E. S. Kurkina

Thermal self-focusing during solar flares

By solving a nonlinear equation for a heat source with a power proportional to Тβ (β > 1), it is shown that heat localization in the transverse cross section of a magnetic tube with a classical thermal conductivity occurs in the blowup regime in the form of microstructures—temperature background cells bounded by hot walls with a spatial scale of <100 m. The reduction in the integral X-ray emissivity observed on board of spacecrafts in the early stage of the flare is attributed to thermal self-focusing, i.e., a decrease in the factor of filling of the flare volume with hot plasma due to the narrowing of the hot walls of the microstructure.

Macroscopic model of diamond crystal growth

Elementary atomic structures of carbon are selected via the deposition of methyl radicals from the gas phase, and a kinetic scheme of the diamond crystal growth process is proposed. A macroscopic model of the growth process is developed in an average field approximation that corresponds to the kinetic scheme. The model is based on a system of homogeneous differential equations of high dimensionality that describe changes in the surface concentrations of elementary carbon structures in every crystal layer. Experimental data are in good agreement with results from simulations. The influence of different parameters and elementary stages of the process on the dynamics of crystal growth is investigated. The rate of one of the most important stages, downward migration, is determined.

Comparative analysis of Monte Carlo methods via the example of calculating the complex dynamics of a lattice model for a chemical reaction

Complex oscillating dynamics of a microscopic model of a chemical reaction occurring on the surface of a catalyst is calculated using Monte Carlo methods. The five most common algorithms are used and complexity and efficiency of each of them are assessed. It is shown that the calculation time can vary by more than two orders of magnitude. The most efficient Monte Carlo algorithm is identified. Using it, mechanisms of the emergence of oscillations and waves at the microlevel in the lattice model containing millions of nodes are investigated.

Mathematical modeling of the dissolving and deposition processes during solution seepage in a porous medium

A mathematical model that describes solution seepage in a porous medium and the processes of mineral dissolving and secondary deposition is proposed. Self-similar solutions describing the motion of the leading and trailing fronts, that is, the boundaries of the complete-dissolving zone, are determined. The main features of the processes under consideration are studied and numerical calculations are performed. It is shown that the model describes well the experimental data on mineral leaching by sulfate solutions. The dynamics of mineral extraction from productive solutions in a medium with a nonuniformacidity distribution are investigated. It is shown that, in the elevated-PH zones, the mineral is dissolved; whereas, in the low-acidity zones, secondary deposition of the mineral occurs. In the latter case, after the work has been completed, the bed may contain more or less considerable mineral resources, depending on the extent of the low-PH zone and its proximity to an extraction well.