Turbulent magnetic dynamo excitation at low magnetic Prandtl number

Planetary and stellar dynamos likely result from turbulent motions in magnetofluids with kinematic viscosities that are small compared to their magnetic diffusivities. Laboratory experiments are in progress to produce similar dynamos in liquid metals. This work reviews recent computations of thresholds in critical magnetic Reynolds number above which dynamo amplification can be expected for mechanically-forced turbulence (helical and non-helical, short wavelength and long wavelength) as a function of the magnetic Prandtl number $P_M$. New results for helical forcing are discussed, for which a dynamo is obtained at $P_M=5\times10^{-3}$. The fact that the kinetic turbulent spectrum is much broader in wavenumber space than the magnetic spectrum leads to numerical difficulties which are bridged by a combination of overlapping direct numerical simulations and subgrid models of magnetohydrodynamic turbulence. Typically, the critical magnetic Reynolds number increases steeply as the magnetic Prandtl number decreases, and then reaches an asymptotic plateau at values of at most a few hundred. In the turbulent regime and for magnetic Reynolds numbers large enough, both small and large scale magnetic fields are excited. The interactions between different scales in the flow are also discussed.Comment: 8 pages, 8 figures, to appear in Physics of Plasma

Hall-MHD small-scale dynamos

Much of the progress in our understanding of dynamo mechanisms has been made within the theoretical framework of magnetohydrodynamics (MHD). However, for sufficiently diffuse media, the Hall effect eventually becomes non-negligible. We present results from three dimensional simulations of the Hall-MHD equations subjected to random non-helical forcing. We study the role of the Hall effect in the dynamo efficiency for different values of the Hall parameter, using a pseudospectral code to achieve exponentially fast convergence. We also study energy transfer rates among spatial scales to determine the relative importance of the various nonlinear effects in the dynamo process and in the energy cascade. The Hall effect produces a reduction of the direct energy cascade at scales larger than the Hall scale, and therefore leads to smaller energy dissipation rates. Finally, we present results stemming from simulations at large magnetic Prandtl numbers, which is the relevant regime in hot and diffuse media such a the interstellar medium.Comment: 11 pages and 11 figure

Nonlinear magneto-optical resonances at D1 excitation of 85Rb and 87Rb in an extremely thin cell

Nonlinear magneto-optical resonances have been measured in an extremely thin cell (ETC) for the D1 transition of rubidium in an atomic vapor of natural isotopic composition. All hyperfine transitions of both isotopes have been studied for a wide range of laser power densities, laser detunings, and ETC wall separations. Dark resonances in the laser induced fluorescence (LIF) were observed as expected when the ground state total angular momentum F_g was greater than or equal to the excited state total angular momentum F_e. Unlike the case of ordinary cells, the width and contrast of dark resonances formed in the ETC dramatically depended on the detuning of the laser from the exact atomic transition. A theoretical model based on the optical Bloch equations was applied to calculate the shapes of the resonance curves. The model averaged over the contributions from different atomic velocity groups, considered all neighboring hyperfine transitions, took into account the splitting and mixing of magnetic sublevels in an external magnetic field, and included a detailed treatment of the coherence properties of the laser radiation. Such a theoretical approach had successfully described nonlinear magneto-optical resonances in ordinary vapor cells. Although the values of certain model parameters in the ETC differed significantly from the case of ordinary cells, the same physical processes were used to model both cases. However, to describe the resonances in the ETC, key parameters such as the transit relaxation rate and Doppler width had to be modified in accordance with the ETC's unique features. Agreement between the measured and calculated resonance curves was satisfactory for the ETC, though not as good as in the case of ordinary cells.Comment: v2: substantial changes and expanded theoretical model; 13 pages, 10 figures; accepted for publication in Physical Review

Steady state existence of passive vector fields under the Kraichnan model

The steady state existence problem for Kraichnan advected passive vector models is considered for isotropic and anisotropic initial values in arbitrary dimension. The model includes the magnetohydrodynamic (MHD) equations, linear pressure model (LPM) and linearized Navier-Stokes (LNS) equations. In addition to reproducing the previously known results for the MHD and linear pressure model, we obtain the values of the Kraichnan model roughness parameter $\xi$ for which the LNS steady state exists.Comment: Improved text & figures, added references & other correction

A uniqueness result for the inverse problem of identifying boundaries from weighted Radon transform

We study the problem of the integral geometry, in which the functions are integrated over hyperplanes in the $n$-dimensional Euclidean space, $n=2m+1$. The integrand is the product of a function of $n$ variables called the density and weight function depending on $2n$ variables. Such an integration is called here the weighted Radon transform, which coincides with the classical one if the weight function is equal to one. It is proved the uniqueness for the problem of determination of the surface on which the integrand is discontinuous.Comment: 10 pages, 1 figur

Stochastic Flux-Freezing and Magnetic Dynamo

We argue that magnetic flux-conservation in turbulent plasmas at high magnetic Reynolds numbers neither holds in the conventional sense nor is entirely broken, but instead is valid in a novel statistical sense associated to the "spontaneous stochasticity" of Lagrangian particle tra jectories. The latter phenomenon is due to the explosive separation of particles undergoing turbulent Richardson diffusion, which leads to a breakdown of Laplacian determinism for classical dynamics. We discuss empirical evidence for spontaneous stochasticity, including our own new numerical results. We then use a Lagrangian path-integral approach to establish stochastic flux-freezing for resistive hydromagnetic equations and to argue, based on the properties of Richardson diffusion, that flux-conservation must remain stochastic at infinite magnetic Reynolds number. As an important application of these results we consider the kinematic, fluctuation dynamo in non-helical, incompressible turbulence at unit magnetic Prandtl number. We present results on the Lagrangian dynamo mechanisms by a stochastic particle method which demonstrate a strong similarity between the Pr = 1 and Pr = 0 dynamos. Stochasticity of field-line motion is an essential ingredient of both. We finally consider briefly some consequences for nonlinear MHD turbulence, dynamo and reconnectionComment: 29 pages, 10 figure

Nonlinearity in a dynamo

Using a rotating flat layer heated from below as an example, we consider effects which lead to stabilizing an exponentially growing magnetic field in magnetostrophic convection in transition from the kinematic dynamo to the full non-linear dynamo. We present estimates of the energy redistribution over the spectrum and helicity quenching by the magnetic field. We also study the alignment of the velocity and magnetic fields. These regimes are similar to those in planetary dynamo simulations.Comment: Accepted to Geophys. Astrophys. Fluid Dyna

Problems and Prospects of Regulating Relations within a Deal Effected with Participation of Artificial Intelligence

Objective: to research the problem of determining the subject of a legally relevant act effected with participation of artificial intelligence, as well as distribution of responsibility for the consequences of its performance.Methods: to illustrate the problematic and practical significance of the issue of legal personality of artificial intelligence, we chose automated procurements for public and corporate needs; the methodological basis of the research is the set of methods of scientific cognition, including comparison, retrospective analysis, analogy, and synthesis.Results: by the example of the sector of competitive procurements for public and corporate needs, the evolution of automation of economic relations up to artificial intelligence introduction was analyzed. Successfully tested reactions to the challenges of stage-by-stage introduction of digital technologies into economic relations were demonstrated, as well as the respective modifications of legal regulation. Based on the current level of technological development, the prospective questions are formulated, associated with the legal regulation of  economic relations implemented with the use of artificial intelligence, first of all, the question of defining the subject of a deal effected with participation of artificial intelligence. As an invitation for discussion after analysis of jurists’ conclusions about the probable variants of the legal status of artificial intelligence, the author proposes variants of answers to the question of its legal personality when effecting a deal. To solve the issue of responsibility for the decisions resulting from the implementation of algorithms of a software and hardware package, we propose several models of distributing such responsibility among its creator, owner, and other persons, whose actions might influence the results of such an algorithm functioning. The proposed conclusions may be used to develop normative regulation both as a set and individually.Scientific novelty: based on the analysis of evolution of the practices of using digital technologies in procurement, the work formulates potential legal problems, determined by the constant automation of economic relations, and proposes legal constructs to solve such problems.Practical significance: the conclusions and proposals of this work are of prospective significance for conceptual comprehension and normative regulation of electronic procurement tools both at corporate and national level

Trends in Banking Activities Influence on the Formation of Points of Socio-Economic Growth in the Regions

The purpose of the article is to identify the characteristics of the impact of banking activities on the formation of points of socio-economic growth in the region on the example of the North-West Federal District. The study used a variety of methods of scientific knowledge of economic and social processes, including: systemic, grouping, theoretical generalization, the method of scientific abstraction, comparative analysis. It was stated that the current level of socio-economic development of the North-West Federal District requires finding effective ways to systematically solve the problems existing in the region, aimed at implementing projects for the development of the economic and social sphere of the region. It is shown that banking institutions, in addition to the financial and credit functions proper perform unique system-forming functions of the activities of all subjects of economic and social relations in obtaining banking services. The article demonstrates the significant economic and social role of banking institutions in the development of the North-West Federal District. It was concluded that banking capital should contribute to the development of production, agriculture and small business, to promote employment and increase incomes of the population. The study showed that the level of interregional differentiation in the North-West Federal District is quite significant, which is an unfavorable factor and does not contribute to the intensive development of the region. Therefore, a number of proposals were formulated, the implementation of which could contribute to a more effective impact on the current situation: namely, bank financing should be more actively directed to less developed regions of the district, and priority should be given to high-tech and innovative industries that will enhance the competitiveness of the district; it is necessary to intensify government procurement with the involvement of bank capital to support the economy of less developed regions of the district; the interaction of regional governments in the North-West Federal District with banking organizations should be improved. Also, banks in the Northwestern Federal District should focus on supporting small and medium-sized businesses, which have significant potential for development in this region. It was emphasized that such an approach would allow for the realization of not only the economic but also the social role of banks, as well as improves the indicators of socio-economic development both of the entire district and of its individual territories