By William T Coffey; Yuri P Kalmykov; John Wiley & Sons.; Wiley InterScience (Online service)
Fractals, Diffusion and leisure in Disordered complicated platforms is a unique guest-edited, two-part quantity of Advances in Chemical Physics that maintains to document fresh advances with major, updated chapters by way of the world over well-known researchers
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Additional resources for Fractals, Diffusion and Relaxation in Disordered Complex Systems, Part B
Sample text
N, appears to be a sequence of random points. Examples of such data are the interbeat intervals of the human heart, interstride intervals of human gait, brain wave data from EEGs and interbreath intervals, to name a few. The processing of time series in each of these cases has made use of random walk concepts in both the processing of the data and in the interpretation of the results. So let us review some of what is known about random walks. 1. Simple Random Walks and Scaling We define the variable of interest as Xj, where j ¼ 0,1,2, .
The second set of data in Fig. 6 is computer-generated Gaussian noise, having the same mean and standard deviation as the experimental data. Note that it is not easy to distinguish between the two data sets. However, the experimental data fluctuate around the mean gait interval and, although small, are nonnegligible because they indicate an underlying complex structure and, as we show, these fluctuations cannot be treated as an uncorrelated random noise. Using a 15-minute SRV time series, from which the data depicted in Fig.
25) decrease with increasing time lag as an inverse power law asymptotically in the time lag as long as a < 1=2. The spectrum of the time series in Eq. (25) is obtained using its discrete Fourier transform ðp 1 ^ o do eiko X ð27Þ Xk ¼ 2p Àp in the discrete convolution form of the solution, Eq. (25), to obtain ^ o^ ^o ¼  xo X ð28Þ D E D E ^ o j2 ^ o j2 ¼ j^ SðoÞ ¼ jX x o j2 j ð29Þ yielding the power spectrum The strength of the fluctuations is assumed to be constant—that is, independent of the frequency.