Turbulence without pressure in d dimensions

The randomly driven Navier-Stokes equation without pressure in d-dimensional space is considered as a model of strong turbulence in a compressible fluid. We derive a closed equation for the velocity-gradient probability density function. We find the asymptotics of this function for the case of the gradient velocity field (Burgers turbulence), and provide a numerical solution for the two-dimensional case. Application of these results to the velocity-difference probability density function is discussed.Comment: latex, 5 pages, revised and enlarge

Influence of a large-scale field on energy dissipation in magnetohydrodynamic turbulence

This is the author accepted manuscript. The final version is available from OUP via the DOI in this record.In magnetohydrodynamic (MHD) turbulence, the large-scale magnetic field sets a preferred local direction for the small-scale dynamics, altering the statistics of turbulence from the isotropic case. This happens even in the absence of a total magnetic flux, since MHD turbulence forms randomly oriented large-scale domains of strong magnetic field. It is therefore customary to study small-scale magnetic plasma turbulence by assuming a strong background magnetic field relative to the turbulent fluctuations. This is done, for example, in reduced models of plasmas, such as reduced MHD, reduced-dimension kinetic models, gyrokinetics, etc., which make theoretical calculations easier and numerical computations cheaper. Recently, however, it has become clear that the turbulent energy dissipation is concentrated in the regions of strong magnetic field variations. A significant fraction of the energy dissipation may be localized in very small volumes corresponding to the boundaries between strongly magnetized domains. In these regions, the reduced models are not applicable. This has important implications for studies of particle heating and acceleration in magnetic plasma turbulence. The goal of this work is to systematically investigate the relationship between local magnetic field variations and magnetic energy dissipation, and to understand its implications for modelling energy dissipation in realistic turbulent plasmas.The authors thank the referee, Alexander Schekochihin, for helpful comments. VZ acknowledges support from NSF grant AST-1411879. SB is partly supported by the National Science Foundation under the grant NSF AGS-1261659 and by the Vilas Associates Award from the University of Wis- consin - Madison. JM acknowledges the support of the EPSRC, through grant EP/M004546/1. We acknowledge PRACE for awarding us access to resource FERMI based in Italy at CINECA, and the STFC DiRAC HPC Facility for access to the COSMA Data Centric system at Durham University and MINERVA at the University of Warwick

Role of cross helicity in magnetohydrodynamic turbulence

Strong incompressible three-dimensional magnetohydrodynamic turbulence is investigated by means of high resolution direct numerical simulations. The simulations show that the configuration space is characterized by regions of positive and negative cross-helicity, corresponding to highly aligned or anti-aligned velocity and magnetic field fluctuations, even when the average cross-helicity is zero. To elucidate the role of cross-helicity, the spectra and structure of turbulence are obtained in imbalanced regions where cross-helicity is non-zero. When averaged over regions of positive and negative cross-helicity, the result is consistent with the simulations of balanced turbulence. An analytical explanation for the obtained results is proposed.Comment: 4 pages, 4 figure

A note on Burgers' turbulence

In this note the Polyakov equation [Phys. Rev. E {\bf 52} (1995) 6183] for the velocity-difference PDF, with the exciting force correlation function $\kappa (y)\sim1-y^{\alpha}$ is analyzed. Several solvable cases are considered, which are in a good agreement with available numerical results. Then it is shown how the method developed by A. Polyakov can be applied to turbulence with short-scale-correlated forces, a situation considered in models of self-organized criticality.Comment: 11 pages, Late

Dynamical Anomalies and Intermittency in Burgers Turbulence

We analyze the field theory of fully developed Burgers turbulence. Its key elements are shock fields, which characterize the singularity statistics of the velocity field. The shock fields enter an operator product expansion describing intermittency. The latter is found to be constrained by dynamical anomalies expressing finite dissipation in the inviscid limit. The link between dynamical anomalies and intermittency is argued to be important in a wider context of turbulence.Comment: revised version, 4 pp., 1 fig., to appear in PR

THE STATE POLICY OF THE RUSSIAN FEDERATION ON THE NORTHERN AND ARCTIC TERRITORIES IN THE 1990S: STAGES, PRIORITIES, MECHANISMS, AND RESULTS

Purpose: The purpose of the study is to determine the state policy of the Russian Federation on the Northern and Arctic territories in the 1990s. Methodology: This is analytical-logical research that has been done through content analysis and documentary and library research. Result: Results showed that First of all Russia abruptly changed the priorities of its policy to the Far North setting the course to leave the region in all spheres. Dozens of polar expeditions from the USA, Norway, and Germany were sent to the Russian sector of polar lands. Russia itself rapidly turned off its economic presence in the North. “The North Pole-31” (drifting polar station) was stopped for 12 years on June 25, 1991. Applications: This research can be used for universities, teachers, and students. Novelty/Originality: In this research, the model of the state policy of the Russian Federation on the northern and arctic territories in the 1990s is presented in a comprehensive and complete manner

Symmetries of the stochastic Burgers equation

All Lie symmetries of the Burgers equation driven by an external random force are found. Besides the generalized Galilean transformations, this equation is also invariant under the time reparametrizations. It is shown that the Gaussian distribution of a pumping force is not invariant under the symmetries and breaks them down leading to the nontrivial vacuum (instanton). Integration over the volume of the symmetry groups provides the description of fluctuations around the instanton and leads to an exactly solvable quantum mechanical problem.Comment: 4 pages, REVTeX, replaced with published versio

Mechanochemistry and solubilization of drugs

The results on solubilization of poorly water-soluble drugs, indomethacin, piroxicam, and meloxicam, with the help of mechanochemical methods are presented. The mechanocomposites of the drugs with various excipients, including soluble polymers and non-soluble fine porous inorganic oxides, were obtained by co-grinding using vibrational and planetary centrifugal mills. The samples obtained revealed higher release rate and apparent solubility of the drugs with respect to the initial ones. Nevertheless, in some cases, e.g. for composites of piroxicam with alumina and ferric oxide, decreasing the release rate and solubility of the drug was observed suggesting the formation of poorly soluble strong drug - carrier associates

Spectral Properties of Compressible Magnetohydrodynamic Turbulence from Numerical Simulations

We analyze the spectral properties of driven, supersonic compressible magnetohydrodynamic (MHD) turbulence obtained via high-resolution numerical experiments, for application to understanding the dynamics of giant molecular clouds. Via angle-averaged power spectra, we characterize the transfer of energy from the intermediate, driving scales down to smaller dissipative scales, and also present evidence for inverse cascades that achieve modal-equipartition levels on larger spatial scales. Investigating compressive versus shear modes separately, we evaluate their relative total power, and find that as the magnetic field strength decreases, (1) the shear fraction of the total kinetic power decreases, and (2) slopes of power-law fits over the inertial range steepen. To relate to previous work on incompressible MHD turbulence, we present qualitative and quantitative measures of the scale-dependent spectral anisotropy arising from the shear-Alfv\'{e}n cascade, and show how these vary with changing mean magnetic field strength. Finally, we propose a method for using anisotropy in velocity centroid maps as a diagnostic of the mean magnetic field strength in observed cloud cores.Comment: 22 pages, 11 figures; Ap.J., accepte