Search

The problem of the cyclic voltammetry investigation of the initial stages of electrochemical phase formation is considered. Analytical expressions are derived for the cyclic voltammograms and the sizes of the independent new-phase nuclei having formed on an indifferent electrode under linear potential sweep conditions for the cases of instantaneous and progressive nucleation followed by diffusion-controlled growth. The current as a function of the overpotential is found to have different dependences on the scan rate for the given limiting cases of nucleation. The results of a numerical simulation are presented. The logarithmic dependences of the maximum and minimum currents on the scan rate are shown to have a slope of –1/2 if nuclei appear in a narrow time interval long before the reverse, their number does not change when the scan rate changes, and their growth is controlled by diffusion. The slope of the dependences is –3/2 when nuclei form before and after the reverse and their number decreases with increasing scan rate. The possibility of using the proposed criteria for the interpretation of the experimental cyclic voltammograms is analyzed and confirmed for the model system (KNO3–NaNO3–AgNO3 melt/iridium substrate/silver) at low concentrations of depositing ions, which provide diffusion control of the process. Both instantaneous nucleation and progressive nucleation are shown to occur in this system, depending on other experimental conditions.

We study the system of two fourth-order nonlinear hyperbolic partial differential equations. The right-hand sides of the equations contain double Laplace operators and the squares of the gradients of the sought functions. Such equations, close to the Boussinesq equation and the Navier–Stokes equations, occur in problems of hydrodynamics. We propose to search for a solution in the form of an ansatz containing quadratic dependence on the spatial variables and arbitrary functions of time. The use of the ansatz allows us to decompose the process of finding the components of the solution depending on the space variables and time. For finding the dependence on the space variables, it is necessary to solve an algebraic system of matrix, vector, and scalar equations. We find the general solution to this system in parametric form. In finding the time-dependent components of the solution to the original system, there arises a system of nonlinear ordinary differential equations. In the particular case when the squares of the gradients are not included in the system, we establish the existence of exact solutions of a certain kind to the original system expressed through arbitrary harmonic functions of the space variables and exponential functions of time. Some examples are given of the constructed exact solutions including solutions periodic in time and anisotropic in space variables. The exact solutions can be used to verify numerical methods for the approximate construction of the solutions to applied boundary value problems.

An analysis of the I–V characteristics makes it possible to determine the mechanisms of conduction corresponding to different states of the flow channels upon resistive switching in porphyrazine films. A variation in the temperature, the structure of the dielectric matrix, and the type of majority charge carriers makes it possible to estimate the applicability of the model of conducting filaments for describing transport and determining the mechanisms of conduction for each state of the system.

We obtain broad sufficient conditions for the boundedness of distribution densities of homogeneous functions on spaces with Gaussian measures. Estimates for the distribution densities of maxima of quadratic forms are obtained.

We consider a generalized Richards equation with power-law nonlinearities modeling filtration in porous media. Conditions are derived under which the problem can be reduced to the linear heat equation or to nonlinear equations with known solutions. The families of explicit exact solutions that can be expressed via elementary functions or Lambert’s $$W $$ -function are found. Some examples illustrating the results are given.

An approach is proposed to perform a mathematical description of the electrochemical formation and growth of binary alloy nuclei on the surface of an indifferent electrode under constant supersaturation (overpotential). This approach considers the total flux of two species of deposited ions in the electrolyte bulk to the surface of hemispherical new-phase nuclei. The concentration profile is averaged with allowance for the mole fraction ratio of the components. The cases of instantaneous and progressive nucleation with diffusion-controlled growth are studied. The overlap of the diffusion zones of the nuclei is analyzed in terms of the Scharifker–Hills model. Equations are derived to calculate the apparent diffusion coefficient of deposited ions, the number of nuclei per unit electrode surface, and the steady-state nucleation rate.

The characteristic features of the diffusion of helium and nitrous oxide diluted by propane to the same extent are experimentally studied at different pressures and concentrations of the diluent gas in the mixture. It is found that, at a certain pressure, convection currents appear in the system which intensify the partial mass transfer, which uncommon for diffusion. An increase in pressure intensifies the mixing of the components of the mixture. An increase in the concentration of the diluent gas in the mixture leads to the stabilization of convection modes. Solving diffusion equations shows that, in systems with a ballast gas, conditions for the nonlinear distribution of the concentrations of the components of the mixture along the length of the channel are implemented which can lead to the appearance of an extremum of the density of the mixture (i.e., inversion of the density gradient of the mixture), which induces the appearance of convection currents. The stability of the mechanical equilibrium of the ternary mixture in a vertical cylindrical channel under the action of gravity and at the predefined concentration gradients of the components is numerically studied. The boundary of the diffusion–convection kinetic transition is determined. The experimental and numerical results are compared in the coordinates of the Rayleigh number and pressure.

This article discusses methods for determining trace gases in the Earth’s atmosphere based on radio translucence of the satellite–Earth or Earth–satellite–Earth route using monochromatic radiation at a given frequency set. The substantiation of a new method using the difference of differential signals on different slopes of the absorption line of the measured gas is carried out, which allows one to increase the spatial selectivity of the measurements and reduce the influence of clouds, precipitation, and third-party gases. The results of calculating the kernels of integral equations when measuring the profile of water vapor in the absorption band of 22.23 GHz are presented. The selectivity of the kernels makes it possible to restore the water-vapor profile both in the lower troposphere layer to heights of 8 km and in the 30–80 km layer. The advantage of the proposed methods is the differential nature of the measurements, which does not require absolute calibration of sources and long-term stability of the equipment. In addition, it becomes possible to register small-scale and rapidly varying processes occurring during the revolution of the satellite in orbit on a spatial scale of 2–10 km. It is precisely this scale of spatiotemporal changes in the concentration of greenhouse gases that can be expected during technological accidents, missile launches, and other anthropogenic influences.

The peculiarities of a convective regime aroused due to instability of mechanical equilibrium of a ternary helium–argon–nitrogen gas mixture at isothermal diffusion are experimentally investigated. The effect of the inclination angle of diffusion channel on the intensity of convective flows is considered. The intensity of the partial transport of components in the inclined channel was measured at increased pressures. The nonlinear dependence of the mixing rate of components on the inclination angle is discovered. It is established that the observed transport of components atypical for diffusion is possible at a certain composition of the gas mixture.

The methods used for the preparation of an Al–Er master alloy as a promising addition to aluminum alloys for enhancing their physical and mechanical characteristics are analytically reviewed. Thermodynamic analysis of the processes that occur during master alloy fabrication in chloride–fluoride melts containing erbium oxide is carried out. Since the data on erbium complexes are lacking or restricted, the thermodynamic values are determined by indirect methods. The study of the phase composition of the chloride–fluoride melts shows that the melting of a salt mixture results in the fluorination of erbium oxide and the formation of the KEr3F10 complex, which is a precursor for erbium reduction and intermetallic compound Al3Er formation. The effect of the flux composition and the technological parameters of aluminothermic reduction on the transition of erbium to the master alloy is studied.

The electrochemical behavior of nickel in the K2WO4–Na2WO4 (1 : 1)–WO3 (35 mol %) and K2WO4–Na2WO4 (1 : 1)–WO3 (50 mol %) polytungstate melts was studied by the cyclic voltammetry. Based on a comparison of the obtained cyclic voltammograms with the data of SEM, EDS and XRD conclusions were drawn about the sequence of processes proceeding on the nickel substrate. Equations of the electrolysis products formation are proposed.

We study a nonlinear system of two elliptic differential equations with nonlinearities depending on a product of powers of the unknown functions. Sufficient conditions for the system to be reducible to a single equation are obtained. Some cases are singled out for which we find classes of exact solutions expressed via elementary and harmonic functions and solutions of the Liouville equation.

This paper considers the stability of singular switched systems with homogeneous functions in the right-hand sides of the corresponding equations. Stability conditions of the complete system with an arbitrary switching mode are established through its decomposition into the isolated subsystems of fast and slow motions. A stabilizing feedback control design method based on measurements of the fast variables only is suggested.

This paper describes a space experiment that is planned to be performed within the framework of the Russian project of the microsatellite CHIBIS AI to meaure ionospheric signal delays to determine the electron density and spatial fluctuations of the ionospheric and magnetospheric plasma. The measurements will be conducted by the phase interferometer method at two levels using signals from the onboard in-phase transmitters and GPS/GLONASS signals. The location of the radiation sources at two levels will make it possible to separate plasma variations in the ionosphere and inner magnetosphere–plasmasphere. The experimental results are of interest both for solving fundamental problems of near-Earth plasma physics and applied problems to improve positioning accuracy using global navigation systems.

Radiation transport of α-particles requires cross sections of inelastic interaction of α-particles with nuclei. At low energies the inelastic interactions are limited to the 9Be(α, n) reaction, whose channel cross sections are assessed only in the specialized evaluated nuclear data library JENDL/AN-2005. The new TPT (Toolkit for Particle Transport) approximation of the 9Be(α, n) reaction cross sections for different channels takes into account the lowest resonance and, at high energies, relies on the exponential decrease in the S-factor, which is a consequence of the theory of direct nuclear reactions.

Under consideration is the problem of stability of switched discrete systems with the generalized homogeneous right-hand sides. The conditions are obtained for the existence of the common Lyapunov function, and a method for its construction is proposed in the form of a combination of the partial Lyapunov functions obtained for isolated subsystems. For a special case of linear three-dimensional systems, some algorithms are proposed for constructing common Lyapunov functions as quadratic and fourth degree forms. Some examples illustrate the effectiveness of the proposed approach.

Differential thermal analysis is used to study the processes that occur during the interaction of erbium fluoride with potassium chloride–sodium fluoride melts, which are used as a flux for the metallothermic synthesis of an Al–Er master alloy. The flux compositions under study are used to synthesize Al–Er master alloys and can be recommended for the preparation of intermediate alloys with a high alloying-element content (15 wt % or more). Experimental studies allowed us to synthesize master alloys having a new chemical composition. The microstructure and the chemical and phase compositions of the master alloys are studied.

Available foreign power-intensive technologies and the absence of domestic production technologies for aluminum–erbium master alloys intended for improving the physicomechanical properties of aluminum alloys make the development of aluminothermic reduction technology of chloride–fluoride melts actual for manufacturing erbium compounds. Thermodynamic analysis of reduction processes is performed for various erbium compounds. Taking into account the physical and chemical properties of erbium compounds, a starting compound, namely, erbium fluoride is found to be preferable. The aluminothermic reduction of the compound from its mixture with sodium fluoride and potassium chloride to form the Al3Er intermetallic compound is characterized by a high thermodynamic probability. Since data on thermodynamic parameters for erbium complex compound are scanty, they are determined by an indirect method. Experimental data on the aluminothermic preparation of an Al–Er master alloy at temperatures of 750–900°C using melts differing in the ErF3/NaF ratio and the KCl content are reported; the structure and the phase composition of the prepared master alloy are studied. The phase composition of the flux used for the preparation of the Al–Er master alloy is determined.