Analysis of Antarctic Ice Core Data (EPICA Dome C) with Flicker-Noise Spectroscopy

Evolution of Earth’s climate system over the past 800,000 years represents a complex process with successions of uneven glacial and interglacial periods. The length, amplitudes, and development of each climate cycle depend on a number of different factors, including the orbital parameters attributed to insolation and the complex responses of the Earth system to solar radiation primarily through the amplification by Earth’s albedo and greenhouse gas and secondarily through a system of heat reservoirs, such as ice sheet and deep ocean, distributed throughout our planet. The purpose of this study is to analyze the transitions related to climate cycles in Antarctic ice core data (EPICA Dome C) of deuterium composition and dust concentration recorded for the past 800,000 years [1] using Flicker-Noise Spectroscopy (FNS), an analytical toolset for the extraction and analysis of information in stochastic time and space series, containing both regular and chaotic components, by using power spectra and difference moments (structural functions) of various orders [2]. 

The FNS nonstationarity factors for the deuterium composition and dust (logarithm) concentration, which represent the normalized discrete derivative of the second-order structural function of the source signal with respect to a given shifted “window” interval, were built for different intervals of averaging to identify the major changes in the dynamics of both time series and their precursors. It is shown that when displayed together with the source signals, the positive peaks in the nonstationarity factors provide more reliable estimates of the transition of the climate system from one sub-period to another within a specific climate cycle as compared to predefined thresholds in dust or deuterium values. For climatic transitions, the power spectral estimates of the nonstationarity factors contain several periodicities in addition to the orbital ones. These frequencies may be attributed to specific heat accumulation and discharge processes in the climate system. The results of this study demonstrate the potential of FNS in the analysis of climate data series and may be used in refining climate transition models.

This study was supported by the Russian Foundation for Basic Research, project no. 08-02-00230a.
[1] Lambert F., et al. (2008) Dust-climate couplings over the past 800,000 years from the EPICA Dome C ice core, Nature 452, 616-619.
[2] Timashev, S. F., Polyakov Yu. S. (2007) Review of flicker noise spectroscopy in electrochemistry, Fluctuations and Noise Letters 7(2), R15-R47.
&#xa

Analytical method for parameterizing the random profile components of nanosurfaces imaged by atomic force microscopy

The functional properties of many technological surfaces in biotechnology, electronics, and mechanical engineering depend to a large degree on the individual features of their nanoscale surface texture, which in turn are a function of the surface manufacturing process. Among these features, the surface irregularities and self-similarity structures at different spatial scales, especially in the range of 1 to 100 nm, are of high importance because they greatly affect the surface interaction forces acting at a nanoscale distance. An analytical method for parameterizing the surface irregularities and their correlations in nanosurfaces imaged by atomic force microscopy (AFM) is proposed. In this method, flicker noise spectroscopy - a statistical physics approach - is used to develop six nanometrological parameters characterizing the high-frequency contributions of jump- and spike-like irregularities into the surface texture. These contributions reflect the stochastic processes of anomalous diffusion and inertial effects, respectively, in the process of surface manufacturing. The AFM images of the texture of corrosion-resistant magnetite coatings formed on low-carbon steel in hot nitrate solutions with coating growth promoters at different temperatures are analyzed. It is shown that the parameters characterizing surface spikiness are able to quantify the effect of process temperature on the corrosion resistance of the coatings. It is suggested that these parameters can be used for predicting and characterizing the corrosion-resistant properties of magnetite coatings.Comment: 7 pages, 3 figures, 2 tables; to be published in Analys

Analysis of cross-correlations in electroencephalogram signals as an approach to proactive diagnosis of schizophrenia

We apply flicker-noise spectroscopy (FNS), a time series analysis method operating on structure functions and power spectrum estimates, to study the clinical electroencephalogram (EEG) signals recorded in children/adolescents (11 to 14 years of age) with diagnosed schizophrenia-spectrum symptoms at the National Center for Psychiatric Health (NCPH) of the Russian Academy of Medical Sciences. The EEG signals for these subjects were compared with the signals for a control sample of chronically depressed children/adolescents. The purpose of the study is to look for diagnostic signs of subjects' susceptibility to schizophrenia in the FNS parameters for specific electrodes and cross-correlations between the signals simultaneously measured at different points on the scalp. Our analysis of EEG signals from scalp-mounted electrodes at locations F3 and F4, which are symmetrically positioned in the left and right frontal areas of cerebral cortex, respectively, demonstrates an essential role of frequency-phase synchronization, a phenomenon representing specific correlations between the characteristic frequencies and phases of excitations in the brain. We introduce quantitative measures of frequency-phase synchronization and systematize the values of FNS parameters for the EEG data. The comparison of our results with the medical diagnoses for 84 subjects performed at NCPH makes it possible to group the EEG signals into 4 categories corresponding to different risk levels of subjects' susceptibility to schizophrenia. We suggest that the introduced quantitative characteristics and classification of cross-correlations may be used for the diagnosis of schizophrenia at the early stages of its development.Comment: 36 pages, 6 figures, 2 tables; to be published in "Physica A

Anomalous diffusion in the dynamics of complex processes

Anomalous diffusion, process in which the mean-squared displacement of system states is a non-linear function of time, is usually identified in real stochastic processes by comparing experimental and theoretical displacements at relatively small time intervals. This paper proposes an interpolation expression for the identification of anomalous diffusion in complex signals for the cases when the dynamics of the system under study reaches a steady state (large time intervals). This interpolation expression uses the chaotic difference moment (transient structural function) of the second order as an average characteristic of displacements. A general procedure for identifying anomalous diffusion and calculating its parameters in real stochastic signals, which includes the removal of the regular (low-frequency) components from the source signal and the fitting of the chaotic part of the experimental difference moment of the second order to the interpolation expression, is presented. The procedure was applied to the analysis of the dynamics of magnetoencephalograms, blinking fluorescence of quantum dots, and X-ray emission from accreting objects. For all three applications, the interpolation was able to adequately describe the chaotic part of the experimental difference moment, which implies that anomalous diffusion manifests itself in these natural signals. The results of this study make it possible to broaden the range of complex natural processes in which anomalous diffusion can be identified. The relation between the interpolation expression and a diffusion model, which is derived in the paper, allows one to simulate the chaotic processes in the open complex systems with anomalous diffusion.Comment: 47 pages, 15 figures; Submitted to Physical Review

Cross-Correlation Earthquake Precursors in the Hydrogeochemical and Geoacoustic Signals for the Kamchatka Peninsula

We propose a new type of earthquake precursor based on the analysis of correlation dynamics between geophysical signals of different nature. The precursor is found using a two-parameter cross-correlation function introduced within the framework of flicker-noise spectroscopy, a general statistical physics approach to the analysis of time series. We consider an example of cross-correlation analysis for water salinity time series, an integral characteristic of the chemical composition of groundwater, and geoacoustic emissions recorded at the G-1 borehole on the Kamchatka peninsula in the time frame from 2001 to 2003, which is characterized by a sequence of three groups of significant seismic events. We found that cross-correlation precursors took place 27, 31, and 35 days ahead of the strongest earthquakes for each group of seismic events, respectively. At the same time, precursory anomalies in the signals themselves were observed only in the geoacoustic emissions for one group of earthquakes.Comment: 21 pages, 5 figures, 1 table; to be published in "Acta Geophysica". arXiv admin note: substantial text overlap with arXiv:1101.147

Stochastic variability in X-ray emission from the black hole binary GRS 1915+105

We examine stochastic variability in the dynamics of X-ray emission from the black hole system GRS 1915+105, a strongly variable microquasar commonly used for studying relativistic jets and the physics of black hole accretion. The analysis of sample observations for 13 different states in both soft (low) and hard (high) energy bands is performed by flicker-noise spectroscopy (FNS), a phenomenological time series analysis method operating on structure functions and power spectrum estimates. We find the values of FNS parameters, including the Hurst exponent, flicker-noise parameter, and characteristic time scales, for each observation based on multiple 2,500-second continuous data segments. We identify four modes of stochastic variability driven by dissipative processes that may be related to viscosity fluctuations in the accretion disk around the black hole: random (RN), power-law (1F), one-scale (1S), and two-scale (2S). The variability modes are generally the same in soft and hard energy bands of the same observation. We discuss the potential for future FNS studies of accreting black holes.Comment: 25 pages, 3 figures, 2 tables; to be published in "The Astronomical Journal