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R/S method for unevenly sampled time series: Application to detecting long-term temporal dependence of droplets transiting through a fixed spatial point in gas–liquid two-phase turbulent jets

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  • Ji, Li-Jun
  • Zhou, Wei-Xing
  • Liu, Hai-Feng
  • Gong, Xin
  • Wang, Fu-Chen
  • Yu, Zun-Hong

Abstract

We perform rescaled range analysis upon the signals measured by a Dual Particle Dynamical Analyzer in gas–liquid two-phase turbulent jets. A novel rescaled range analysis is proposed to investigate these unevenly sampled signals. The Hurst exponents of velocity and other passive scalars in the bulk of spray are obtained to be 0.59 ± 0.02 and the fractal dimension is hence 1.41 ± 0.02, which is in remarkable agreement with and much more precise than previous results. These scaling exponents are found to be independent of the configuration and dimensions of the nozzle and the fluid flows. Therefore, such type of systems form a universality class with invariant scaling properties.

Suggested Citation

  • Ji, Li-Jun & Zhou, Wei-Xing & Liu, Hai-Feng & Gong, Xin & Wang, Fu-Chen & Yu, Zun-Hong, 2009. "R/S method for unevenly sampled time series: Application to detecting long-term temporal dependence of droplets transiting through a fixed spatial point in gas–liquid two-phase turbulent jets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(17), pages 3345-3354.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:17:p:3345-3354
    DOI: 10.1016/j.physa.2009.05.006
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    References listed on IDEAS

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    1. Wei-Xing Zhou & Didier Sornette & Vladilen Pisarenko, 2003. "New Evidence Of Discrete Scale Invariance In The Energy Dissipation Of Three-Dimensional Turbulence: Correlation Approach And Direct Spectral Detection," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 14(04), pages 459-470.
    2. Alvarez-Ramirez, Jose & Echeverria, Juan C. & Rodriguez, Eduardo, 2008. "Performance of a high-dimensional R/S method for Hurst exponent estimation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(26), pages 6452-6462.
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    Cited by:

    1. Teng, Yue & Shang, Pengjian, 2018. "Detrended fluctuation analysis based on higher-order moments of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 311-322.
    2. Li Wang & Xing-Lu Gao & Wei-Xing Zhou, 2023. "Testing for intrinsic multifractality in the global grain spot market indices: A multifractal detrended fluctuation analysis," Papers 2306.10496, arXiv.org.
    3. Lahmiri, Salim, 2015. "Long memory in international financial markets trends and short movements during 2008 financial crisis based on variational mode decomposition and detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 130-138.

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