Narrow Results

On the basis of the lattice Boltzmann method for the Navier–Stokes equation, we have done a numerical experiment of a forced turbulence in real space and time. Our new findings are summarized into two points. Firstly, in the analysis of the mean-field behavior of the velocity field using the exit-time statistics, we have verified Kolmogorov's scaling and Taylor's hypothesis at the same time. Secondly, in the analysis of the intermittent velocity fluctuations using a non-equilibrium probability distribution function and the wavelet denoising, we have clarified that the coherent vortices sustain the power-law velocity correlation in the non-equilibrium state.

Based on the daily price data of Shanghai and London gold spot markets, we applied detrended cross-correlation analysis (DCCA) and detrended moving average cross-correlation analysis (DMCA) methods to quantify power-law cross-correlation between domestic and international gold markets. Results show that the cross-correlations between the Chinese domestic and international gold spot markets are multifractal. Furthermore, forward DMCA and backward DMCA seems to outperform DCCA and centered DMCA for short-range gold series, which confirms the comparison results of short-range artificial data in L. Y. He and S. P. Chen [Physica A 390 (2011) 3806–3814]. Finally, we analyzed the local multifractal characteristics of the cross-correlation between Chinese domestic and international gold markets. We show that multifractal characteristics of the cross-correlation between the Chinese domestic and international gold markets are time-varying and that multifractal characteristics were strengthened by the financial crisis in 2007–2008.