By Yuri P. Kalmykov, William T. Coffey, Stuart A. Rice
Fractals, Diffusion, and leisure in Disordered complicated structures is a different guest-edited, two-part quantity of Advances in Chemical Physics that keeps to file fresh advances with major, up to date chapters by means of the world over well-known researchers.
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Additional info for Fractals Diffusion And Relaxation In Disordered Complex Systems
3. Various Inverse Power-Law Autocorrelation Functions Consider the following form of the autocorrelation function, CðtÞ ¼ hXðtÞXðt þ tÞi ¼ 1 ð1 þ jtja Þ b=a ð36Þ where the random process X(t) is still Gaussian, see Gneiting and Schlather  for a complete discussion of this correlation function and its implications. Any combination of parameters 0 < a 2 and b > 0 is allowed, in which case (36) is referred to as the Cauchy class of correlation functions. Now consider the two asymptotic limits.
76. We can see that the slope of the HRV data is midway fractal physiology, complexity, and the fractional calculus 13 between the dashed curves depicting an uncorrelated random process (slope ¼ 1/2) and one that is deterministically regular (slope ¼ 1). We emphasize that the conclusions we draw here are not from this single figure or set of data presented; these are only representative of a much larger body of work. The conclusions are based on a large number of similar observations [23,24] made using a variety of data processing techniques, all of which yield results consistent with the scaling of the HRV time series indicated in Fig.
8 A typical fit to the aggregated variance versus the aggregated mean for BRV and HRV time series obtained by West et al. . The points are calculated from the data and the solid curve is the best least-square fit to the data. 80). It is evident from these two graphs that the allometric relation given by Eq. (9) does indeed fit both data sets extremely well and lies well within the regular and random boundaries, indicated by the dashed curves. fractal physiology, complexity, and the fractional calculus 17 the small number of data in the breathing sequence.
Fractals Diffusion And Relaxation In Disordered Complex Systems by Yuri P. Kalmykov, William T. Coffey, Stuart A. Rice