Scaling analysis of phase fluctuations in experimental three-phase flows

The characterization of complex patterns arising from three-phase (e.g., oil-gas-water) flows is an important problem with significant engineering and industrial applications. Based solely on measured conductance fluctuation signals from experimental three-phase flows, we propose a method to characterize and distinguish three commonly observed flow patterns. Using the phase characterization method, we first calculate the instantaneous phase from the signals. Then, through performing a scaling analysis, detrended fluctuation analysis (DFA), we extract scaling behaviors associated with the phase fluctuations and find that the DFA scaling exponent is sensitive to the transition among different flow patterns, which can be used to characterize nonlinear dynamics of the three-phase flow. From a novel perspective, we investigate the three-phase flow in terms of phase characterization and scaling analysis. The results indicate that our method can provide new insights into the exploration of complex mechanism in flow pattern transition. The effectiveness of the method is demonstrated and its broader applicability is articulated.     

Detrended fluctuation analysis of heart intrabeat dynamics

We investigate scaling properties of electrocardiogram (ECG) recordings of healthy subjects and heart failure patients based on detrended fluctuation analysis (DFA). While the vast majority of scaling analysis has focused on the characterization of the long-range correlations of interbeat (i.e., beat-to-beat) dynamics, in this work we consider instead the characterization of intrabeat dynamics. That is, here we use DFA to study correlations for time scales smaller than one heart beat period (about 0.75 s). Our results show that intrabeat dynamics of healthy subject are less correlated than for heart failure dynamics. As in the case of interbeat dynamics, the DFA scaling exponents can be used to discriminate healthy and pathological data. It is shown that 0.5 h recordings suffices to characterize the ECG correlation properties.     

Effect of coarse-graining on detrended fluctuation analysis

Several studies have investigated the scaling behavior in naturally occurring biological and physical processes using techniques such as detrended fluctuation analysis (DFA). Data acquisition is an inherent part of these studies and maps the continuous process into digital data. The resulting digital data is discretized in amplitude and time, and shall be referred to as coarse-grained realization in the present study. Since coarse-graining precedes scaling exponent analysis, it is important to understand its effects on scaling exponent estimators such as DFA. In this brief communication, k-means clustering is used to generate coarse-grained realizations of data sets with different correlation properties, namely: anti-correlated noise, long-range correlated noise and uncorrelated noise. It is shown that the coarse-graining can significantly affect the scaling exponent estimates. It is also shown that scaling exponent can be reliably estimated even at low levels of coarse-graining and the number of the clusters required varies across the data sets with different correlation properties.     

Scaling characteristics of ocean wave height time series

Fluctuations in the significant wave height can be quantified by using scaling statistics. In this paper, the scaling properties of the significant wave height were explored by using a large data set of hourly series from 25 monitoring stations located off the west coast of the US. Detrended fluctuation analysis (DFA) was used to investigate the scaling properties of the series. DFA is a robust technique that can be used to detect long-range correlations in nonstationary time series. The significant wave height data was analyzed by using scales from hourly to monthly. It was found that a common scaling behavior can be observed for all stations. A breakpoint in the scaling region around 4-5 days was apparent. Spectral analysis confirms this result. This breakpoint divided the scaling region into two distinct parts. The first part was for finer scales (up to 4 days) which exhibited Brown noise characteristics, while the second one showed 1/f noise behavior at coarser scales (5 days to 1 month). The first order and the second order DFA (DFA1 and DFA2) were used to check the effect of seasonality. It was found that there were no differences between DFA1 and DFA2 results, indicating that there is no effect of trends in the wave height time series. The resulting scaling coefficients range from 0.696 to 0.890 indicating that the wave height exhibits long-term persistence. There were no coherent spatial variations in the scaling coefficients.     

Effects of quantization on detrended fluctuation analysis

Detrended fluctuation analysis(DFA) is a method foro estimating the long-range power-law correlation exponent in noisy signals.It has been used successfully in many different fields,especially in the research of physiological signals.As an inherent part of these studies,quantization of continuous signals is inevitable.In addition,coarse-graining,to transfer original signals into symbol series in symbolic dynamic analysis,can also be considered as a quantization-like operation.Therefore,it is worth considering whether the quantization of signal has any effect on the result of DFA and if so,how large the effect will be.In this paper we study how the quantized degrees for three types of noise series(anti-correlated,uncorrelated and long-range power-law correlated signals) affect the results of DFA and find that their effects are completely different.The conclusion has an essential value in choosing the resolution of data acquisition instrument and in the processing of coarse-graining of signals.     

Non-uniform scaling behavior in ultra-low-frequency (ULF) earthquake-related geomagnetic signals

Investigating highly non-stationary time series, which typically exhibit long-range correlations, is a classic problem in physics. Here, we analyze the scaling properties of the dynamics of ultra-low-frequency (ULF) geomagnetic data (in the frequency range between 1 mHz and 10 Hz) observed at Izu Peninsula in Japan. On the basis of the detrended fluctuation analysis (DFA), deviations from uniform power-law scaling were quantified. Our findings point out to a significant non-uniform scaling behavior in ULF geomagnetic data in relationship with the occurrence of intense seismic clusters.     

Levels of complexity in turbulent time series for weakly and high Reynolds number

We use the detrended fluctuation analysis (DFA), the detrended cross correlation analysis (DCCA) and the magnitude and sign decomposition analysis to study the fluctuations in the turbulent time series and to probe long-term nonlinear levels of complexity in weakly and high turbulent flow. The DFA analysis indicate that there is a time scaling region in the fluctuation function, segregating regimes with different scaling exponents. We discuss that this time scaling region is related to inertial range in turbulent flows. The DCCA exponent implies the presence of power-law cross correlations. In addition, we conclude its multifractality for high Reynold’s number in inertial range. Further, we find that turbulent time series exhibit complex features by magnitude and sign scaling exponents.     

Temporal-spatial diversities of long-range correlation for relative humidity over China

Long-range correlations of daily relative humidity anomaly records from 191 weather stations over China during 1951-2000 are analyzed by means of fluctuation analysis (FA) and detrended fluctuation analysis (DFA). The information about trends in the relative humidity records can be obtained by comparing the FA curve with DFA curves. The daily relative humidity fluctuations are found to be power-law correlated and their average scaling exponent is higher than that of the temperature fluctuations, indicating that the relative humidity fluctuations take different statistical behavior from other meteorological quantities and there exists a stronger persistence in the relative humidity fluctuations. Furthermore, it is also found that these power-law scaling properties vary from station to station and show both spatial and temporal diversities, which may be explained by a proposed mechanism.     

Scaling analysis of the effects of load on hand tremor movements in essential tremor

In this paper we have used the Wavelet Transform (WT) and the Detrended Fluctuation Analysis (DFA) methods to analyze hand tremor movements in essential tremor (ET), in two different recording conditions (before and after the addition of wrist-cuff load). We have analyzed the time series comprised of peak-to-peak (PtP) intervals, extracted from regions around the first three main frequency components of the power spectra (PwS) of the recorded tremors, in order to substantiate results related to the effects of load on ET, to distinguish between multiple sources of ET, and to separate the influence of peripheral factors on ET.Our results show that, in ET, the dynamical characteristics, that is, values of respective scaling exponents, of the main frequency component of recorded tremors change after the addition of load. Our results also show that in all the observed cases the scaling behavior of the calculated functions changes as well—the calculated WT scalegrams and DFA functions display a shift in the position of the crossover when the load is added. We conclude that the difference in behavior of the WT and DFA functions between different conditions in ET could be associated with the expected pathology in ET, or with some additional mechanism that controls movements in ET patients, and causes the observed changes in scaling behavior.     

Chaotic SVD method for minimizing the effect of exponential trends in detrended fluctuation analysis

The Detrended Fluctuation Analysis (DFA) and its extensions (MF-DFA) have been used extensively to determine possible long-range correlations in self-affine signals. However, recent studies have reported the susceptibility of DFA to trends which give rise to spurious crossovers and prevent reliable estimation of the scaling exponents. In this study, a smoothing algorithm based on the Chaotic Singular-Value Decomposition (CSVD) is proposed to minimize the effect of exponential trends and distortion in the log-log plots obtained by DFA techniques. The effectiveness of the technique is demonstrated on monofractal and multifractal data corrupted with exponential trends.     

Detrending fluctuation analysis based on high-pass filtering

Detrended fluctuation analysis (DFA) is a scaling method commonly used for detecting long-range correlations in non-stationary time series. The DFA method uses a trend based on polynomial fitting to extract and quantify fluctuations at different time scales. Basically, such procedure acts as a (non-dynamical) high-pass filter that removes time series components below a given time scale. As an alternative to the polynomial fitting approach, this paper proposes a DFA method based on well-known high-pass filters (e.g., Butterworth, elliptic, etc.). Numerical results show that the proposed DFA approach yields results similar to traditional DFA method. Maybe, the main advantage of the proposed DFA method is that efficient implementations of high-pass filters are available commercially.     

A hybrid detrending method for fractional Gaussian noise

Determining trend and implementing detrending operations are important steps in data analysis. Yet there is neither precise definition of “trend” nor any logical algorithm for extracting it. In this paper, we propose a Hybrid Detrending Method (HDM) which is based on the Empirical Mode Decomposition (EMD) and the Detrended Fluctuation Analysis (DFA). Our method can remove the polynomial and sinusoidal trends from the fractional Gaussian noise (fGn) background. We illustrate the method by selected examples from artificial time series and climate data. In comparison with existing frequency domain based detrending methods, our method is a posteriori, the trend defined by our method is only derived from the data. Further, our method also preserves the scaling behavior of the original signals.     

Analysis of temporal fluctuations in Bach’s sinfonias

The correlation structures in 15 Bach’s sinfonias were analyzed. Each sinfonia is characterized by the superposition of three voices. Each voice is a sequence of pitches. Each voice was transformed in a time series, in which the sampling time was given by the smallest pitch duration in that voice. The scaling properties of the three voices of each sinfonia was quantified by means of the estimate of the scaling exponent, performed using the power spectral density (PSD) and the detrended fluctuation analysis (DFA). The results show that the voice time series are persistent. The DFA was applied not only to any single voice time series, but also to couples (2-DFA) of voices and to the triple (3-DFA) of voices. It was found that the first voice of each sinfonia modulates the scaling behavior of the whole sinfonia.     

XRF法在四川盆地须家河组沉积相研究中的应用

X射线荧光光谱仪在地质样品测定上的应用还不是很广泛,而将X射线荧光光谱法应用到沉积相的研究中则更少。将X射线荧光光谱法(XRF)应用到川中地区上三叠统须家河组二段沉积环境及古气候的识别中,针对四川盆地上三叠统须家河组二段沉积相及沉积环境有争议的问题,特别是须二段地层属于陆相沉积还是海相沉积的问题,采集了四川盆地内四个有代表性地区的须家河组样品,采用X 射线荧光光谱法分析须家河组各段沉积物的元素含量及变化特征,并根据不同相带及沉积环境的元素含量标志,定量分析须家河组沉积相带与沉积环境。研究结果表明： 须家河组二段的Sr/Ba值、Mn/Fe 值和Sr/Ca值均落在陆相沉积的范围内,且与须家河组三-四段的元素含量特征无明显差异,Sr/Cu元素比分析结果表明须家河组沉积时期为温暖—湿润的古气候环境,结果证明四川盆地上三叠统须家河组二段属于温湿气候下的陆相沉积,且与须家河组三-四段沉积环境相类似。X射线荧光光谱法与常规化学分析法实验结果相对误差小于3%,该方法简单易行,为沉积相及沉积环境的识别提供了一种简单、可行且能够定量分析的研究方法。为解决有争议地层沉积相的问题提供了一种较可行的新方法,推动了X射线荧光光谱分析法在地质上的应用。     

Scaling properties of image textures: A detrending fluctuation analysis approach

The aim of this paper is to explore the application of detrended fluctuation analysis (DFA) to study roughness features of images. Unidimensional sequences at different image orientations are extracted and their average scaling exponent is estimated. In this form, the existence of anisotropies can be detected when considerable variations in the scaling exponent at different image orientation are observed. Different images from grass to solar granulation are analyzed and the underlying physics of such results is briefly commented.     

Universal scaling behaviors of meteorological variables’ volatility and relations with original records

Volatility series (defined as the magnitude of the increments between successive elements) of five different meteorological variables over China are analyzed by means of detrended fluctuation analysis (DFA for short). Universal scaling behaviors are found in all volatility records, whose scaling exponents take similar distributions with similar mean values and standard deviations. To reconfirm the relation between long-range correlations in volatility and nonlinearity in original series, DFA is also applied to the magnitude records (defined as the absolute values of the original records). The results clearly indicate that the nonlinearity of the original series is more pronounced in the magnitude series.     

脑电信号的标度分析及其在睡眠状态区分中的应用

脑电信号具有长程幂律相关性及多重分形的标度特性,并随生理病理状态改变.本文首次针对睡眠脑电信号应用单重分形去趋势波动分析(detrended fluctuation analysis,简记为DFA)方法与多重分形奇异谱对睡眠脑电信号的标度特征进行系统的对比研究.发现DFA标度指数α对于不同导联和样本组间的差异较为敏感,随睡眠状态的变化不规律;而多重分形奇异强度区间Δα随睡眠状态的变化更为规律,睡眠Ⅰ期至Ⅳ期不断增大,并且导联间差异和样本组间差异均较小.多重分形Δα参数更适合作为判定睡眠状态的定量参数.     

ToF-SIMS studies of Bacillus using multivariate analysis with possible identification and taxonomic applications

In this paper we discuss the application of ToF-SIMS with an Au₃⁺ primary ion beam, combined with principal components analysis (PCA) and discriminant function analysis (DFA) for the identification of individual strains of two Bacillus species. The ToF-SIMS PC-DFA methodology is capable of distinguishing bacteria at the strain level based on analysis of surface chemical species. By classifying the data using hierarchical cluster analysis (HCA) we are able to show quantitative separation of species and of these strains. This has taxonomic implications in the areas of rapid identification of pathogenic microbes isolated from the clinic, food and environment.     

Non-linear characteristics and long-range correlations in Asian stock markets

We test several non-linear characteristics of Asian stock markets, which indicates the failure of efficient market hypothesis and shows the essence of fractal of the financial markets. In addition, by using the method of detrended fluctuation analysis (DFA) to investigate the long range correlation of the volatility in the stock markets, we find that the crossover phenomena exist in the results of DFA. Further, in the region of small volatility, the scaling behavior is more complicated; in the region of large volatility, the scaling exponent is close to 0.5, which suggests the market is more efficient. All these results may indicate the possibility of characteristic multifractal scaling behaviors of the financial markets.     

Studies of relativistic backward-wave oscillator operation in thecross-excitation regime

We first reported the operation of a relativistic backward-wave oscillator (BWO) in the so-called cross-excitation regime in 1998. This instability, whose general properties were predicted earlier through numerical studies, resulted from the use of a particularly shallow rippled-wall waveguide [slow wave structure (SWS)] that was installed in an experiment to diagnose pulse shortening in a long-pulse electron beam-driven high-power microwave (HPM) source. This SWS was necessary to accommodate laser interferometry measurements along the SWS during the course of microwave generation. Since those early experiments, we have studied this regime in greater detail using two different SWS lengths. We have invoked time-frequency analysis, the smoothed-pseudo Wigner-Ville distribution in particular, to interpret the heterodyned signals of the radiated power measurements. These recent results are consistent with earlier theoretical predictions for the onset and voltage scaling for this instability. This paper presents data for a relativistic BWO operating in the single-frequency regime for two axial modes, operating in the cross-excitation regime, and discusses the interpretation of the data, as well as the methodology used for its analysis. Although operation in the cross-excitation regime is typically avoided due to its poorer efficiency, it may prove useful for future HPM effects studies