The NNTMM code: Mathematical modeling, optimization, and data analysis through neural networks

The concept, functional capabilities, graphic interface, and application technology for the NNTMM code (Neural Network Tool for Mathematical Modeling), designed for analyzing large amounts of experimental and computational data in an interactive mode, are described. The software can be used to solve a wide range of applied problems where automated extraction of meaningful information from randomly presented data is required, along with data classification, clear representation of established relationships and dependences, analysis of parameter importance, and prediction. Examples of using the NNTMM code to analyze data in controlled nuclear fusion problems are presented.     

The ScopeShell graphic interface: Support for computational experiments and data visualization

We consider problems of the visualization and automation of routine tasks that arise in the process of a computational experiment. We describe ScopeShell, a state-of-the-art universal platform independent graphic interface for computational codes that includes data visualization and the monitoring of calculations on distributed computing systems. We describe the concept behind ScopeShell, along with the interface’s functionality and methods of application. The ScopeShell system is used to support computational experiments in the field of controlled thermonuclear fusion. The system considerably increases the efficiency of research requiring the application of voluminous computer codes.     

Mechanism of growth of ZnO single crystals from hydrothermal alkali solutions

The results obtained in experiments on the growth of zinc oxide, ZnO, under hydrothermal conditions are generalized. The polar growth and nonstoichiometry of ZnO crystals are analyzed in terms of crystal chemistry with due regard for the physicochemical conditions of the growth medium. The effect of the Li⁺ and of di-and trivalent metal (Co²⁺, Fe²⁺, Mn²⁺, Fe³⁺, Mn³⁺, Sc³⁺, In³⁺) impurities on the kinetics and some physical characteristics of ZnO crystals are studied, and the chemical reactions occurring on the surfaces of the (0001) and \((000\bar 1)\) faces are considered.     

One-dimensional quasilinear eigenvalue and eigenfunction problem

We consider a one-dimensional quasilinear eigenvalue and eigenfunction problem. The simplification of the problem by replacing a second-order elliptic operator by a one-dimensional one permits carrying out an efficient and unified study of the structure of the spectrum and the multiplicity of eigenvalues for a wide range of functions specifying the nonlinearity. This opens up the possibility of preliminarily analyzing specific properties of solutions of such problems for partial differential equations, in particular, the equilibrium of a toroidal plasma, since the spectrum of the problem and its multiplicity depend only weakly on the space dimension.     

The chemical action of oxygen on a heater during growth of refractory oxide crystals from melt

The behavior of the W-O₂ system has been investigated at 2400 K in the pressure range from 1 to 1 × 10^?5 bar. The chemical composition of the solid and vapor phases for the ratio W: O₂ = 1: 1 was calculated by minimizing the Gibbs free energy. It is shown that the only solid phase in the system is metallic tungsten (0.333–0.355 mol), whereas trioxide WO₃ dominates in the vapor phase; its concentration may reach 99%. It is concluded that providing an inert atmosphere in the growth chamber with a pressure of 1 bar decreases the concentration of atomic and molecular oxygen in the vapor phase and decreases its effect on the tungsten heater.     

Problem on multiple eigenvalues and positive eigenfunctions for a one-dimensional second-order quasilinear equation

We consider the eigenvalue and eigenfunction problem for a one-dimensional secondorder quasilinear differential equation. We analyze a number of versions of the function f specifying the nonlinearity for which the problem has multiple eigenvalues.