scholarly journals Air-chemistry "turbulence": power-law scaling and statistical regularity

2011 ◽  
Vol 11 (16) ◽  
pp. 8395-8413 ◽  
Author(s):  
H.-m. Hsu ◽  
C.-Y. Lin ◽  
A. Guenther ◽  
J. J. Tribbia ◽  
S. C. Liu
Keyword(s):  
Time Series ◽  
Air Quality ◽  
Power Law ◽  
Atmospheric Chemistry ◽  
Heavy Tails ◽  
Structural Information ◽  
Time Lag ◽  
Fluctuation Analysis ◽  
Statistical Regularity ◽  
Statistical Regularities

Abstract. With the intent to gain further knowledge on the spectral structures and statistical regularities of surface atmospheric chemistry, the chemical gases (NO, NO2, NOx, CO, SO2, and O3) and aerosol (PM10) measured at 74 air quality monitoring stations over the island of Taiwan are analyzed for the year of 2004 at hourly resolution. They represent a range of surface air quality with a mixed combination of geographic settings, and include urban/rural, coastal/inland, plain/hill, and industrial/agricultural locations. In addition to the well-known semi-diurnal and diurnal oscillations, weekly, and intermediate (20 ~ 30 days) peaks are also identified with the continuous wavelet transform (CWT). The spectra indicate power-law scaling regions for the frequencies higher than the diurnal and those lower than the diurnal with the average exponents of −5/3 and −1, respectively. These dual-exponents are corroborated with those with the detrended fluctuation analysis in the corresponding time-lag regions. These exponents are mostly independent of the averages and standard deviations of time series measured at various geographic settings, i.e., the spatial inhomogeneities. In other words, they possess dominant universal structures. After spectral coefficients from the CWT decomposition are grouped according to the spectral bands, and inverted separately, the PDFs of the reconstructed time series for the high-frequency band demonstrate the interesting statistical regularity, −3 power-law scaling for the heavy tails, consistently. Such spectral peaks, dual-exponent structures, and power-law scaling in heavy tails are important structural information, but their relations to turbulence and mesoscale variability require further investigations. This could lead to a better understanding of the processes controlling air quality.

scholarly journals Air-chemistry "turbulence": power-law scaling and statistical regularity

2011 ◽  
Vol 11 (3) ◽  
pp. 9635-9672
Author(s):  
H.-m. Hsu ◽  
C.-Y. Lin ◽  
A. Guenther ◽  
J. J. Tribbia ◽  
S. C. Liu
Keyword(s):  
Air Quality ◽  
Power Law ◽  
Atmospheric Chemistry ◽  
Heavy Tails ◽  
Time Lag ◽  
Fluctuation Analysis ◽  
Statistical Regularity ◽  
Air Chemistry ◽  
Statistical Regularities ◽  
Air Quality Monitoring Stations

Abstract. With the intent to gain further knowledge on the spectral structures and statistical regularities of surface atmospheric chemistry, the chemical gases (NO, NO2, NOx, CO, SO2, and O3) and aerosol (PM10) measured at 74 air quality monitoring stations over the island of Taiwan are analyzed for the year of 2004 at hourly resolution. They represent a range of surface air quality with a mixed combination of geographic settings, and include urban/rural, coastal/inland, and plain/hill locations. In addition to the well-known semi-diurnal and diurnal oscillations, weekly, intermediate (20 ~ 30 days) and intraseasonal (30 ~ 100 days) peaks are also identified with the continuous wavelet transform (CWT). The spectra indicate power-law scaling regions for the frequencies higher than the diurnal and those lower than the diurnal with the average exponents of −5/3 and −1, respectively. These dual-exponents are corroborated with those with the detrended fluctuation analysis in the corresponding time-lag regions. After spectral coefficients from the CWT decomposition are grouped according to the spectral bands, and inverted separately, the PDFs of the reconstructed time series for the high-frequency band demonstrate the interesting statistical regularity, −3 power-law scaling for the heavy tails, consistently. Such spectral peaks, dual-exponent structures, and power-law scaling in heavy tails are intriguingly interesting, but their relations to turbulence and mesoscale variability require further investigations. This could lead to a better understanding of the processes controlling air quality.

MODELING CROSS-CORRELATIONS OF TRAFFIC FLOW

2010 ◽  
Vol 20 (10) ◽  
pp. 3323-3328 ◽  
Author(s):  
PENGJIAN SHANG ◽  
KEQIANG DONG ◽  
SANTI KAMAE
Keyword(s):  
Time Series ◽  
Traffic Flow ◽  
Power Law ◽  
Cross Correlation ◽  
Heavy Tails ◽  
Fluctuation Analysis ◽  
Cross Correlation Analysis ◽  
Cross Correlations ◽  
Large Increment ◽  
Active Research

The study of diverse natural and nonstationary signals has recently become an area of active research for physicists. This is because these signals exhibit interesting dynamical properties such as scale invariance, volatility correlation, heavy tails and fractality. The focus of the present paper is on the intriguing power-law autocorrelations and cross-correlations in traffic series. Detrended Cross-Correlation Analysis (DCCA) is used to study the traffic flow fluctuations. It is demonstrated that the time series, observed on the Anhua-Bridge highway in the Beijing Third Ring Road (BTRR), may exhibit power-law cross-correlations when they come from two adjacent sections or lanes. This indicates that a large increment in one traffic variable is more likely to be followed by large increment in the other traffic variable. However, for traffic time series derived from nonadjacent sections or lanes, we find that even though they are power-law autocorrelated, there is no cross-correlation between them with a unique exponent. Our results show that DCCA techniques based on Detrended Fluctuation Analysis (DFA) can be used to analyze and interpret the traffic flow.

scholarly journals Technical Note: Long-term memory effect in the atmospheric CO<sub>2</sub> concentration at Mauna Loa

2006 ◽  
Vol 6 (6) ◽  
pp. 11957-11970 ◽  
Author(s):  
C. Varotsos ◽  
M.-N. Assimakopoulos ◽  
M. Efstathiou
Keyword(s):  
Carbon Dioxide ◽  
Time Series ◽  
Power Law ◽  
Carbon Dioxide Concentration ◽  
Global Climate Models ◽  
Fluctuation Analysis ◽  
Original Time Series ◽  
Mauna Loa ◽  
Carbon Dioxide Concentrations ◽  
Original Time

Abstract. The monthly mean values of the atmospheric carbon dioxide concentration derived from in-situ air samples collected at Mauna Loa Observatory, Hawaii, during 1958–2004 (the longest continuous record available in the world) are analyzed by employing the detrended fluctuation analysis to detect scaling behavior in this time series. The main result is that the fluctuations of carbon dioxide concentrations exhibit long-range power-law correlations (long memory) with lag times ranging from four months to eleven years, which correspond to 1/f noise. This result indicates that random perturbations in the carbon dioxide concentrations give rise to noise, characterized by a frequency spectrum following a power-law with exponent that approaches to one; the latter shows that the correlation times grow strongly. This feature is pointing out that a correctly rescaled subset of the original time series of the carbon dioxide concentrations resembles the original time series. Finally, the power-law relationship derived from the real measurements of the carbon dioxide concentrations could also serve as a tool to improve the confidence of the atmospheric chemistry-transport and global climate models.

Fluctuations and determinism of respiratory impedance in asthma and chronic obstructive pulmonary disease

2010 ◽  
Vol 109 (6) ◽  
pp. 1582-1591 ◽  
Author(s):  
Michael Muskulus ◽  
Annelies M. Slats ◽  
Peter J. Sterk ◽  
Sjoerd Verduyn-Lunel
Keyword(s):  
Time Series ◽  
Power Law ◽  
Respiratory System ◽  
Single Frequency ◽  
Fluctuation Analysis ◽  
High Temporal Resolution ◽  
Deterministic System ◽  
Forced Oscillation Technique ◽  
Respiratory Impedance ◽  
Wasserstein Distances

Asthma and COPD are chronic respiratory diseases that fluctuate widely with regard to clinical symptoms and airway obstruction, complicating treatment and prediction of exacerbations. Time series of respiratory impedance obtained by the forced oscillation technique are a convenient tool to study the respiratory system with high temporal resolution. In previous studies it was suggested that power-law-like fluctuations exist also in the healthy lung and that respiratory system impedance variability differs in asthma. In this study we elucidate such differences in a population of well-characterized subjects with asthma ( n = 13, GINA 1+2), COPD ( n = 12, GOLD I+II), and controls ( n = 10) from time series at single frequency (12 min, f = 8 Hz). Maximum likelihood estimation did not rule out power-law behavior, accepting the null hypothesis in 17/35 cases ( P > 0.05) and with significant differences in exponents for COPD ( P < 0.03). Detrended fluctuation analysis exhibited scaling exponents close to 0.5, indicating few correlations, with no differences between groups ( P > 0.14). In a second approach, we considered asthma and COPD as dynamic diseases, corresponding to changes of unknown parameters in a deterministic system. The similarity in shape between the combined probability distributions of normalized resistance and reactance was quantified by Wasserstein distances and reliably distinguished the two diseases (cross-validated predictive accuracy 0.80; sensitivity 0.83, specificity 0.77 for COPD). Wasserstein distances between 3+3 dimensional phase space reconstructions resulted in marginally better classification (accuracy 0.84, sensitivity 0.83, specificity 0.85). These latter findings suggest that the dynamics of respiratory impedance contain valuable information for the diagnosis and monitoring of patients with asthma and COPD, whereas the value of the stochastic approach is not clear presently.

scholarly journals Discriminating low frequency components from long range persistent fluctuations in daily atmospheric temperature variability

2009 ◽  
Vol 9 (14) ◽  
pp. 4537-4544 ◽  
Author(s):  
M. Lanfredi ◽  
T. Simoniello ◽  
V. Cuomo ◽  
M. Macchiato
Keyword(s):  
Time Series ◽  
Long Range ◽  
Power Law ◽  
Low Frequency ◽  
Atmospheric Temperature ◽  
Fluctuation Analysis ◽  
Climate Modelling ◽  
Scale Free ◽  
Statistical Confidence ◽  
Frequency Components

Abstract. This study originated from recent results reported in literature, which support the existence of long-range (power-law) persistence in atmospheric temperature fluctuations on monthly and inter-annual scales. We investigated the results of Detrended Fluctuation Analysis (DFA) carried out on twenty-two historical daily time series recorded in Europe in order to evaluate the reliability of such findings in depth. More detailed inspections emphasized systematic deviations from power-law and high statistical confidence for functional form misspecification. Rigorous analyses did not support scale-free correlation as an operative concept for Climate modelling, as instead suggested in literature. In order to understand the physical implications of our results better, we designed a bivariate Markov process, parameterised on the basis of the atmospheric observational data by introducing a slow dummy variable. The time series generated by this model, analysed both in time and frequency domains, tallied with the real ones very well. They accounted for both the deceptive scaling found in literature and the correlation details enhanced by our analysis. Our results seem to evidence the presence of slow fluctuations from another climatic sub-system such as ocean, which inflates temperature variance up to several months. They advise more precise re-analyses of temperature time series before suggesting dynamical paradigms useful for Climate modelling and for the assessment of Climate Change.

scholarly journals MULTIFRACTAL ANALYSIS OF STRESS TIME SERIES DURING ULTRATHIN LUBRICANT FILM MELTING

2010 ◽  
Vol 09 (01) ◽  
pp. 19-35 ◽  
Author(s):  
ALEXEI V. KHOMENKO ◽  
IAKOV A. LYASHENKO ◽  
VADIM N. BORISYUK
Keyword(s):  
Time Series ◽  
Power Law ◽  
Lubricant Film ◽  
Fluctuation Analysis ◽  
Power Law Distribution ◽  
Stick Slip ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Flat Surfaces ◽  
Self Similar ◽  
Detrended Fluctuation

Melting of an ultrathin lubricant film confined between two atomically flat surfaces is studied using the rheological model for viscoelastic matter approximation. Phase diagram with domains, corresponding to sliding, dry, and two types of stick-slip friction regimes has been built taking into account additive noises of stress, strain, and temperature of the lubricant. The stress time series have been obtained for all regimes of friction using the Stratonovich interpretation. It has been shown that self-similar regime of lubricant melting is observed when intensity of temperature noise is much larger than intensities of strain and stress noises. This regime is defined by homogenous distribution, at which characteristic stress scale is absent. We study stress time series obtained for all friction regimes using multifractal detrended fluctuation analysis. It has been shown that multifractality of these series is caused by different correlations that are present in the system and also by a power-law distribution. Since the power-law distribution is related to small stresses, this case corresponds to self-similar solid-like lubricant.

scholarly journals Investigating non-uniform scaling behaviour in temporal fluctuations of seismicity

2008 ◽  
Vol 8 (5) ◽  
pp. 973-976 ◽  
Author(s):  
L. Telesca ◽  
M. Lovallo
Keyword(s):  
Time Series ◽  
Power Law ◽  
Central Italy ◽  
Fluctuation Analysis ◽  
Temporal Fluctuations ◽  
Scaling Behaviour ◽  
Scaling Region ◽  
Detrended Fluctuation ◽  
Large Earthquakes ◽  
Uniform Scaling

Abstract. Scaling behaviour in nonstationary time series can be successfully detected using the detrended fluctuation analysis (DFA). Observational time series often do not show a stable and uniform scaling behaviour, given by the presence of a unique clear scaling region. The deviations from uniform power-law scaling, which suggest the presence of changing dynamics in the system under study, can be identified and quantified using an appropriate instability index. In this framework, the scaling behaviour of the 1981–2007 seismicity in Umbria-Marche (central Italy), which is one of the most seismically active areas in Italy, was investigated. Significant deviations from uniform power-law scaling in the seismic temporal fluctuations were revealed mostly linked with the occurrence of rather large earthquakes or seismic clusters.

scholarly journals DETRENDED FLUCTUATION ANALYSIS OF THE TCP-RED ALGORITHM

2009 ◽  
Vol 19 (12) ◽  
pp. 4237-4245 ◽  
Author(s):  
XI CHEN ◽  
SIU-CHUNG WONG ◽  
CHI K. TSE ◽  
LJILJANA TRAJKOVIĆ
Keyword(s):  
Time Series ◽  
Long Range ◽  
Power Law ◽  
Detrended Fluctuation Analysis ◽  
Time Series Data ◽  
Analytical Models ◽  
Series Data ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Detrended Fluctuation

It has been observed that Internet gateways employing Transport Control Protocol (TCP) and the Random Early Detection (RED) control algorithm may exhibit instability and oscillatory behavior. Most control methods proposed in the past have been based on analytical models that rely on statistical measurements of network parameters. In this paper, we apply the detrended fluctuation analysis (DFA) method to analyze stability of the TCP-RED system. The DFA is used to analyze time-series data and generate power-law scaling exponents, which indicate the long-range correlations of the time series. We quantify the stability of the TCP-RED system by examining the variation of the DFA power-law scaling exponent when the system parameters are varied. We also study the long-range power-law correlations of TCP window periods.

Scaling analysis of hyperchaotic time series

2017 ◽  
Vol 28 (07) ◽  
pp. 1750094 ◽  
Author(s):  
J. S. Murguía
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Power Law ◽  
Detrended Fluctuation Analysis ◽  
Dynamical Evolution ◽  
Fluctuation Analysis ◽  
Discrete Wavelet ◽  
Scaling Analysis ◽  
Detrended Fluctuation ◽  
Hyperchaotic Systems

The time series of the states of several well-known hyperchaotic systems are analyzed numerically using the detrended fluctuation analysis based on the discrete wavelet transform. We report the finding of significant scaling behaviors (power-law like) in some of these time series, which can be used as an additional characteristic distinguishing the dynamical evolution of such systems.

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