Markov Properties of Electrical Discharge Current Fluctuations in Plasma

Using the Markovian method, we study the stochastic nature of electrical discharge current fluctuations in the Helium plasma. Sinusoidal trends are extracted from the data set by the Fourier-Detrended Fluctuation analysis and consequently cleaned data is retrieved. We determine the Markov time scale of the detrended data set by using likelihood analysis. We also estimate the Kramers-Moyal’s coefficients of the discharge current fluctuations and derive the corresponding Fokker-Planck equation. In addition, the obtained Langevin equation enables us to reconstruct discharge time series with similar statistical properties compared with the observed in the experiment. We also provide an exact decomposition of temporal correlation function by using Kramers-Moyal’s coefficients. We show that for the stationary time series, the two point temporal correlation function has an exponential decaying behavior with a characteristic correlation time scale. Our results confirm that, there is no definite relation between correlation and Markov time scales. However both of them behave as monotonic increasing function of discharge current intensity. Finally to complete our analysis, the multifractal behavior of reconstructed time series using its Keramers-Moyal’s coefficients and original data set are investigated. Extended self similarity analysis demonstrates that fluctuations in our experimental setup deviates from Kolmogorov (K41) theory for fully developed turbulence regime.     

Recurrence quantification analysis of electrostatic fluctuations in fusion plasmas

We have investigated plasma turbulence at the edge of a tokamak plasma using data from electrostatic potential fluctuations measured in the Brazilian tokamak TCABR. Recurrence quantification analysis has been used to provide diagnostics of the deterministic content of the series. We have focused our analysis on the radial dependence of potential fluctuations and their characterization by recurrence-based diagnostics. Our main result is that the deterministic content of the experimental signals is most pronounced at the external part of the plasma column just before the plasma radius. Since the chaoticity of the signals follows the same trend, we have concluded that the electrostatic plasma turbulence at the tokamak plasma edge can be partially explained by means of a deterministic nonlinear system.     

Correlations and variability in electrical signals related to earthquake activity

Evaluating complex fluctuations in geoelectric time series is an important task not only for earthquake prediction but also for understanding complex processes related to earthquake preparation. Previous studies have reported alterations, such as the emergence of correlated dynamics in geoelectric potentials prior to an important earthquake (EQ). However, the presence of correlations and its relation with variability has not been widely explored. In this work we apply the detrended fluctuation analysis and the multiscale entropy methods to analyze the fluctuations of geoelectric time series monitored in two sites located in Mexico. We systematically calculate the correlation exponents and the sample entropy (S_E) of geoelectric time series. Important differences in the scaling exponents and entropy profiles for several time scales are observed. In particular, a complex behavior, characterized by a high entropy across several scales and crossover in the correlation exponents, is observed in the vicinity of an that occurred on Sept. 14, 1995. Moreover, we compare the changes in the entropy of the original data with their corresponding shuffled version to see whether correlations in the original data are related to variability.     

An observational picture of solar-wind MHD turbulence

Summary A review of the available information on the MHD fluctuations in the solar wind is given. The most general properties of the picture which derives from the satellite measurements are discussed. The very important result which seems to appear is the fact that the low-frequency MHD fluctuations are characteristic of a turbulent state. Clearly this state cannot be represented by the usual models based on the hypothesis of the presence of simple waves in the solar wind. It is then rather natural to suppose that these observational data should be usefully analysed only through the theoretical methods developed to study the strong MHD turbulence. Moreover, this analysis is rather stimulating since the solar wind offers us one of the rare possibilities to have observational tests of the theoretical models of strong MHD turbulence.     

Statistical models for spatial patterns of heavy particles in turbulence

The dynamics of heavy particles suspended in turbulent flows is of fundamental importance for a wide range of questions in astrophysics, atmospheric physics, oceanography, and technology. Laboratory experiments and numerical simulations have demonstrated that heavy particles respond in intricate ways to turbulent fluctuations of the carrying fluid: non-interacting particles may cluster together and form spatial patterns even though the fluid is incompressible, and the relative speeds of nearby particles can fluctuate strongly. Both phenomena depend sensitively on the parameters of the system. This parameter dependence is difficult to model from first principles since turbulence plays an essential role. Laboratory experiments are also very difficult, precisely since they must refer to a turbulent environment. But in recent years it has become clear that important aspects of the dynamics of heavy particles in turbulence can be understood in terms of statistical models where the turbulent fluctuations are approximated by Gaussian random functions with appropriate correlation functions. In this review, we summarise how such statistical-model calculations have led to a detailed understanding of the factors that determine heavy-particle dynamics in turbulence. We concentrate on spatial clustering of heavy particles in turbulence. This is an important question because spatial clustering affects the collision rate between the particles and thus the long-term fate of the system.     

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。     

标量湍流的能量传输特性

应用直接数值模拟数据,从标量湍流传输的三波关系出发,进行湍流及标量湍流传输谱的多尺度分析,研究不同尺度间的能量传输性质,证实标量能量的传输与湍动能传输具有不同性质,大尺度速度脉动对标量传输有较大贡献,尤其是与标量小尺度脉动的相互作用,使标量模拟需要有比速度场更高的网格分辨率;并发现标量湍流的能量传输具有明显的非局部性;另外,定义了能量传输系数,发现在相同的Re数和Pe数条件下,标量湍流的对流惯性较速度脉动的惯性子区宽.     

Statistical physics and physiology: monofractal and multifractal approaches.

Even under healthy, basal conditions, physiologic systems show erratic fluctuations resembling those found in dynamical systems driven away from a single equilibrium state. Do such "nonequilibrium" fluctuations simply reflect the fact that physiologic systems are being constantly perturbed by external and intrinsic noise? Or, do these fluctuations actually, contain useful, "hidden" information about the underlying nonequilibrium control mechanisms? We report some recent attempts to understand the dynamics of complex physiologic fluctuations by adapting and extending concepts and methods developed very recently in statistical physics. Specifically, we focus on interbeat interval variability as an important quantity to help elucidate possibly non-homeostatic physiologic variability because (i) the heart rate is under direct neuroautonomic control, (ii) interbeat interval variability is readily measured by noninvasive means, and (iii) analysis of these heart rate dynamics may provide important practical diagnostic and prognostic information not obtainable with current approaches. The analytic tools we discuss may be used on a wider range of physiologic signals. We first review recent progress using two analysis methods--detrended fluctuation analysis and wavelets--sufficient for quantifying monofractual structures. We then describe recent work that quantifies multifractal features of interbeat interval series, and the discovery that the multifractal structure of healthy subjects is different than that of diseased subjects.     

Allan deviation analysis of financial return series

We perform a scaling analysis for the return series of different financial assets applying the Allan deviation (ADEV), which is used in the time and frequency metrology to characterize quantitatively the stability of frequency standards since it has demonstrated to be a robust quantity to analyze fluctuations of non-stationary time series for different observation intervals. The data used are opening price daily series for assets from different markets during a time span of around ten years. We found that the ADEV results for the return series at short scales resemble those expected for an uncorrelated series, consistent with the efficient market hypothesis. On the other hand, the ADEV results for absolute return series for short scales (first one or two decades) decrease following approximately a scaling relation up to a point that is different for almost each asset, after which the ADEV deviates from scaling, which suggests that the presence of clustering, long-range dependence and non-stationarity signatures in the series drive the results for large observation intervals.     

Effect of non-Kolmogorov turbulence on beam spreading in satellite laser communication

In the past half a century, satellite laser communication has caught the attention of scientists due to its distinct advantages in comparison with conventional satellite microwave communication. For ground-to-satellite and satellite-to-ground data links, the atmosphere is a part of the communication channel; thus, atmospheric turbulence severely degrades the performance of satellite laser communication systems. In general, the Kolmogorov turbulence model is used to study the effect of atmosphere turbulence on satellite laser communications since it has been confirmed by numerous direct measurements of temperature and humidity fluctuations in the atmospheric boundary layer. However, increasing experimental evidence and theoretical investigations have shown that the Kolmogorov theory is sometimes inadequate to describe atmospheric statistics properly, in particular, in some domains of the atmosphere. We analyze the joint influence of Kolmogorov turbulence from the ground to 6 km and non-Kolmogorov turbulence above 6 km on the spot size associated with the uplink and downlink propagation channels for a satellite laser communication system in the geosynchronous orbit, using a power spectrum of non-Kolmogorov turbulence with power law ?5 that describes the refractiveindex fluctuations in the atmosphere above 6 km and considering the combined power spectrum of Kolmogorov and non-Kolmogorov turbulence. Before this analysis, we study the joint influence of the Kolmogorov turbulence from the ground to 6 km and non-Kolmogorov turbulence above 6 km on the scintillation indices of laser beams.     

Effect of non-kolmogorov turbulence on angle-of-arrival fluctuations of starlight

We revised a non-Kolmogorov turbulent power spectrum for the refractive-index fluctuations based on the consistency between the structure function and its power spectrum and the experimental data of recent lidar measurements. We investigate the joint influence of Kolmogorov turbulence from the ground up to 6 km and non-Kolmogorov turbulence above 6 km on the fluctuations in the angle of arrival (AOA) of starlight. WE show that the AOA fluctuations of starlight are mainly determined by Kolmogorov turbulence nearby the receiver. Non-Kolmogorov turbulence is responsible for 20–40% of the total AOA fluctuations for different apertures of the receiver. In addition, the AOA fluctuations induced by non-Kolmogorov turbulence depend on the receiver aperture, outer scale, and intensity of non-Kolmogorov turbulence.     

Approaching complexity by stochastic methods: From biological systems to turbulence

This review addresses a central question in the field of complex systems: given a fluctuating (in time or space), sequentially measured set of experimental data, how should one analyze the data, assess their underlying trends, and discover the characteristics of the fluctuations that generate the experimental traces? In recent years, significant progress has been made in addressing this question for a class of stochastic processes that can be modeled by Langevin equations, including additive as well as multiplicative fluctuations or noise. Important results have emerged from the analysis of temporal data for such diverse fields as neuroscience, cardiology, finance, economy, surface science, turbulence, seismic time series and epileptic brain dynamics, to name but a few. Furthermore, it has been recognized that a similar approach can be applied to the data that depend on a length scale, such as velocity increments in fully developed turbulent flow, or height increments that characterize rough surfaces. A basic ingredient of the approach to the analysis of fluctuating data is the presence of a Markovian property, which can be detected in real systems above a certain time or length scale. This scale is referred to as the Markov-Einstein (ME) scale, and has turned out to be a useful characteristic of complex systems. We provide a review of the operational methods that have been developed for analyzing stochastic data in time and scale. We address in detail the following issues: (i) reconstruction of stochastic evolution equations from data in terms of the Langevin equations or the corresponding Fokker-Planck equations and (ii) intermittency, cascades, and multiscale correlation functions.     

Intermittent distribution of inertial particles in turbulent flows

We consider inertial particles suspended in an incompressible turbulent flow. Because of particles' inertia their flow is compressible, which leads to fluctuations of concentration significant for heavy particles. We show that the statistics of these fluctuations is independent of details of the velocity statistics, which allows us to predict that the particles cluster on the viscous scale of turbulence and describe the probability distribution of concentration fluctuations. We discuss the possible role of the clustering in the physics of atmospheric aerosols, in particular, in cloud formation.     

Structural ion-sound plasma turbulence as a self-similar random process

It is shown that the experimentally investigated structural ion-sound plasma turbulence is a self-similar stationary random process. The self-similarity parameter is determined by two temporal laws: the nonrandom character of the appearance of nonlinear structures (nonlinear ion-sound solitons) in the plasma, and the nonlinear interaction between them. As the distance from the threshold of the ion-sound current instability increases, the self-similar random process approaches a Gaussian random process, but this limit has not been attained experimentally. The possibility of recording superlong time series of the fluctuations of the signal of the plasma process and processing of the time series by the R/S analysis method has made it possible to prove self-similarity of the plasma structural turbulence. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 3, 203–208 (10 August 1999)     

On‐line Determination of Aggregate Size and Morphology in Suspensions

Information concerning the aggregation state of fine solid particles is an important element for process control and monitoring of product quality in many applications of industrial slurries. This work deals with the application of different in‐line methods to the characterization of silica aggregate size and morphology. All of these methods exploit turbidity signals, obtained by various means including: from analysis of turbidity fluctuations in homogeneous suspension and from overall turbidity decrease during particle settling. This work also presents the opportunity to report progress in morphological and optical models of small aggregates. As a result of these models, the morphological characteristics of the aggregates along with the number of their constituting particles are derived from experimental results. Similarities between the different methods are examined and discussed.     

Characterizing and modelling cyclic behaviour in non-stationary time series through multi-resolution analysis

A method based on wavelet transform is developed to characterize variations at multiple scales in non-stationary time series. We consider two different financial time series, S&P CNX Nifty closing index of the National Stock Exchange (India) and Dow Jones industrial average closing values. These time series are chosen since they are known to comprise of stochastic fluctuations as well as cyclic variations at different scales. The wavelet transform isolates cyclic variations at higher scales when random fluctuations are averaged out; this corroborates correlated behaviour observed earlier in financial time series through random matrix studies. Analysis is carried out through Haar, Daubechies-4 and continuous Morlet wavelets for studying the character of fluctuations at different scales and show that cyclic variations emerge at intermediate time scales. It is found that Daubechies family of wavelets can be effectively used to capture cyclic variations since these are local in nature. To get an insight into the occurrence of cyclic variations, we then proceed to model these wavelet coefficients using genetic programming (GP) approach and using the standard embedding technique in the reconstructed phase space. It is found that the standard methods (GP as well as artificial neural networks) fail to model these variations because of poor convergence. A novel interpolation approach is developed that overcomes this difficulty. The dynamical model equations have, primarily, linear terms with additive Padé-type terms. It is seen that the emergence of cyclic variations is due to an interplay of a few important terms in the model. Very interestingly GP model captures smooth variations as well as bursty behaviour quite nicely.      

Spectral line shapes modeling in turbulent plasmas

In this work we investigate the influence of low frequency turbulence on Doppler spectral line shapes in magnetized plasmas. Low frequency refers here to fluctuations whose typical time scale is much larger than those characterizing the atomic processes, such as radiative decay, collisions and charge exchange. This ordering is in particular relevant for drift wave turbulence, ubiquitous in edge plasmas of fusion devices. Turbulent fluctuations are found to affect line shapes through both the spatial and time averages introduced by the measurement process. The profile is expressed in terms of the fluid fields describing the plasma. Assuming the spectrometer acquisition time to be much larger than the turbulent time scale, an ordering generally fulfilled in experiments, allows to develop a statistical formalism. We proceed by successively investigating the effects of density, fluid velocity and temperature fluctuations on the Doppler profile of a spectral line emitted by a charge exchange population of neutrals. Line shapes, and especially line wings are found to be affected by ion temperature or fluid velocity fluctuations, and can in some cases exhibit a power-law behavior. These effects are shown to be measurable with existing techniques, and their interpretation in each particular case would rely on already existing tools. From a fundamental point of view, this study gives some insights in the appearance of non-Boltzmann statistics, such as Lévy statistics, when dealing with averaged experimental data.     

Fluctuation analysis of meteo-marine data

We study long-term behaviour of air temperature, wave heights and wind speed time series recorded for the period 1993–1997 at a meteo-marine station located in the Adriatic Sea. The scaling analysis shows that fluctuations of air temperature display long-range autocorrelations, while those for wave heights show a more complex behaviour, crossing over from a persistent regime at intermediate time scales (up to about 20 days) to an anti-persistence behaviour at longer times. Furthermore, the crosscorrelations of their records are found to be large, with a covariance of about -0.3 (indicating anti-crosscorrelations) within the full 5-years period, giving a quantitative measure of the actual coupling between the two data sets. Wind speed fluctuations are found to be strongly crosscorrelated (about 0.6) with those of wave heights, indicating as expected that wind is the main driving force for wave height fluctuations.     

Order parameter analysis of seismicity of the Mexican Pacific coast

The natural time domain has shown to be an important tool to obtain relevant information hidden in time series of complex systems not easily obtainable by means of standard analysis methods. By assuming that tectonism is a complex system and that earthquakes are similar to a phase transition, it is possible to define an order parameter for seismicity in the context of the natural time domain. In this work we analyze the statistical features of the order parameter (OP) computed for the seismic Mexican catalog spanning from 1974 to 2012. We found that in four out of the six regions the pdf of the order parameter fluctuations is similar with that earlier reported by other authors, but in two of these regions noticeable differences are identified. Also, except for Michoacán, the scaled pdfs analysis of all regions collapse on a universal curve with non-Gaussian tails.     

A Markov model of financial returns

We address the general problem of how to quantify the kinematics of time series with stationary first moments but having non stationary multifractal long-range correlated second moments. We show that a Markov process is sufficient to model important aspects of the multifractality observed in financial time series and propose a kinematic model of price fluctuations. We test the proposed model by analyzing index closing prices of the New York Stock Exchange and the DEM/USD tick-by-tick exchange rates obtained from Reuters EFX. We show that the model captures the characteristic features observed in actual financial time series, including volatility clustering, time scaling and fat tails in the probability density functions, power-law behavior of volatility correlations and, most importantly, the observed nonuniversal multifractal singularity spectrum. Motivated by our finding of strong agreement between the model and the data, we argue that at least two independent stochastic Gaussian variables are required to adequately model price fluctuations.