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.     

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.     

基于长程相关性特征的北京气候中心气候系统模式对中国气温的模拟性能评估

传统对数值模式模拟效果的评估主要是基于均值、趋势、概率密度分布、极值等方面的特征比较模拟要素与观测值的差异或是通过分析模拟值与观测值之间的相关性来定量判断.这类评估方法主要考虑了模式模拟结果与观测资料在统计上的差异,缺乏对两者在动力学特征上的比较.鉴于此,本文基于气象观测资料演变过程中所展现的长程相关性特征,利用去趋势波动分析方法对观测资料和模式模拟数据进行标度分析,研究模式模拟结果是否具有类似于观测资料中的长程相关性特征,进而通过比较观测资料和模式模拟结果的标度指数,从大气演变的内在动力学特征上对模式模拟性能进行评估.本文对北京气候中心气候系统模式对中国地表气温的模拟性能进行了评估,结果表明,该模式能够较好地反映出中国区域气温要素的长程相关性特征,对东北、西北中东部、江淮、江南东部等地模拟效果较好,但对于青藏高原地区及西北大部、华北、黄淮等地的模拟效果相对较差,其中对青藏高原地区和西北西部的模拟效果最差.     

Preservation of long range temporal correlations under extreme random dilution

Many natural time series exhibit long range temporal correlations that may be characterized by power-law scaling exponents. However, in many cases, the time series have uneven time intervals due to, for example, missing data points, noisy data, and outliers. Here we study the effect of randomly missing data points on the power-law scaling exponents of time series that are long range temporally correlated. The Fourier transform and detrended fluctuation analysis (DFA) techniques are used for scaling exponent estimation. We find that even under extreme dilution of more than 50%, the value of the scaling exponent remains almost unaffected. Random dilution is also applied on heart interbeat interval time series. It is found that dilution of 70%-80% of the data points leads to a reduction of only 8% in the scaling exponent; it is also found that it is possible to discriminate between healthy and heart failure subjects even under extreme dilution of more than 90%.     

A multifractal detrended fluctuation analysis of trading behavior of individual and institutional traders in Tehran stock market

Employing the multifractal detrended fluctuation analysis (MF-DFA), the multifractal properties of trading behavior of individual and institutional traders in the Tehran Stock Exchange (TSE) are numerically investigated. Using daily trading volume time series of these two categories of traders, the scaling exponents, generalized Hurst exponents, generalized fractal dimensions and singularity spectrum are derived. Furthermore, two main sources of multifractality, i.e. temporal correlations and fat-tailed probability distributions are also examined. We also compare our results with data of S&P 500. Results of this paper suggest that for both classes of investors in TSE, multifractality is mainly due to long-range correlation while for S&P 500, the fat-tailed probability distribution is the main source of multifractality.     

Global climate models violate scaling of the observed atmospheric variability

We test the scaling performance of seven leading global climate models by using detrended fluctuation analysis. We analyze temperature records of six representative sites around the globe simulated by the models, for two different scenarios: (i) with greenhouse gas forcing only and (ii) with greenhouse gas plus aerosol forcing. We find that the simulated records for both scenarios fail to reproduce the universal scaling behavior of the observed records and display wide performance differences. The deviations from the scaling behavior are more pronounced in the first scenario, where also the trends are clearly overestimated.     

Scaling of fluctuations and critical exponents

We present a new technique to describe the abnormal behavior of certain fluctuation observables in the critical regime of quantum statistical systems which undergo a phase transition. The idea is to rescale the local fluctuation operators by a relevant external parameter of the system, in addition to the usual scaling with the inverse square root of the volume. The scaling indices used in this scaling procedure are directly related to the critical exponents. Furthermore, it is explained that this new method of scaling preserves the CCR structure of the algebra of macroscopic fluctuations. Finally, scaling indices are computed for the relevant microscopic observables at all temperatures in a mean field approximation for a quantum anharmonic crystal. These indices yield the same critical exponents as predicted by mean field theory.     

Novel scaling behavior of the Ising model on curved surfaces

We demonstrate the nontrivial scaling behavior of Ising models defined on (i) a donut-shaped surface and (ii) a curved surface with a constant negative curvature. By performing Monte Carlo simulations, we find that the former model has two distinct critical temperatures at which both the specific heat C(T) and magnetic susceptibility χ(T) show sharp peaks. The critical exponents associated with the two critical temperatures are evaluated by the finite-size scaling analysis; the result reveals that the values of these exponents vary depending on the temperature range under consideration. In the case of the latter model, it is found that static and dynamic critical exponents deviate from those of the Ising model on a flat plane; this is a direct consequence of the constant negative curvature of the underlying surface.     

Lorenz系统长程相关性研究

以典型的混沌系统——Lorenz系统为研究对象,运用去趋势涨落分析方法对不同初值和不同参数条件下系统的长程相关性进行研究.结果表明：系统长程相关性与系统初值所处相空间位置有关,初值越靠近不稳定平衡点,系统长程相关性越强,其标度指数α就越大,系统可预测性也就越好.当系统完全处于混沌状态时,随着控制参数r逐步增大其动力学结构的混沌特性更加明显,标度指数α都呈下降趋势,系统长程相关性逐渐减弱,系统可预测性也随之减弱.这揭示了长程相关性与系统可预测性的对应关系.对系统进行 关键词： Lorenz系统 长程相关性 去趋势涨落分析 可预测性     

Critical line broadening of the EPR in the two-dimensional antiferromagnet crystals Rb2MnCl4 and Rb2Mn0,8Cd0,2Cl4

The EPR spectrum of quasi-two-dimensional antiferromagnets Rb₂Mn_xCd_1?xCl₄ (x=1,0; 0,8) has been studied in a critical temperature range. Two theoretical approaches - the scaling theory and the soliton's theory - are used to explain experimental data on temperature of the EPR linewidth. In the first interpretation critical exponents are determined. For both crystal two temperature regions with different critical exponents are found. It is shown that the soliton's theory with an anomaleous great excitement energy describes the experimental data satisfactory.     

Space-magnitude dependent scaling behaviour in seismic interevent series revealed by detrended fluctuation analysis

The scaling behaviour of the 1981-2007 seismicity data in central Italy, which is one of the most seismically active areas in Italy is investigated. In particular we examined the earthquakes located in a circular area centred on the epicentre of the strongest event, occurred in September 26, 1997 (duration magnitude M_D=5.8). On the base of the detrended fluctuation analysis (DFA), we found that in the magnitude range between 2.5 and 2.9 the scaling exponents fall into disjoint sets for events relatively close and far from the epicentre of the strongest event.     

Self-affine analysis of protein energy

We study the time series of the total energy of polypeptides and proteins. These time series were generated by molecular dynamics methods and analyzed by applying detrended fluctuation analysis to estimate the long-range power-law correlation, i.e. to measure scaling exponents α. Such exponents were calculated for all systems and their values follow environment conditions, i.e., they are temperature dependent and also, in a continuum medium approach, vary according to the dielectric constants (we simulated ?=2 and ?=80). The procedure was applied to investigate polyalanines, and other realistic models of proteins (Insect Defensin A and Hemoglobin). The present findings exhibit results that are consistent with previous ones obtained by other methodologies.     

Scaling relationship between effective critical exponents throughout the crossover region in thin Ising films

The Monte Carlo (MC) approach is used to check the validity of the scaling relationship for the effective critical exponents in thin Ising films. We investigate this relationship not just in the critical region but throughout the crossover to the expected two-dimensional behavior. Our results indicate that this scaling relationship is very well-fulfilled throughout the entire crossover temperature region, as predicted by a previous renormalization group analysis. The two-dimensional universality class of Ising films is confirmed by means of data collapsing plots for plates with increasing L, up to L=100. The evolution of the maximum value of the effective critical exponents with film thickness is discussed. Received 22 April 1999     

非Kolmogorov大气湍流温度谱标度指数的测量与分析

 阐述了非Kolmogorov湍流谱理论以及湍流谱标度指数的测量与计算方法。在近地面多个地点对大气湍流温度起伏进行了多次的实验观测，结果表明：实际大气湍流温度谱标度指数多数不等于-5/3，并且通常在-2到-1之间变化。分析了湍流温度谱标度指数与湍流发展程度的相关性，利用小波分析方法展现了不同湍流强度下湍流温度脉动能量在各尺度之间的分配状态，发现湍流温度谱标度指数的绝对值在一定程度上随湍流强度的增加而增大。     

Computer simulation of the critical behavior of 3D disordered ising model

The critical behavior of the disordered ferromagnetic Ising model is studied numerically by the Monte Carlo method in a wide range of variation of concentration of nonmagnetic impurity atoms. The temperature dependences of correlation length and magnetic susceptibility are determined for samples with various spin concentrations and various linear sizes. The finite-size scaling technique is used for obtaining scaling functions for these quantities, which exhibit a universal behavior in the critical region; the critical temperatures and static critical exponents are also determined using scaling corrections. On the basis of variation of the scaling functions and values of critical exponents upon a change in the concentration, the conclusion is drawn concerning the existence of two universal classes of the critical behavior of the diluted Ising model with different characteristics for weakly and strongly disordered systems.     

两组份复合材料光学非线性性质的临界行为

对两组份非线性复合材料的光学非线性性质的临界行为进行了研究。考虑第一组份为非线性材料,其电流、电压间服从I=g1V x1V^β关系;而第二组份为线性材料,电流、电压间满足I—g2V,其中g1,x1是第一组份的线性电导和光学非线性极化率,g2是第二组份的线性电导,β是第一组份材料的光学非线性指数。分别采用了有效介质近似和相对电阻涨落的标度理论两种方法计算了系统有效响应的临界指数随光学非线性指数及维数的变化规律。用不同的方法得到系统的有效线性电导g和有效光学非线性极化率xe(β)的临界指数M(β)和N(β)的结论也不同。有效介质近似得到M(β)=1和N(β)=(β 1)/2,即M(β)与β和d都无关,而N(β)只与有β关而与d无关;而相对电阻涨落标度理论方法得到的M(β)和N(β)与β和d都有关。     

Low-frequency dielectric response in the quasi-one-dimensional organic conductor (TMTSF)2PF6

A unique and rare opportunity of revealing the nature of the spin-density-wave (SDW) fluctuation in the quasi-one-dimensional organic conductor (TMTSF)₂PF₆ has been provided by our AC impedance measurements above the SDW transition temperature. A close resemblance of the low-frequency dielectric response in the range between 20 K and the temperature of maximum resistivity T_max ∼ 80 K to that in the SDW ground state was revealed, with quite compatible exponents for their power law dependencies. The SDW fluctuation has thus been identified in the 2D Fermi liquid regime, which can be regarded as a precursor phase of the SDW ground state.     

Long-range correlations in two-dimensional spatio-temporal seismic fluctuations

We analysed the scaling behaviour of the two-dimensional (2-D) sequence (Δs, Δt) of the 1981–1998 southern California seismicity, where Δs is the distance between two consecutive earthquakes (jump) and Δt is their interevent interval. The 2-D seismic spatio-temporal fluctuations were investigated by means of the detrended fluctuation analysis (DFA), well-known methodology used to detect scaling behaviour in observational time series possibly affected by nonstationarities. The estimated scaling exponents α_DFA, larger than 0.5, indicate the presence of persistent long-range correlations in the 2-D sequence analysed. The variation of the scaling exponent with the increase of threshold magnitude shows a two-fold behaviour: in the range between 1.5 (the completeness magnitude of the catalog) and 3.0, the scaling exponent is quite constant and denoting a flicker-noise dynamics; while for magnitudes larger than 3.0 it decreases with the increase of magnitude, indicating a tendency toward a 2-D space–time Poissonian process for large events.