Chemical instabilities during oxidation of 1,4-naphthalenediol in a homogeneous medium: II. Thermodynamic analysis and mathematical modeling

A possible mechanism of 1,4-naphthalenediol oxidation in the oscillatory regime has been considered, and a mathematical model describing the kinetics has been developed. Based on a thermodynamic Lyapunov function, it has been shown that the source of chemical instabilities is in the existence of autocatalytic steps and dynamic feedbacks. Qualitative analysis and numerical solution of the set of differential equations that model the reaction kinetics have been performed. The character of the stationary state and the possibility of bifurcations have been determined. The mathematical model satisfactorily describes the processes occurring in the system.     

Linear analysis of convective instability of a fluid in a horizontal annular cavity occupied by a porous medium

The problem of convective instability in an infinite horizontal annular porous stratum located in an impermeable rock mass is considered. Using the Bubnov-Galerkin method, the values of the first seven critical Rayleigh numbers are found. The forms of the corresponding critical motions are established. The change in the modes of instability of the critical motions when the thickness of the porous stratum is varied is analyzed.Makhachkala. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 19–25, May–June, 1996.     

Nonlinear (Fluctuational) dynamics and mathematical modeling of homogenous oxidation of biological substrates

Nonlinear dynamics and mathematical modeling approaches were presented for studying chemical oscillations during homogeneous oxidation of biological substrates in the presence of oxygenated complexes of iron(II). It was shown that examination of fluctuational dynamics is only possible via consistent use of several algorithms for time series processing and that flicker-noise spectroscopic technique is best suited to deriving the most exhaustive information from the patterns of temporal variation of signals. The qualitative analysis was performed, and numerical solution was found for the system of differential equations modeling the reactions kinetics. The nature of the steady state was elucidated, and the possibility of Andronov-Hopf type bifurcation with realization of an oscillatory mode was demonstrated.     

The Dynamics of Homogeneous Oxidation of Cysteine in the Presence of Oxygenated Complexes of Cobalt(II) with o-Disalicylidene-Phenylenediamine and Cytosine in a Reactor with Mixing

Moscow University Chemistry Bulletin - The homogeneous process of cysteine oxidation in a stirred reactor is studied. We found that oscillatory mode can be realized in the cysteine–cobalt(II)...     

Fluctuations of the Impurity Photoconductivity in Crystals of Cadmium Sulfoselenide Doped with Potassium: Nonequilibrium Thermodynamics and Mathematical Modeling

Moscow University Chemistry Bulletin - The results of the analysis of the fluctuations of the impurity photoconductivity in monocrystals of cadmium sulfoselenides doped with potassium upon their...     

Analysis (Simulation) of Ni-63 beta-voltaic cells based on silicon solar cells

Beta-voltaic cells based on standard silicon solar cells with bilateral coating with beta-radiation sources in the form of ⁶³Ni isotope have been studied experimentally and by numerical simulation. The optimal parameters of the cell, including its thickness, the doping level of the substrate, the depth of the p–n junction on its front side, and the p⁺ layer on the back side, as well as the activity of the source material, have been calculated. The limiting theoretical values of the open-circuit voltage (0.26 V), short-circuiting current (2.1 μA), the output power of the cell (0.39 μW), and the efficiency of the conversion of the radioactive energy onto the electric energy (4.8%) have been determined for a beta-source activity of 40 mCi. The results of numerical analysis have been compared with the experimental data.     

Carbon sorbents for immobilization of tritium-containing waste oils

Emission of tritium from the pump oil-carbon sorbent-cement compositions (where the carbon sorbent is thermally expanded graphite or charcoal fabricated by thermal or radiation evaporation of a cellulose material) was studied. The compositions are characterized by a high hold-up ability with respect to oil components, when the matrix is contacted with water. The apparent diffusion coefficients of tritium are equal to 10⁻¹⁵–10⁻¹⁶ m² s⁻¹. The compositions are found to be resistant to radiation and can be recommended for solidification of radioactive waste oils.     

Mathematical model of chemical oscillations arising in a homogeneous system of cysteine and oxygenated complexes of iron(II)

A mathematical model of the homogeneous oxidation kinetics of cysteine in the presence of oxygenated complexes of iron(II) with dimethylglyoxime and cytosine expressed in the form of a system of three nonlinear differential equations is analyzed. The model is simplified by stoichiometric analysis of the suggested kinetic scheme. As determined on the basis of qualitative analysis of the system of differential equations, a single stationary state with the singular point assigned to the focus—spatial saddle type, from which a bifurcation of the Andronov-Hopf type can occur, is implemented. Upon solving numerically the system of differential equations for different initial conditions, it is found that the mathematical model has a solution in the form of a limit cycle, and the process runs in an oscillatory mode at such initial concentrations of the catalyst and cysteine that are comparable to their contents at which chemical oscillations are observed in experiments.     

Free-convection Flow of a Binary Mixture in a Thin Porous Ring

The problem of natural convection of a binary mixture in a thin porous ring is considered. In the simplified formulation steady-state solutions of the problem are obtained. The stability of these solutions is investigated and a stability map is plotted in the plane of the Rayleigh numbers calculated from the temperature and concentration. It is shown that an auto-oscillation convection regime is established in the ring under certain conditions. It is also found that there is a region of variation of the seepage and diffusion-seepage Rayleigh numbers in which three steady-state solutions are stable.