hypothesis. Using high-frequency share price, exchange rate and stock data, we show how price dynamics exhibited important deviations from efficiency for time periods of up to 15 min; thereafter, price dynamics was consistent with a geometric Brownian motion. The intraday behaviour of the series also indicated that price dynamics at trade opening and close was hardly consistent with efficiency, which would enable investors to exploit price deviations from fundamental values. This result is consistent with intraday volume, volatility and transaction time duration patterns.