PROBLEMS OF GEOCOSMOS

Proceedings of the 7th International Conference "Problems of Geocosmos" (St. Petersburg, Russia, 26-30 May 2008)
The term ”scale-free” has been coined in statistical mechanics of turbulent and/or critical phenomena to
describe correlated perturbations with no characteristic scales other than the scales dictated by the finite size
of the system, as opposed to scale-dependent perturbations reflecting physical conditions that vary across
different scales [29]. Considered in the context of other geophysical processes, the nighttime auroral activity
provides one of the most impressive examples of scale-free behavior in Nature. Thus, the energy probability
distribution of electron emission regions as seen by the POLAR satellite exhibits power-law shape over
about 6 orders of magnitude [23]. By combining POLAR data with ground-based TV observations [10], the
power-law scaling range has been extended up to 11 orders of magnitude (Fig. 2). The consistency of the
power-law slopes obtained from high-resolution ground-based auroral observations and those characterizing
POLAR ultra-violet imager (UVI) data reveals an extremely wide range of power-law scaling of energy
dissipation in the nighttime magnetosphere.
(a)
(b)
Fig. 2. (a) A diagram explaining the
idea of spatiotemporal tracking of
auroral emission regions in time
series of POLAR UVI frames
(LBH-long filter). (b) Power-law
probability distributions of electron
emission areas obtained from
ground-based all-sky camera data
(triangles) and the POLAR UVI
observations (squares) [10, 23].
It is worth noting that these scale-free statistics represent long-term ensembles-averaged properties of
nighttime magnetospheric disturbances, and they can mask a more complex dynamics on the level of specific
plasma sheet structures responsible for the generation of various forms of auroral precipitations. Our recent
results [24, 25] confirm the causal relationship between the auroral precipitation statistics and the nonuniform
morphology of the central plasma sheet. They show that the inner and the outer plasma sheet regions
are responsible for distinct scaling modes of the auroral precipitation dynamics which can a manifestation of
two competing substrm scenarios represented by the current disruption and the midtail magnetic
reconnection models [13, 20]. Exploring such second-order scaling effects could help build a more solid
theoretical link between the statistical and dynamical plasma descriptions, evaluate predictability of different
classes of magnetospheric disturbances, and obtain statistical guidelines for designing future space missions
targeted at multiscale plasma phenomena.
Example 3: Human heart rate variability
This section illustrates an intermittent stochastic behavior in a quite different system – the system of
human homeostasis, monitored by the low-frequency component of heart rate variability (HRV) [9,17]. HRV
is the temporal variability of the beat-to-beat RR-interval in human electrocardiogram which exhibits distinct
intermittent properties in the frequency range 10 –5 − 10 –2 Hz [14]. In many cases, this variability is described
by the power-law 1/f β dependence of Fourier power spectral density on the frequency f [9]. Typically, 1/f β
HRV spectra with constant β are observed in healthy people, whereas pathologies and malfunctions are
associated with more complex forms of spectral behavior. The connection between the broken fractality and
the disease [15-18, 22] indicates a possibility of using 1/f β fluctuations for the purposes of clinical
diagnostics, and stimulates further investigation of this phenomenon. In our previous studies, we have
explored fractal and multifractal properties of HRV using a variety of time series analysis tools [15,17,18].
The results have confirmed that the low-frequency HRV is a sensitive marker of homeostatic processes. Here
we present new results showing that intermittency measures of HRV can be used for early identification of
pathological conditions.
In addition to power-law spectral exponent β, we consider two intermittency parameters (a and T)
describing nonstationary behavior of standard deviation in HRV signals as explained in Fig. 3. In medical
applications, extreme abnormal values of σ and β are informative state parameters. The interpretation of σ
is largely empirical and is carried out on the individual basis for different sets of symptoms. Earlier, we have
proposed an interpretative system for σ understanding measurements in the SOC region of HRV regulation
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