Detrended fluctuation analysis of numerical density and viscous fingering patterns

Baroni, Mariana Pelissari Monteiro Aguiar; Wit, A. De; Rosa, Reinaldo R.

doi:10.1209/0295-5075/92/64002

Cited by 12 publications

(7 citation statements)

References 25 publications

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“…And it is not included in this study. For a detailed description of this step-by-step method, see Peng et al (1994), Little et al (2006), Baroni et al (2010), and Veronese et al (2011).…”

Section: Persistence In Time Seriesmentioning

confidence: 99%

Nonlinear fluctuation analysis for a set of 41 magnetic clouds measured by the Advanced Composition Explorer (ACE) spacecraft

González

Mendes

et al. 2014

Nonlin. Processes Geophys.

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Abstract. The statistical distribution of values in the signal and the autocorrelations (interpreted as the memory or persistence) between values are attributes of a time series. The autocorrelation function values are positive in a time series with persistence, while they are negative in a time series with anti-persistence. The persistence of values with respect to each other can be strong, weak, or nonexistent. A strong correlation implies a "memory" of previous values in the time series. The long-range persistence in time series could be studied using semivariograms, rescaled range, detrended fluctuation analysis and Fourier spectral analysis, respectively. In this work, persistence analysis is to study interplanetary magnetic field (IMF) time series. We use data from the IMF components with a time resolution of 16 s. Time intervals corresponding to distinct processes around 41 magnetic clouds (MCs) in the period between March 1998 and December 2003 were selected. In this exploratory study, the purpose of this selection is to deal with the cases presenting the three periods: plasma sheath, MC, and post-MC. We calculated one exponent of persistence (e.g., α, β, Hu, Ha) over the previous three time intervals. The persistence exponent values increased inside cloud regions, and it was possible to select the following threshold values: α (j ) = 1.392, Ha (j ) = 0.327, and Hu (j ) = 0.875. These values are useful as another test to evaluate the quality of the identification. If the cloud is well structured, then the persistence exponent values exceed thresholds. In 80.5 % of the cases studied, these tools were able to separate the region of the cloud from neighboring regions. The Hausdorff exponent (Ha) provides the best results.

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“…And it is not included in this study. For a detailed description of this step-by-step method, see Peng et al (1994), Little et al (2006), Baroni et al (2010), and Veronese et al (2011).…”

Section: Persistence In Time Seriesmentioning

confidence: 99%

Nonlinear fluctuation analysis for a set of 41 magnetic clouds measured by the Advanced Composition Explorer (ACE) spacecraft

González

Mendes

et al. 2014

Nonlin. Processes Geophys.

Self Cite

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show abstract

“…It is useful for characterizing temporal patterns that appear to be due to long-range memory stochastic processes (Veronese et al, 2011). A detailed description of this method, step by step, see Peng et al (1994), Baroni et al (2010), Veronese et al (2011), and Little et al (2006).…”

Section: Persistence In Time Seriesmentioning

confidence: 99%

Conjugate fluctuation analysis for a set of 41 magnetic clouds measured by the ACE spacecraft

González¹,

González²,

Mendes³

et al. 2014

Preprint

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Abstract. The statistical distribution of values in the signal and the autocorrelations (interpreted as the memory or persistence) between values are attributes of a time series. The autocorrelation function values are positive in a~time series with persistence, while it are negative in a time series with anti persistence. The persistence of values with respect to each other can be strong, weak, or nonexistent. A strong correlation implies a "memory" of previous values in the time series. The long-range persistence in time series could be studied using semivariograms, rescaled-range, detrended fluctuation analysis and Fourier spectral analysis, respectively. In this work the persistence analysis has been used to study IMF time series. We use data from the IMF GSM-components with time resolution of 16 s. Time intervals corresponding to distinct processes around 41 MCs in the period between March 1998 and December 2003 were selected. In this exploratory study the purpose with this selection is to deal with the cases presenting the three periods: plasma sheath, MC and post-MC. We calculated one exponent of persistence (e.g., α, β, Hu, Ha) over the previous three time intervals. The persistence exponent values increased inside cloud regions, and it was possible select the following threshold values: 〈α(j)〉 =1.392; 〈Ha(j)〉 = 0.327; 〈Hu(j)〉 =0.875. These values are useful as another test to evaluate the quality of the identification. If the cloud is well-structured, then the persistence exponents values exceed thresholds. In 80.5% of the cases studied, these tools were able to separate the region of the cloud from neighboring regions. The Hausdorff exponent (Ha) provides the best results.

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“…It is useful for characterizing variability patterns that appear to be due to long-range temporal correlations. The DFA technique has been used, in the last twenty years, to compute the values of the scaling exponents in several applications from physiological data to signals in physics and finance (e.g., [6,7,4,8]).…”

Section: Appendix -Detrended Fluctuation Analysismentioning

confidence: 99%

“…An easy-to-use virtual advanced time series analysis package should contain a specific selection of common statistical, plotting and modelling functions as, for example, Detrended Fluctuation Analysis (DFA) [2,3]. It is usually applied for robust characterization of long-range correlation in relatively short nonlinear time series (e.g., [4,5]). In general, all data analysis packages support a wide variety of traditional methods, but are limited when handling nonlinear time series using advanced tools.…”

Section: Introductionmentioning

confidence: 99%

The VLADA white paper: building an active Virtual Lab for Advanced Data Analysis

Dantas

Rosa

Sant³

et al. 2011

JCIS

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This technical white paper describes the design and initial implementation of a virtual environment for straightforward and robust data analysis intended for students and researchers acting in science and technology. The Virtual Laboratory for Advanced Data Analysis (VLADA) aims to fill a growing demand for scientific mathematical and statistical tools validated and coupled with appropriate high performance computing infrastructure into a single computing environment available on the Web using advanced parallel processing and object-oriented programming. This work proposes to provide: (i) a detailed study on the feasibility of building a such virtual environment with large international access, and (ii) a description of a preliminary single prototype including a standard method for advanced time series analysis. The main steps taken to develop such a laboratory, including preliminary software engineering implementation, are shown in this paper.

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Detrended fluctuation analysis of numerical density and viscous fingering patterns

Cited by 12 publications

References 25 publications

Nonlinear fluctuation analysis for a set of 41 magnetic clouds measured by the Advanced Composition Explorer (ACE) spacecraft

Nonlinear fluctuation analysis for a set of 41 magnetic clouds measured by the Advanced Composition Explorer (ACE) spacecraft

Conjugate fluctuation analysis for a set of 41 magnetic clouds measured by the ACE spacecraft

The VLADA white paper: building an active Virtual Lab for Advanced Data Analysis

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