Dispersive stabilization of the inverse cascade for the Kolmogorov flow

It is shown by perturbation techniques and numerical simulations that the inverse cascade of kink-antikink annihilations, characteristic of the Kolmogorov flow in the slightly supercritical Reynolds number regime, is halted by the dispersive action of Rossby waves in the beta-plane approximation. For beta tending to zero, the largest excited scale is proportional to the logarithm of one over beta and differs strongly from what is predicted by standard dimensional phenomenology which ignores depletion of nonlinearity.Comment: 4 pages, LATEX, 3 figures. v3: revised version with minor correction

Assessment of the impact of chemical pollution of ferrous metallurgy enterprises on forests using satellite photographs

The considered operating ferrous metallurgy enterprise uses three different technological modes of steel smelting, each of which is characterized by an individual composition of the ingredients of chemical pollutant emissions into the atmosphere affecting the state of the forest areas around this enterprise. Based on the decoding of satellite pixel photographs of forest areas, the technological mode with the least impact on forest areas was determined. It corresponds to the condition of the minimum area of ecological zones around the ferrous metallurgy enterprise. The authors propose an assessment of the impact of chemical pollution of ferrous metallurgy enterprises on forests in the form of areas of ecological zones of the state of forest vegetation and the volume of biomass in its various parts. The mosaic of ecological zones of forest areas is determined from their satellite pixel photographs using an original algorithm of "controlled cluster analysis". The main recommendation for ferrous metallurgy enterprises to choose one of several alternative technological modes is as follows: the choice of technological mode should be based on a comparison of sizes of the areas of ecological zones. In this case, the technological mode with the smallest dimensions of the area is selected. Assessment of the damage caused by the chemical pollution of the plant to forest areas was determined by the area of ecological zones and the volume of biomass loss in forest areas in comparison with the background areas. The boundaries of ecological zones can be determined according to the "dose-effect" dependencies typical for the considered region

Hydrodynamic fluctuations in the Kolmogorov flow: Linear regime

The Landau-Lifshitz fluctuating hydrodynamics is used to study the statistical properties of the linearized Kolmogorov flow. The relative simplicity of this flow allows a detailed analysis of the fluctuation spectrum from near equilibrium regime up to the vicinity of the first convective instability threshold. It is shown that in the long time limit the flow behaves as an incompressible fluid, regardless of the value of the Reynolds number. This is not the case for the short time behavior where the incompressibility assumption leads in general to a wrong form of the static correlation functions, except near the instability threshold. The theoretical predictions are confirmed by numerical simulations of the full nonlinear fluctuating hydrodynamic equations.Comment: 20 pages, 4 figure

Multifractal Analysis of the Mechanical PropOKerties of the Texture of Biopolymer-Inorganic Composites of Chitosan-Silicon Dioxide

An original multifractal algorithm is proposed for calculating the fractal characteristics of the cluster texture of biopolymer-inorganic (BIN) composites from microphotographic images (MPIs) of their texture, which allows one to determine the quantitative dependence of the mechanical properties of biopolymer–inorganic composites on the characteristics of their cluster texture. As a result of the studies conducted on the MPI texture of the “chitosan-silicon dioxide” BIN composites using a multifractal algorithm, it was found that such important indicators as strength and plasticity can be quantitatively described using generalized fractal pixel dimensions of MPI samples of the BIN composite. It was established that when the amount of silicon dioxide in the samples of the BIN composite changes, the mechanical characteristics of the BIN composites, such as strength and plasticity, can be quantitatively described using generalized fractal pixel dimensions of the MPIs of the BIN composite samples

Multifractal Analysis of the Mechanical PropOKerties of the Texture of Biopolymer-Inorganic Composites of Chitosan-Silicon Dioxide

An original multifractal algorithm is proposed for calculating the fractal characteristics of the cluster texture of biopolymer-inorganic (BIN) composites from microphotographic images (MPIs) of their texture, which allows one to determine the quantitative dependence of the mechanical properties of biopolymer–inorganic composites on the characteristics of their cluster texture. As a result of the studies conducted on the MPI texture of the “chitosan-silicon dioxide” BIN composites using a multifractal algorithm, it was found that such important indicators as strength and plasticity can be quantitatively described using generalized fractal pixel dimensions of MPI samples of the BIN composite. It was established that when the amount of silicon dioxide in the samples of the BIN composite changes, the mechanical characteristics of the BIN composites, such as strength and plasticity, can be quantitatively described using generalized fractal pixel dimensions of the MPIs of the BIN composite samples