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On von Kármán spectrum from a view of fractal

100%

Li M., Leng J.

Waves, Wavelets and Fractals

2015

vol. 1

issue 1

Von Kármán originally deduced his spectrum of wind speed fluctuation based on the Stockes-Navier equation. That derivation, however, is insufficient to exhibit the fractal information of time series, such as wind velocity fluctuation. This paper gives a novel derivation of the von Kármán spectrum based on fractional Langevin equation, aiming at establishing the relationship between the conventional von Kármán spectrum and fractal dimension. Thus, the present results imply that a time series that follows the von Kármán spectrum can be taken as a specifically fractional Ornstein-Uhlenbeck process with the fractal dimension 5/3, providing a new view of the famous spectrum of von Kármán’s from the point of view of fractals. More importantly, that also implies a novel relationship between two famous spectra in fluid mechanics, namely, the Kolmogorov’s spectrum and the von Kármán’s. Consequently, the paper may yet be useful in practice, such as ocean engineering and shipbuilding.

Determination of europium by using the chemical oscillating system of Ce(IV)-KBrO3-acetone-oxalic acid-H2SO4

71%

Gao J., Zhang Y., Ren J., Li M., Yang W.

A sensitive and convenient method for the determination of trace europium ions using an oscillating chemical reaction involving Ce(IV) - KBrO3 - acetone - oxalic acid - H2SO4 was proposed. The results indicated that the changes in oscillating period (T) was linearly proportional to the negative logarithmic concentration of Eu3+ (-log C) in the range of 1.41 × 10−8 ˜ 1.41 × 10−4 mol L−1 (r = 0.9982) with a detection limit of 1.04 × 10−9 mol L−1. The recoveries were limited to the range of 99.5% to 100.8%. Under the same conditions, other rare earth ions did not interfere with the determination of Eu3+. In addition, a perturbation mechanism was also discussed briefly. [...]

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On von Kármán spectrum from a view of fractal

Determination of europium by using the chemical oscillating system of Ce(IV)-KBrO3-acetone-oxalic acid-H2SO4