A. Bershadskii

Extended self-similarity of the small-scale cosmic microwave background anisotropy

The extended self-similarity (ESS) of cosmic microwave background (CMB) radiation has been studied using recent data obtained by the space-craft based Wilkinson Microwave Anisotropy Probe. Using the ESS and the high angular scale resolution (arcminutes) of the data it is shown that the CMB temperature space increments exhibit considerable and systematic declination from Gaussianity for high order moments at the small angular scales. Moreover, the CMB space increment ESS exponents have remarkably close values to the ESS exponents observed in turbulence (in magnetohydrodynamic turbulence).

Self-averaging phenomenon and multiscaling in Hong Kong stock market

It is shown that a natural self-averaging phenomenon can transform the initially (on a microscopic level) lognormal distribution into bi-lognormal one. Comparison with Hong Kong stock market (Hang Seng index) is used to show that this mechanism is working for different time lags and, therefore, the mechanism can be a reason for profound multiscaling observed for this system.

Finite-Reynolds-number effects in turbulence using logarithmic expansions

Experimental or numerical data in turbulence are invariably obtained at finite Reynolds numbers whereas theories of turbulence correspond to infinitely large Reynolds numbers. A proper merger of the two approaches is possible only if corrections for finite Reynolds numbers can be quantified. This paper heuristically considers examples in two classes of finite-Reynolds-number effects. Expansions in terms of logarithms of appropriate variables are shown to yield results in agreement with experimental and numerical data in the following instances: the third-order structure function in isotropic turbulence, the mixed-order structure function for the passive scalar and the Reynolds shear stress around its maximum point. Results suggestive of expansions in terms of the inverse logarithm of the Reynolds number, also motivated by experimental data, concern the tendency for turbulent structures to cluster along a line of observation and (more speculatively) for the longitudinal velocity derivative to become singular at some finite Reynolds number. We suggest an elementary hydrodynamical process that may provide a physical basis for the expansions considered here, but note that the formal justification remains tantalizingly unclear.

Multiscale self-organized criticality and powerful X-ray flares

Abstract.A combination of spectral and moments analysis of the continuous X-ray flux data is used to show consistency of statistical properties of the powerful solar flares with 2D BTW prototype model of self-organized criticality.

Isotherms clustering in cosmic microwave background

Abstract Isotherms clustering in cosmic microwave background (CMB) has been studied using the 3-year WMAP data on cosmic microwave background radiation. It is shown that the isotherms clustering could be produced by the baryon–photon fluid turbulence in the last scattering surface. The Taylor-microscale Reynolds number of the turbulence is estimated directly from the CMB data as Re λ ∼ 10 2 .

Multifractal and probabilistic properties of DNA sequences

Abstract It is shown that an empirical multifractal spectrum describing spatial inhomogeneity of the human β globin gene is consistent with stretched lognormal distribution generated by an analytic branching cascade with branching dimension equal to 2.

Transitional dynamics of the solar convection zone

Solar activity is studied using a cluster analysis of the time-fluctuations of sunspot number. In the historic period (1850–1932) the cluster exponent α0.37 (strong clustering) for the high-activity components of the solar cycles. In the modern period (last seven solar cycles: 1933–2007) the cluster exponent was α0.50 (random, white-noise–like). Comparing these results with the corresponding data from laboratory experiments on convection it is shown that in the historic period the emergence of sunspots in the solar photosphere was dominated by turbulent photospheric convection. In the modern period, this domination was broken by a new more active dynamics of the inner layers of the convection zone. Cluster properties of the solar-wind magnetic field and the aa-geomagnetic-index also support this result. Long-range chaotic dynamics in the solar activity is briefly discussed.

Transitional solar dynamics and global warming

Solar activity is studied using a cluster analysis of the time-fluctuations of the sunspot number. It is shown that in an Historic period the high activity components of the solar cycles exhibit strong clustering, whereas in a Modern period (last seven solar cycles: 1933–2007) they exhibit a white-noise (non-)clustering behavior. Using this observation, it is shown that in the Historic period, emergence of the sunspots in the solar photosphere was strongly dominated by turbulent photospheric convection. In the Modern period, this domination was broken by a new more active dynamics of the inner layers of the convection zone. Then, it is shown that the dramatic change of the sun dynamics at the transitional period (between the Historic and Modern periods, solar cycle 1933–1944) had a clear detectable impact on the Earth’s climate. A scenario of a chain of transitions in the solar convective zone is suggested in order to explain the observations, and a forecast for global warming is suggested on the basis of this scenario. A relationship between the recent transitions and solar long-period chaotic dynamics has been found.

Chaotic climate response to long-term solar forcing variability

It is shown that global climate exhibits chaotic response to solar forcing variability in a vast range of time scales: from annual to multi-millennial. Unlike linear systems, where periodic forcing leads to periodic response, nonlinear chaotic response to periodic forcing can result in exponentially decaying broad-band power spectrum with decay rate Te equal to the period of the forcing. It is shown that power spectrum of a reconstructed time series of Northern Hemisphere temperature anomaly for the past 2000 years has an exponentially decaying broad-band part with Te11 y, i.e. the observed decay rate Te equals the mean period of the solar activity. It is also shown that, power spectrum of a reconstruction of atmospheric-CO2 time fluctuations for the past 650000 years, has an exponentially decaying broad-band part with Te41000 years, i.e. the observed decay rate Te equals the period of the obliquity periodic forcing. A possibility of a chaotic solar forcing of the climate has been also discussed. These results clarify the role of solar forcing variability in long-term global-climate dynamics (in particular in the unsolved problem of the glaciation cycles) and help in construction of adequate dynamic models of the global climate.It is shown that global climate exhibits chaotic response to solar forcing variability in a vast range of timescales: from annual to multi-millennium. Unlike linear systems, where periodic forcing leads to periodic response, nonlinear chaotic response to periodic forcing can result in exponentially decaying broad-band power spectrum with decay rate Te equal to the period of the forcing. It is shown that power spectrum of a reconstructed time series of Northern Hemisphere temperature anomaly for the past 2,000 years has an exponentially decaying broad-band part with Te ≃ 11 yr, i.e. the observed decay rate Te equals the mean period of the solar activity. It is also shown that power spectrum of a reconstruction of atmospheric CO2 time fluctuations for the past 650,000 years, has an exponentially decaying broad-band part with Te ≃ 41, 000 years, i.e. the observed decay rate Te equals the period of the obliquity periodic forcing. A possibility of a chaotic solar forcing of the climate has been also discussed. These results clarify role of solar forcing variability in long-term global climate dynamics (in particular in the unsolved problem of the glaciation cycles) and help in construction of adequate dynamic models of the global climate.

Multifractal statistics and underlying kinetics of neuron spiking time-series

Abstract Probabilistic and multifractal properties of spiking time-series obtained in vivo from singular neurons belonging to red nucleus of the rat brain are analyzed. Lognormal and “−1” power-law probability distributions of interspike intervals are observed for healthy and for genetically depressive rats, respectively. A simple thermodynamic model is elaborated to interpret obtained results. Investigation of long-range interspike correlations (both probabilistic and multifractal) gives indications that the genetically defined depression is related to individual neurons kinetic problems rather than to the brain system disorder.