Chaotic diffusion caused by close encounters with several massive asteroids The (4) Vesta case

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

DFA e análise de agrupamento aplicadas a perfis de porosidade neutrônico em poços de petróleo

Peng was the first to work with the Technical DFA (Detrended Fluctuation Analysis), a tool capable of detecting auto-long-range correlation in time series with non-stationary. In this study, the technique of DFA is used to obtain the Hurst exponent (H) profile of the electric neutron porosity of the 52 oil wells in Namorado Field, located in the Campos Basin -Brazil. The purpose is to know if the Hurst exponent can be used to characterize spatial distribution of wells. Thus, we verify that the wells that have close values of H are spatially close together. In this work we used the method of hierarchical clustering and non-hierarchical clustering method (the k-mean method). Then compare the two methods to see which of the two provides the best result. From this, was the parameter � (index neighborhood) which checks whether a data set generated by the k- average method, or at random, so in fact spatial patterns. High values of � indicate that the data are aggregated, while low values of � indicate that the data are scattered (no spatial correlation). Using the Monte Carlo method showed that combined data show a random distribution of � below the empirical value. So the empirical evidence of H obtained from 52 wells are grouped geographically. By passing the data of standard curves with the results obtained by the k-mean, confirming that it is effective to correlate well in spatial distribution

Rescaled range analysis of pluviometric records in SA o pound Paulo State, Brazil

This paper presents an analysis of pluviometric precipitation time series obtained from 45 data collection points, with daily rain measurements (in mm), from 45 counties within the nine climatic regions of the state of SA o pound Paulo, mostly for the period of 1950-1997. SA o pound Paulo State (Brazil) is situated between the inter-tropical climatic zone, dominated by tropical and equatorial masses, and the sub-tropical climatic zone controlled by tropical and polar air masses. Due to this location the State can be divided into three climatic zones: south-east and south-west, which are permanently humid, and north with a well defined dry period. Rescaled range analysis, or R/S analysis, has been used to investigate the scale properties of the time series. We found two clear values for the Hurst exponent, one for a period of 10 to 200 days (H(1)), and another for a period above 210 days (H(2)). The value of H(1) lies between 0.6 to 0.7 for all climatic zones indicating characteristics of persistence. However, H(2) is (i) close to 0.5 for the littoral area, showing random characteristics, (ii) close to 0.6 for mountain areas, indicating persistence characteristics, and (iii) close to 0.4 for the plane area, irrespective of whether the climate is dry or humid, and shows anti-persistence characteristics.

Fractal concepts in relation to soil water diffusivity

Fractal geometry would appear to offer promise for new insight on water transport in unsaturated soils, This study was conducted to evaluate possible fractal influence on soil water diffusivity, and/or the relationships from which it arises, for several different soils, Fractal manifestations, consisting of a time-dependent diffusion coefficient and anomalous diffusion arising out of fractional Brownian motion, along with the notion of space-filling curves were gleaned from the literature, It was found necessary to replace the classical Boltzmann variable and its time t(1/2) factor with the basic fractal power function and its t(n) factor, For distinctly unsaturated soil water content theta, exponent n was found to be less than 1/2, but it approached 1/2 as theta approached its sated value, This function n = n(theta), in giving rise to a time-dependent, anomalous soil water diffusivity D, was identified with the Hurst exponent H of fractal geometry, Also, n approaching 1/2 at high water content is a behavior that makes it possible to associate factal space filling with soil that approaches water saturation, Finally, based on the fractally interpreted n = n(theta), the coalescence of both D and 8 data is greatly improved when compared with the coalescence provided by the classical Boltzmann variable.

Sensitivity, specificity and predictive values of linear and nonlinear indices of heart rate variability in stable angina patients

Background: Decreased heart rate variability (HRV) is related to higher morbidity and mortality. In this study we evaluated the linear and nonlinear indices of the HRV in stable angina patients submitted to coronary angiography. Methods. We studied 77 unselected patients for elective coronary angiography, which were divided into two groups: coronary artery disease (CAD) and non-CAD groups. For analysis of HRV indices, HRV was recorded beat by beat with the volunteers in the supine position for 40 minutes. We analyzed the linear indices in the time (SDNN [standard deviation of normal to normal], NN50 [total number of adjacent RR intervals with a difference of duration greater than 50ms] and RMSSD [root-mean square of differences]) and frequency domains ultra-low frequency (ULF) ≤ 0,003 Hz, very low frequency (VLF) 0,003 - 0,04 Hz, low frequency (LF) (0.04-0.15 Hz), and high frequency (HF) (0.15-0.40 Hz) as well as the ratio between LF and HF components (LF/HF). In relation to the nonlinear indices we evaluated SD1, SD2, SD1/SD2, approximate entropy (-ApEn), α1, α2, Lyapunov Exponent, Hurst Exponent, autocorrelation and dimension correlation. The definition of the cutoff point of the variables for predictive tests was obtained by the Receiver Operating Characteristic curve (ROC). The area under the ROC curve was calculated by the extended trapezoidal rule, assuming as relevant areas under the curve ≥ 0.650. Results: Coronary arterial disease patients presented reduced values of SDNN, RMSSD, NN50, HF, SD1, SD2 and -ApEn. HF ≤ 66 ms§ssup§2§esup§, RMSSD ≤ 23.9 ms, ApEn ≤-0.296 and NN50 ≤ 16 presented the best discriminatory power for the presence of significant coronary obstruction. Conclusion: We suggest the use of Heart Rate Variability Analysis in linear and nonlinear domains, for prognostic purposes in patients with stable angina pectoris, in view of their overall impairment. © 2012 Pivatelli et al.; licensee BioMed Central Ltd.

Poincaré plot indexes of heart rate variability: Relationships with other nonlinear variables

The Poincaré plot for heart rate variability analysis is a technique considered geometrical and non-linear, that can be used to assess the dynamics of heart rate variability by a representation of the values of each pair of R-R intervals into a simplified phase space that describes the system's evolution. The aim of the present study was to verify if there is some correlation between SD1, SD2 and SD1/SD2 ratio and heart rate variability nonlinear indexes either in disease or healthy conditions. 114 patients with arterial coronary disease and 65 healthy subjects underwent 30. minute heart rate registration, in supine position and the analyzed indexes were as follows: SD1, SD2, SD1/SD2, Sample Entropy, Lyapunov Exponent, Hurst Exponent, Correlation Dimension, Detrended Fluctuation Analysis, SDNN, RMSSD, LF, HF and LF/HF ratio. Correlation coefficients between SD1, SD2 and SD1/SD2 indexes and the other variables were tested by the Spearman rank correlation test and a regression analysis. We verified high correlation between SD1/SD2 index and HE and DFA (α1) in both groups, suggesting that this ratio can be used as a surrogate variable. © 2013 Elsevier B.V.

Weakly anomalous diffusion with non-Gaussian propagators

A poorly understood phenomenon seen in complex systems is diffusion characterized by Hurst exponent H approximate to 1/2 but with non-Gaussian statistics. Motivated by such empirical findings, we report an exact analytical solution for a non-Markovian random walk model that gives rise to weakly anomalous diffusion with H = 1/2 but with a non-Gaussian propagator.

Alzheimer random walk model: Two previously overlooked diffusion regimes

A non-Markovian one-dimensional random walk model is studied with emphasis on the phase-diagram, showing all the diffusion regimes, along with the exactly determined critical lines. The model, known as the Alzheimer walk, is endowed with memory-controlled diffusion, responsible for the model's long-range correlations, and is characterized by a rich variety of diffusive regimes. The importance of this model is that superdiffusion arises due not to memory per se, but rather also due to loss of memory. The recently reported numerically and analytically estimated values for the Hurst exponent are hereby reviewed. We report the finding of two, previously overlooked, phases, namely, evanescent log-periodic diffusion and log-periodic diffusion with escape, both with Hurst exponent H = 1/2. In the former, the log-periodicity gets damped, whereas in the latter the first moment diverges. These phases further enrich the already intricate phase diagram. The results are discussed in the context of phase transitions, aging phenomena, and symmetry breaking.

Sensitivity, specificity and predictive values of linear and nonlinear indices of heart rate variability in stable angina patients

Abstract Background Decreased heart rate variability (HRV) is related to higher morbidity and mortality. In this study we evaluated the linear and nonlinear indices of the HRV in stable angina patients submitted to coronary angiography. Methods We studied 77 unselected patients for elective coronary angiography, which were divided into two groups: coronary artery disease (CAD) and non-CAD groups. For analysis of HRV indices, HRV was recorded beat by beat with the volunteers in the supine position for 40 minutes. We analyzed the linear indices in the time (SDNN [standard deviation of normal to normal], NN50 [total number of adjacent RR intervals with a difference of duration greater than 50ms] and RMSSD [root-mean square of differences]) and frequency domains ultra-low frequency (ULF) ≤ 0,003 Hz, very low frequency (VLF) 0,003 – 0,04 Hz, low frequency (LF) (0.04–0.15 Hz), and high frequency (HF) (0.15–0.40 Hz) as well as the ratio between LF and HF components (LF/HF). In relation to the nonlinear indices we evaluated SD1, SD2, SD1/SD2, approximate entropy (−ApEn), α1, α2, Lyapunov Exponent, Hurst Exponent, autocorrelation and dimension correlation. The definition of the cutoff point of the variables for predictive tests was obtained by the Receiver Operating Characteristic curve (ROC). The area under the ROC curve was calculated by the extended trapezoidal rule, assuming as relevant areas under the curve ≥ 0.650. Results Coronary arterial disease patients presented reduced values of SDNN, RMSSD, NN50, HF, SD1, SD2 and -ApEn. HF ≤ 66 ms2, RMSSD ≤ 23.9 ms, ApEn ≤−0.296 and NN50 ≤ 16 presented the best discriminatory power for the presence of significant coronary obstruction. Conclusion We suggest the use of Heart Rate Variability Analysis in linear and nonlinear domains, for prognostic purposes in patients with stable angina pectoris, in view of their overall impairment.

Topological invariance and spatial scaling of surface roughness in two highly eroded zones of Mexico: a comparative study

The Fractal Image Informatics toolbox (Oleschko et al., 2008 a; Torres-Argüelles et al., 2010) was applied to extract, classify and model the topological structure and dynamics of surface roughness in two highly eroded catchments of Mexico. Both areas are affected by gully erosion (Sidorchuk, 2005) and characterized by avalanche-like matter transport. Five contrasting morphological patterns were distinguished across the slope of the bare eroded surface of Faeozem (Queretaro State) while only one (apparently independent on the slope) roughness pattern was documented for Andosol (Michoacan State). We called these patterns ?the roughness clusters? and compared them in terms of metrizability, continuity, compactness, topological connectedness (global and local) and invariance, separability, and degree of ramification (Weyl, 1937). All mentioned topological measurands were correlated with the variance, skewness and kurtosis of the gray-level distribution of digital images. The morphology0 spatial dynamics of roughness clusters was measured and mapped with high precision in terms of fractal descriptors. The Hurst exponent was especially suitable to distinguish between the structure of ?turtle shell? and ?ramification? patterns (sediment producing zone A of the slope); as well as ?honeycomb? (sediment transport zone B) and ?dinosaur steps? and ?corals? (sediment deposition zone C) roughness clusters. Some other structural attributes of studied patterns were also statistically different and correlated with the variance, skewness and kurtosis of gray distribution of multiscale digital images. The scale invariance of classified roughness patterns was documented inside the range of five image resolutions. We conjectured that the geometrization of erosion patterns in terms of roughness clustering might benefit the most semi-quantitative models developed for erosion and sediment yield assessments (de Vente and Poesen, 2005).

Are European equity markets efficient? New evidence from fractal analysis

We report an empirical analysis of long-range dependence in the returns of eight stock market indices, using the Rescaled Range Analysis (RRA) to estimate the Hurst exponent. Monte Carlo and bootstrap simulations are used to construct critical values for the null hypothesis of no long-range dependence. The issue of disentangling short-range and long-range dependence is examined. Pre-filtering by fitting a (short-range) autoregressive model eliminates part of the long-range dependence when the latter is present, while failure to pre-filter leaves open the possibility of conflating short-range and long-range dependence. There is a strong evidence of long-range dependence for the small central European Czech stock market index PX-glob, and a weaker evidence for two smaller western European stock market indices, MSE (Spain) and SWX (Switzerland). There is little or no evidence of long-range dependence for the other five indices, including those with the largest capitalizations among those considered, DJIA (US) and FTSE350 (UK). These results are generally consistent with prior expectations concerning the relative efficiency of the stock markets examined. © 2011 Elsevier Inc.

O paradoxo da superdifusão de uma caminhada aleatória com memória exponencial

The random walk models with temporal correlation (i.e. memory) are of interest in the study of anomalous diffusion phenomena. The random walk and its generalizations are of prominent place in the characterization of various physical, chemical and biological phenomena. The temporal correlation is an essential feature in anomalous diffusion models. These temporal long-range correlation models can be called non-Markovian models, otherwise, the short-range time correlation counterparts are Markovian ones. Within this context, we reviewed the existing models with temporal correlation, i.e. entire memory, the elephant walk model, or partial memory, alzheimer walk model and walk model with a gaussian memory with profile. It is noticed that these models shows superdiffusion with a Hurst exponent H > 1/2. We study in this work a superdiffusive random walk model with exponentially decaying memory. This seems to be a self-contradictory statement, since it is well known that random walks with exponentially decaying temporal correlations can be approximated arbitrarily well by Markov processes and that central limit theorems prohibit superdiffusion for Markovian walks with finite variance of step sizes. The solution to the apparent paradox is that the model is genuinely non-Markovian, due to a time-dependent decay constant associated with the exponential behavior. In the end, we discuss ideas for future investigations.

Análise de DFA e de agrupamento do perfil de densidade de poços de petróleo

In recent years, the DFA introduced by Peng, was established as an important tool capable of detecting long-range autocorrelation in time series with non-stationary. This technique has been successfully applied to various areas such as: Econophysics, Biophysics, Medicine, Physics and Climatology. In this study, we used the DFA technique to obtain the Hurst exponent (H) of the profile of electric density profile (RHOB) of 53 wells resulting from the Field School of Namorados. In this work we want to know if we can or not use H to spatially characterize the spatial data field. Two cases arise: In the first a set of H reflects the local geology, with wells that are geographically closer showing similar H, and then one can use H in geostatistical procedures. In the second case each well has its proper H and the information of the well are uncorrelated, the profiles show only random fluctuations in H that do not show any spatial structure. Cluster analysis is a method widely used in carrying out statistical analysis. In this work we use the non-hierarchy method of k-means. In order to verify whether a set of data generated by the k-means method shows spatial patterns, we create the parameter Ω (index of neighborhood). High Ω shows more aggregated data, low Ω indicates dispersed or data without spatial correlation. With help of this index and the method of Monte Carlo. Using Ω index we verify that random cluster data shows a distribution of Ω that is lower than actual cluster Ω. Thus we conclude that the data of H obtained in 53 wells are grouped and can be used to characterize space patterns. The analysis of curves level confirmed the results of the k-means

Comparação da análise de diferentes perfis de poços pelo método DFA

The study of complex systems has become a prestigious area of science, although relatively young . Its importance was demonstrated by the diversity of applications that several studies have already provided to various fields such as biology , economics and Climatology . In physics , the approach of complex systems is creating paradigms that influence markedly the new methods , bringing to Statistical Physics problems macroscopic level no longer restricted to classical studies such as those of thermodynamics . The present work aims to make a comparison and verification of statistical data on clusters of profiles Sonic ( DT ) , Gamma Ray ( GR ) , induction ( ILD ) , neutron ( NPHI ) and density ( RHOB ) to be physical measured quantities during exploratory drilling of fundamental importance to locate , identify and characterize oil reservoirs . Software were used : Statistica , Matlab R2006a , Origin 6.1 and Fortran for comparison and verification of the data profiles of oil wells ceded the field Namorado School by ANP ( National Petroleum Agency ) . It was possible to demonstrate the importance of the DFA method and that it proved quite satisfactory in that work, coming to the conclusion that the data H ( Hurst exponent ) produce spatial data with greater congestion . Therefore , we find that it is possible to find spatial pattern using the Hurst coefficient . The profiles of 56 wells have confirmed the existence of spatial patterns of Hurst exponents , ie parameter B. The profile does not directly assessed catalogs verification of geological lithology , but reveals a non-random spatial distribution