arXiv subjects

A. Bershadskii

Publications and source records attributed to A. Bershadskii.

At least 73 records · Page 4Linked to original sources

arXiv2016

Superfluid (quantum) turbulence and distributed chaos

Properties of distributed chaos in superfluid (quantum) turbulence have been studied using the data of recent direct numerical simulations (HVBK two-fluid model for He II, and a moving grid in the frames of Gross-Pitaevskii model of the Bose-Einstein condensates at low temperatures). It is found that for the viscous (normal) component of the velocity field in He II the viscosity dominates the distributed chaos with the stretched exponential spectrum $\exp(-k/k_β)^β$ and $β= 2/3$. For the superfluid component the distributed chaos is dominated by the vorticity correlation integral with $β=1/2$ (the soft spontaneous breaking of the space translational symmetry - homogeneity). For very low temperature the distributed chaos is tuned to the large-scale coherent motions: the viscous (normal) component is tuned to the fundamental mode, whereas the superfluid component is subharmonically tuned. For the Gross-Pitaevskii superfluid turbulence incompressible part of the energy spectrum (containing the vortices contribution) also indicates the distributed chaos dominated by the vorticity correlation integral ($β=1/2$) and the subharmonic tuning to the large-scale coherent motions.

physics.flu-dyn↗

arXiv2016

Distributed chaos in turbulent wakes

Soft and hard spontaneous breaking of space translational symmetry (homogeneity) have been studied in turbulent wakes by means of distributed chaos. In the case of the soft translational symmetry breaking the vorticity correlation integral $\int_{V} \langle {\boldsymbol ω} ({\bf x},t) \cdot {\boldsymbol ω} ({\bf x} + {\bf r},t) \rangle_{V} d{\bf r}$ dominates the distributed chaos and the chaotic spectra $\exp-(k/k_β)^{β}$ have $β=1/2$. In the case of the hard translational symmetry breaking, control on the distributed chaos is switched from one type of fundamental symmetry to another (in this case to Lagrangian relabeling symmetry). Due to the Noether's theorem the relabeling symmetry results in the inviscid helicity conservation and helicity correlation integral $I=\int \langle h({\bf x},t)~h({\bf x}+{\bf r}, t)\rangle d{\bf r}$ (Levich-Tsinober invariant) dominates the distributed chaos with $β=1/3$. Good agreement with the experimental data has been established for turbulent wakes behind a cylinder, behind grids (for normal and super-fluids) and for bubbling flows. In the last case even small concentration of bubbles leads to a drastic change of the turbulent velocity spectra due to the hard spontaneous symmetry breaking in the bubbles' wakes.

physics.flu-dyn↗

arXiv2016

Polymer additives in fluid turbulence and distributed chaos

The fluids and polymers have different fundamental symmetries. Namely, the Lagrangian relabeling symmetry of fluids is absent for polymers (while the translational and rotational symmetries are still present). This fact results in spontaneous breaking of the relabeling symmetry in fluid turbulence even at a tiny polymer addition. Since helicity conservation in inviscid fluid motions is a consequence of the relabeling symmetry (due to the Noether's theorem) violation of this conservation by the polymer additives results in the strong effects in the distributed chaos. The distributed chaos in turbulence with the spontaneously broken relabeling symmetry is characterized by stretched exponential spectra $\propto \exp(-k/k_β)^β$ with $β=2/5$. The spectral range of this distributed chaos is extended in direction of the small wavenumbers and $k_β$ becomes much larger in comparison with the pure fluid (Newtonian) case. This results in substantial suppression of small-scale turbulence and large-scale mixing enhancement. Good agreement with results of direct numerical simulations (DNS) and experimental data has been established for a channel flow (DNS), for Rayleigh-Taylor turbulent convection (DNS) and for Rayleigh-Benard turbulent convection (experiment).

physics.flu-dyn↗

arXiv2016

Distributed chaos tuned to large scale coherent motions in turbulence

It is shown, using direct numerical simulations and laboratory experiments data, that distributed chaos is often tuned to large scale coherent motions in anisotropic inhomogeneous turbulence. The examples considered are: fully developed turbulent boundary layer (range of coherence: $14 < y^{+} < 80$), turbulent thermal convection (in a horizontal cylinder), and Cuette-Taylor flow. Two ways of the tuning have been described: one via fundamental frequency (wavenumber) and another via subharmonic (period doubling). For the second way the large scale coherent motions are a natural component of distributed chaos. In all considered cases spontaneous breaking of space translational symmetry is accompanied by reflexional symmetry breaking.

physics.flu-dyn↗

arXiv2016

Strong turbulent convection: distributed chaos and large-scale circulation

Two types of spontaneous breaking of the space translational symmetry in distributed chaos have been considered for turbulent thermal convection at large values of Rayleigh number. First type is related to boundaries and second type is related to appearance of inertial range of scales. The first type is dominated by vorticity correlation integral: $\int_{V} \langle {\boldsymbol ω} ({\bf x},t) \cdot {\boldsymbol ω} ({\bf x} + {\bf r},t) \rangle_{V} d{\bf r}$ and is characterized by stretched exponential spectrum $\exp-(k/k_β)^{β}$ with $β=1/2$. The second type is dominated by energy correlation integral: $\int_{V} \langle {\bf u}^2 ({\bf x},t) ~ {\bf u}^2({\bf x} + {\bf r},t) \rangle_{V} d{\bf r}$ and is characterized by $β=3/5$. Good agreement has been established with laboratory experimental data obtained at large values of Rayleigh number $Ra \sim 10^{11}-10^{14}$ (the range relevant to solar photosphere) in upright cylinder cells. Taylor hypothesis transforms the wavenumber spectrum into frequency spectrum $\exp-(f/f_β)^{1/2}$. It is shown that turnover frequency of large-scale circulation (wind): $f_w = f_β/2$. Results of an experiment in horizontal cylinder are also briefly discussed. The analysis suggests that in this case the large-scale circulation can be considered as a natural (harmonic) part of the distributed chaos.

physics.flu-dyn↗

arXiv2016

Distributed chaos and helicity in turbulence

The distributed chaos driven by Levich-Tsinober (helicity) integral: $I=\int \langle h({\bf x},t)~h({\bf x}+{\bf r}, t)\rangle d{\bf r}$ has been studied. It is shown that the helical distributed chaos can be considered as basis for complex turbulent flows with interplay between large-scale coherent structures and small-scale turbulence, such as Cuette-Taylor flow, wake behind cylinder and turbulent flow in the Large Plasma Device (LAPD) with inserted limiters. In the last case appearance of the helical distributed chaos, caused by the limiters, results in improvement of radial particle confinement.

physics.flu-dyn↗

arXiv2016

Turbulence and distributed chaos with spontaneously broken symmetry

It is shown that in turbulent flows the distributed chaos with spontaneously broken translational space symmetry (homogeneity) has a stretched exponential spectrum $\exp-(k/k_β)^{β}$ with $β=1/2$. Good agreement has been established between the theory and the data of direct numerical simulations of isotropic homogeneous turbulence (energy dissipation rate field), of a channel flow (velocity field), of a fully developed boundary layer flow (velocity field), and the experimental data at the plasma edges of different fusion devices (stellarators and tokamaks). An astrophysical application to the large-scale galaxies distribution has been briefly discussed and good agreement with the data of recent Sloan Digital Sky Survey SDSS-III has been established.

physics.flu-dyn↗

arXiv2016

Distributed chaos and solitons at the edges of magnetically confined plasmas

It is shown, using results of measurements of ion saturation current in the plasma edges of different magnetic fusion confinement devices (tokamaks and stellarators), that the plasma dynamics in the edges is dominated by distributed chaos with spontaneously broken translational symmetry at low magnetic field, and with spontaneously broken reflexional symmetry (by helical solitons) at high magnetic field.

nlin.CD↗

arXiv2016

Decaying turbulence and developing chaotic attractors

Competition between two main attractors of the distributed chaos, one associated with translational symmetry (homogeneity) and another associated with rotational symmetry (isotropy), has been studied in freely decaying turbulence. It is shown that, unlike the case of statistically stationary homogeneous isotropic turbulence, the attractor associated with rotational symmetry (and controlled by Loitsyanskii integral) can dominate turbulent local dynamics in an intermediate stage of the decay, because the attractor associated with translational symmetry (and controlled by Birkhoff-Saffman integral) is still not developed enough. The DNS data have been used in order to support this conclusion.

physics.flu-dyn↗

arXiv2016

Distributed chaos and isotropic turbulence

Power spectrum of the distributed chaos can be represented by a weighted superposition of the exponential functions which is converged to a stretched exponential $\propto \exp-(k/k_β)^{β}$. An asymptotic theory has been developed in order to estimate the value of $β$ for the isotropic turbulence. This value has been found to be $β=3/4$. Excellent agreement has been established between this theory and the data of direct numerical simulations not only for the velocity field but also for the passive scalar, energy dissipation rate, and magnetic fields. One can conclude that the isotropic turbulence emerges from the distributed chaos.

physics.flu-dyn↗

arXiv2015

Deterministic chaos in the large-scale universe: data versus speculations

It is shown, that the both angular CMB Doppler spectrum: $C_l$ (Planck space telescope - cosmic microwave background [1]) and the 3D galaxy-galaxy power spectrum: $P(k)$ (Sloan Digital Sky Survey SDSS-II [2]), exhibit a considerable range with an exponential decay: $370 < l < 2500$ and $0.05 < k < 0.27~~(h/Mpc)$, respectively. The rates of the exponential decay are $l_c \simeq 300$ for $C_l \sim \exp-(l/l_c)$ and $k_c \simeq 0.09~~(h/Mpc)$ for $P(k) \sim \exp-(k/k_c)$. A waviness is observed along a straight line representing the exponential decay in the log-linear scale graphs of these spectra. In both cases the waviness has period (distance between peaks) equal to the same $l_c$ and $k_c$ as for the exponential decay. It means that the waviness is generated by the same, presumably chaotic, mechanism that generates the exponential decay. A more complex, distributed, chaos is observed in the Baryon Oscillation Spectroscopic Survey (the largest component of the SDSS-III containing nearly one million galaxies) [3]. In this case the $P(k)$ spectrum is a weighted superposition of the exponentials. At assumption that dynamics of the dispersive waves, driving the distributed chaos, is dominated by the effects of a surface tension this weighted superposition of the exponentials is converged to a compact form of a stretched exponential $P(k) \sim \exp-(k/k_b)^{1/2}$, in good agreement with the data.

nlin.CD↗

arXiv2012

Nonlinear problems of complex natural systems: Sun and climate dynamics

Universal role of the nonlinear one-third subharmonic resonance mechanism in generation of the strong fluctuations in such complex natural dynamical systems as global climate and global solar activity is discussed using wavelet regression detrended data. Role of the oceanic Rossby waves in the year-scale global temperature fluctuations and the nonlinear resonance contribution to the El Nino phenomenon have been discussed in detail. The large fluctuations of the reconstructed temperature on the millennial time-scales (Antarctic ice cores data for the past 400,000 years) are also shown to be dominated by the one-third subharmonic resonance, presumably related to Earth precession effect on the energy that the intertropical regions receive from the Sun. Effects of Galactic turbulence on the temperature fluctuations are discussed in this content. It is also shown that the one-third subharmonic resonance can be considered as a background for the 11-years solar cycle, and again the global (solar) rotation and chaotic propagating waves play significant role in this phenomenon. Finally, a multidecadal chaotic coherence between the detrended solar activity and global temperature has been briefly discussed.

nlin.CD↗

arXiv2011

Prime numbers: periodicity, chaos, noise

Logarithmic gaps have been used in order to find a periodic component of the sequence of prime numbers, hidden by a random noise (stochastic or chaotic). The recovered period for the sequence of the first 10000 prime numbers is equal to 8\pm1 (subject to the prime number theorem). For small and moderate values of the prime numbers (first 2000 prime numbers) this result has been directly checked using the twin prime killing method.

math.NT↗

arXiv2011

Prime numbers and spontaneous neuron activity

Logarithmic gaps have been used in order to find a periodic component of the sequence of prime numbers, hidden by a random noise (stochastic or chaotic). It is shown that multiplicative nature of the noise is the main reason for the successful application of the logarithmic gaps transforming the multiplicative noise into an additive one. A relation of this phenomenon to spontaneous neuron activity and to chaotic brain computations has been discussed.

q-bio.NC↗

arXiv2011

Broken chaotic clocks of brain neurons and depression

Irregular spiking time-series obtained in vitro and in vivo from singular brain neurons of different types of rats are analyzed by mapping to telegraph signals. Since the neural information is coded in the length of the interspike intervals and their positions on the time axis, this mapping is the most direct way to map a spike train into a signal which allows a proper application of the Fourier transform methods. This analysis shows that healthy neurons firing has periodic and chaotic deterministic clocks while for the rats representing genetic animal model of human depression these neuron clocks might be broken, that results in decoherence between the depressive neurons firing. Since depression is usually accompanied by a narrowing of consciousness this specific decoherence can be considered as a cause of the phenomenon of the consciousness narrowing as well. This suggestion is also supported by observation of the large-scale chaotic coherence of the posterior piriform and entorhinal cortices' electrical activity at transition from anesthesia to the waking state with full consciousness.

q-bio.NC↗

arXiv2011

Chaotic neuron clock

A simple threshold model of neuron firing (with the neuron membrane electrochemical potential governed by the chaotic Rossler attractor) has been analyzed by mapping the generated irregular spiking time-series into telegraph signals. In this model the fundamental frequency of the chaotic Rossler attractor provides (with a period doubling) the strong periodic component of the generated irregular signal. The exponentially decaying broad-band part of the spectrum of the Rossler attractor has been transformed by the threshold firing mechanism into a scaling tale. These results are compared with irregular spiking time-series obtained in vitro from a spontaneous activity of hippocampal (CA3) singular neurons (rat's brain slice culture). The comparison shows good agreement between the model and experimentally obtained spectra.

q-bio.NC↗

arXiv2011

Correlations between large prime numbers

It is shown that short-range correlations between large prime numbers (~10^5 and larger) have a Poissonian nature. Correlation length ζ= 4.5 for the primes ~10^5 and it is increasing logarithmically according to the prime number theorem. For moderate prime numbers (~10^4) the Poissonian distribution is not applicable while the correlation length surprisingly continues to follow to the logarithmical law. A chaotic (deterministic) hypothesis has been suggested to explain the moderate prime numbers apparent randomness.

math.NT↗

arXiv2010

Dynamic cluster-scaling in DNA

It is shown that the nucleotide sequences in DNA molecules have cluster-scaling properties (discovered for the first time in turbulent processes: Sreenivasan and Bershadskii, 2006, J. Stat. Phys., 125, 1141-1153.). These properties are relevant to both types of nucleotide pair-bases interactions: hydrogen bonds and stacking interactions. It is shown that taking into account the cluster-scaling properties can help to improve heterogeneous models of the DNA dynamics. Two human genes: BRCA2 and NRXN1, have been considered as examples.

q-bio.BM↗