arXiv subjects
Publications and source records attributed to A. Bershadskii.
Using the WMAP cosmic microwave background data it is shown that collisions between Alfven wave packets and the cascades generated by these collisions (the Iroshnikov model) can determine the photon temperature fluctuations for arcminute scales on the last scattering surface.
A logarithmic scaling for structure functions, in the form $S_p \sim [\ln (r/η)]^{ζ_p}$, where $η$ is the Kolmogorov dissipation scale and $ζ_p$ are the scaling exponents, is suggested for the statistical description of the near-dissipation range for which classical power-law scaling does not apply. From experimental data at moderate Reynolds numbers, it is shown that the logarithmic scaling, deduced from general considerations for the near-dissipation range, covers almost the entire range of scales (about two decades) of structure functions, for both velocity and passive scalar fields. This new scaling requires two empirical constants, just as the classical scaling does, and can be considered the basis for extended self-similarity.
Broad theoretical arguments are proposed to show, formally, that the magnitude G of the temperature gradients in turbulent thermal convection at high Rayleigh numbers obeys the same advection-diffusion equation that governs the temperature fluctuation T, except that the velocity field in the new equation is substantially smoothed. This smoothed field leads to a -1 scaling of the spectrum of G in the same range of scales for which the spectral exponent of T lies between -7/5 and -5/3. This result is confirmed by measurements in a confined container with cryogenic helium gas as the working fluid for Rayleigh number Ra=1.5x10^{11}. Also confirmed is the logarithmic form of the autocorrelation function of G. The anomalous scaling of dissipation-like quantities of T and G are identical in the inertial range, showing that the analogy between the two fields is quite deep.
Using experimental data on thermal convection, obtained at a Rayleigh number of 1.5 $\times 10^{11}$, it is shown that the temperature structure functions $<ΔT_{r}^p>$, where $ΔT_r$ is the absolute value of the temperature increment over a distance $r$, can be well represented in an intermediate range of scales by $r^{ζ_p} ϕ(r)^{p}$, where the $ζ_p$ are the scaling exponents appropriate to the passive scalar problem in hydrodynamic turbulence and the function $ϕ(r) = 1-a(\ln r/r_h)^2$. Measurements are made in the midplane of the apparatus near the sidewall, but outside the boundary layer.
Using data obtained in a laboratory thermal convection experiment at high Rayleigh numbers, it is shown that the multiscaling properties of the observed mean wind reversals are quantitatively consistent with analogous multiscaling properties of the Bak-Tang-Wiesenfeld prototype model of self-organized criticality in two dimensions.
It is shown that the statistical properties of the magnitude of the magnetic field in turbulent electrically conducting media resemble, in the inertial range, those of passive scalars in fully developed three-dimensional fluid turbulence. This conclusion, suggested by the data from Advanced Composition Explorer, is supported by a brief analysis of the appropriate magnetohydrodynamic equations.
Temperature time traces are obtained in turbulent thermal convection at high Rayleigh numbers. Measurements are made in the midplane of the apparatus, near the sidewall but outside the boundary layer. A telegraph approximation for temperature traces is generated by setting the fluctuation amplitude to 1 or 0 depending on whether or not it exceeds the mean value. Unlike the standard diagnostics of intermittency, the telegraph approximation allows one to distinguish the tendency of events to cluster ("clusterization") from their large-scale variability in amplitude. A qualitative conclusion is that amplitude intermittency might mitigate clusterization effects.
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 {\it 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).
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.
The question: whether quantum coherent states can sustain decoherence, heating and dissipation over time scales comparable to the dynamical timescales of the brain neurons, is actively discussed in the last years. Positive answer on this question is crucial, in particular, for consideration of brain neurons as quantum computers. This discussion was mainly based on theoretical arguments. In present paper nonlinear statistical properties of the Ventral Tegmental Area (VTA) of genetically depressive limbic brain are studied {\it in vivo} on the Flinders Sensitive Line of rats (FSL). VTA plays a key role in generation of pleasure and in development of psychological drug addiction. We found that the FSL VTA (dopaminergic) neuron signals exhibit multifractal properties for interspike frequencies on the scales where healthy VTA dopaminergic neurons exhibit bursting activity. For high moments the observed multifractal (generalized dimensions) spectrum coincides with the generalized dimensions spectrum calculated for a spectral measure of a {\it quantum} system (so-called kicked Harper model, actively used as a model of quantum chaos). This observation can be considered as a first experimental ({\it in vivo}) indication in the favour of the quantum (at least partially) nature of the brain neurons activity.
Multiscaling properties of the Anderson localization of the cosmic electromagnetic fields before the recombination time are studied and results of a numerical simulation for a random banded matrix ensemble are found to be in good agreement with the large-scale cosmic data.
Multiscaling analysis of differential flux dissipation rate of galactic cosmic rays (Carbon nuclei) is performed in the energy ranges: 56.3-73.4 Mev/nucleon and 183.1-198.7 MeV/nucleon, using the data collected by ACE/CRIS spacecraft instrument for 2000 year. The analysis reveals strong (turbulence-like) intermittency of the flux dissipation rate for the short-term intervals: 1-30 hours. It is also found that type of the intermittency can be different in different energy ranges.
Scaling properties of the cosmic microwave background (CMB) radiation are studied using satellite (COBE-DMR maps), balloon-borne and ground-based (combined QMASK map) data. Quantitative consistency is found between the multiscaling properties of the COBE-DMR and QMASK CMB maps. Surprisingly, it is found that the observed CMB temperature multiscaling resembles quantitatively the multiscaling properties of fluid turbulence, that indicates primordial plasma turbulence as an origin of the CMB temperature space anisotropy.