Self-similar formation of the Kolmogorov spectrum in the Leith model of turbulence

The last stage of evolution toward the stationary Kolmogorov spectrum of hydrodynamic turbulence is studied using the Leith model [1] . This evolution is shown to manifest itself as a reflection wave in the wavenumber space propagating from the largest toward the smallest wavenumbers, and is described by a self-similar solution of a new (third) kind. This stage follows the previously studied stage of an initial explosive propagation of the spectral front from the smallest to the largest wavenumbers reaching arbitrarily large wavenumbers in a finite time, and which was described by a self-similar solution of the second kind [2, 3, 4]. Nonstationary solutions corresponding to“warm cascades” characterised by a thermalised spectrum at large wavenumbers are also obtained

The Kelvin-wave cascade in the vortex filament model

The energy transfer mechanism in zero temperature superfluid turbulence of helium-4 is still a widely debated topic. Currently, the main hypothesis is that weakly nonlinear interacting Kelvin waves transfer energy to sufficiently small scales such that energy is dissipated as heat via phonon excitations. Theoretically, there are at least two proposed theories for Kelvin-wave interactions. We perform the most comprehensive numerical simulation of weakly nonlinear interacting Kelvin-waves to date and show, using a specially designed numerical algorithm incorporating the full Biot-Savart equation, that our results are consistent with nonlocal six-wave Kelvin wave interactions as proposed by L'vov and Nazarenko.Comment: 6 pages, 6 figure

Steady states in Leith's model of turbulence

We present a comprehensive study and full classification of the stationary solutions in Leith's model of turbulence with a generalised viscosity. Three typical types of boundary value problems are considered: Problems 1 and 2 with a finite positive value of the spectrum at the left (right) and zero at the right (left) boundaries of a wave number range, and Problem 3 with finite positive values of the spectrum at both boundaries. Settings of these problems and analysis of existence of their solutions are based on a phase–space analysis of orbits of the underlying dynamical system. One of the two fixed points of the underlying dynamical system is found to correspond to a 'sharp front' where the energy flux and the spectrum vanish at the same wave number. The other fixed point corresponds to the only exact power-law solution—the so-called dissipative scaling solution. The roles of the Kolmogorov, dissipative and thermodynamic scaling, as well as of sharp front solutions, are discussed

Improving the indicators of schoolchildren’s adaptation to physical activity using an individual approach, taking into account the types of vegetative regulation

Purpose: physiological substantiation of the physical activity selection based on the differences in the functional state of schoolchildren with different types of cardiovascular system autonomic regulation.Methods: 60 schoolchildren, 12 years old, were examined. The experimental group consisted of schoolchildren who were engaged in physical exercises for 6 months according to the developed individual typological program. Students in the control group followed the school programm. The assessment of the functional state was carried out by the method of “Express assessment of the physical health of schoolchildren” and the method of diagnosing indicators of heart rate variability.Results: at the beginning of the survey, the indicators in the experimental group and the control group were determined by the characteristics of 4 types of autonomic regulation: I, II, III, IV. Of these, I, II corresponded to the predominance of sympathetic-tonic destabilizing influences on the cardiovascular system, in IV parasympathetic influences prevailed, manifested in the asthenia of the functional state of students. Whereas type III refers to the physiological norm and manifested itself in the form of a balance of regulatory influences of the parts of the autonomic nervous system.Conclusions: at the control examination, the indicators of adaptation and health improved in all types of schoolchildren, while in the control group there was no positive dynamics of indicators of adaptation and health. This testifies to the effectiveness of individually typologically oriented classes at a physical education lesson as having a health-improving effect on schoolchildren

Superconductivity in the Cuprates as a Consequence of Antiferromagnetism and a Large Hole Density of States

We briefly review a theory for the cuprates that has been recently proposed based on the movement and interaction of holes in antiferromagnetic (AF) backgrounds. A robust peak in the hole density of states (DOS) is crucial to produce a large critical temperature once a source of hole attraction is identified. The predictions of this scenario are compared with experiments. The stability of the calculations after modifying some of the original assumptions is addressed. We find that if the dispersion is changed from an antiferromagnetic band at half-filling to a tight binding $cosk_x + cosk_y$ narrow band at $=0.87$, the main conclusions of the approach remain basically the same i.e. superconductivity appears in the $d_{x^2 - y^2}$-channel and $T_c$ is enhanced by a large DOS. The main features distinguishing these ideas from more standard theories based on antiferromagnetic correlations are here discussed.Comment: RevTex, 7 pages, 5 figures are available on reques

Specific features of state regulation of operations with cryptocurrencies in the conditions of digitalization

Purpose: The article investigates specific features of state regulation of operations with cryptocurrencies in the conditions of the world economy digitalization. Design/Methodology/Approach: In order to form the state regulation of operations with cryptocurrencies, which create additional risks for the national currencies functioning in international financial and credit relations, it is necessary to consider this phenomenon first, from the position of a complete ban on the use of cryptocurrencies as a means of payment, second, in combination of a ban on the use of cryptocurrencies as means of payment, third, from the possibility of expanding the range of cryptocurrency users by including legal entities into it and fourth, the full legalization of the cryptocurrency. Findings: The authors developed and proposed a set of measures aimed at the formation of common standards and norms of state regulation of operations with cryptocurrencies in international financial relations. Practical Implications: The results of the study can be applied in the development of legal regulation of virtual currencies not only at the national level, but also at the international level. Originality/Value: The main contribution of the study is to identify possible risks in the sphere of state regulation of cryptocurrencies based on the experience of some countries: from formal permission (including recommendations on possible risks) or the application of general principles of regulation in the field of payments to the complete ban of such activities.peer-reviewe